Solved: Translate the following statement into a

The fact that 2(x + 3) = 2x + 6 is because of the ______ Property. (p. 10)

The fact that 3x = 0 implies that x = 0 is a result of the ____ Property. (p. 13)

The domain of the variable in the expression x x - 4 is ____. .(p.21)

True or False Multiplying both sides of an equation by any number results in an equivalent equation.

An equation that is satisfied for every value of the variable for which both sides are defined is called a(n) ____ .

An equation of the form ax + b = 0 is called a(n) equation _____ or a(n) ____equation.

True or False The solution of the equation 3x - 8 = 0 . 3 IS S .

True or False Some equations have no solution.

In Problems 9-16, mentally solve each equation. 7 x = 21

In Problems 9-16, mentally solve each equation. 6x = -24

In Problems 9-16, mentally solve each equation. 3x + 15 = 0

In Problems 9-16, mentally solve each equation. 6x + 18 = 0

In Problems 9-16, mentally solve each equation. 2X - 3 = 0

In Problems 9-16, mentally solve each equation. 3x + 4 = 0

In Problems 9-16, mentally solve each equation. 1 x = 5

In Problems 9-16, mentally solve each equation. 2 9 -x = - 3 2

In Problems 17-64, solve each equation. 3x + 4 = x

In Problems 17-64, solve each equation. 2x + 9 = 5x

In Problems 17-64, solve each equation. 2t - 6 = 3 - t

In Problems 17-64, solve each equation. 5 Y + 6 = -18 - Y

In Problems 17-64, solve each equation. 6 - x = 2x + 9

In Problems 17-64, solve each equation. 3 - 2x = 2 - x

In Problems 17-64, solve each equation. 3 + 2n = 4n + 7

In Problems 17-64, solve each equation. 6 - 2m = 3m + 1

In Problems 17-64, solve each equation. 2(3 + 2x) = 3(x - 4)

In Problems 17-64, solve each equation. 3(2 - x) = 2x - 1

In Problems 17-64, solve each equation. 8x - (3x + 2) = 3x - 10

In Problems 17-64, solve each equation. 7 - (2x - 1) = 10

In Problems 17-64, solve each equation. 3x+2 = 1 1 x

In Problems 17-64, solve each equation. 1 2 "3 x = 2 -"3x

In Problems 17-64, solve each equation. 1x -5 = 3x

In Problems 17-64, solve each equation. 1 1 -2: x = 6

In Problems 17-64, solve each equation. 2p = 1p + 1

In Problems 17-64, solve each equation. 1 1 4 - --p =- 2 3 3

In Problems 17-64, solve each equation. 0.9t = 0.4 + O.1t

In Problems 17-64, solve each equation. 0.9t = 1 + t

In Problems 17-64, solve each equation. x ; 1 + x ; 2 = 2

In Problems 17-64, solve each equation. 2x + 1 - 3 + 16 = 3x

In Problems 17-64, solve each equation. += 3

In Problems 17-64, solve each equation. 4 5 --5 = - y 2y

In Problems 17-64, solve each equation. 1 + 2 = 3

In Problems 17-64, solve each equation. 311 - - - = - x 3 6

In Problems 17-64, solve each equation. (x + 7)(x - 1) = (x + 1)2

In Problems 17-64, solve each equation. (x + 2)(x - 3) = (x + 3)2

In Problems 17-64, solve each equation. x(2x -3) = (2x + 1)(x -4)

In Problems 17-64, solve each equation. x(1 + 2x) = (2x -1)(x -2)

In Problems 17-64, solve each equation. Z (Z2 + 1) = 3 + Z3

In Problems 17-64, solve each equation. w (4-w2) = 8 - w3

In Problems 17-64, solve each equation. x 2 . . --x-2 +3=--x-2

In Problems 17-64, solve each equation. 2x -6 --=---2 x+3 x+3

In Problems 17-64, solve each equation. 2x 4 3 . , --x2 -4 ----x2 -4 ---x + 2

In Problems 17-64, solve each equation. x 4 3 --+ --= -?-- x2-9 x+3 r-9

In Problems 17-64, solve each equation. x = 3 --- x + 2

In Problems 17-64, solve each equation. 3x --= 2 x-I

In Problems 17-64, solve each equation. 2x 5 _ 3 = x ! 5

In Problems 17-64, solve each equation. -4 -3 --=-- . x+4 x+6

In Problems 17-64, solve each equation. 6t + 7 3t + S \ 4t -= 1 2t -4

In Problems 17-64, solve each equation. Sw + 5 4w - 3 --- lOw -7 5w + 7

In Problems 17-64, solve each equation. 4 ---3 + ------ 7 x-2 x+5 (x+5)(x-2)

In Problems 17-64, solve each equation. . +- 1 -= 1 2x+3 x-I (2x+3)(x-1)

In Problems 17-64, solve each equation. 2 + 3 = 5--- y+3 y-4 y+6

In Problems 17-64, solve each equation. 5 4 -3 5z -11 +--2z - 3 5 -z

In Problems 17-64, solve each equation. x x + 3 _ -3 ' x2 -1 -x 2 - X -x2 + X

In Problems 17-64, solve each equation. x+1 x+4 -3 64. 2 - --- X + 2x x2 + X x2 + 3x + 2

In Problems 65-68, use a calculator to solve each equation. Round the solution to two decimal places. 3.2x + 65.S71 = 19.2 3

In Problems 65-68, use a calculator to solve each equation. Round the solution to two decimal places. 6.2x -- S -= 0.195 3.72

In Problems 65-68, use a calculator to solve each equation. Round the solution to two decimal places. IS . 14.72 -21.5Sx = -x + 2.4 2.11

In Problems 65-68, use a calculator to solve each equation. Round the solution to two decimal places. lS.6 3x --= -x -20 2.6 2. 32

In Problems 69-74, solve each equation. The letters a, b, and c are constants. ax - b = c , a '* 0

In Problems 69-74, solve each equation. The letters a, b, and c are constants. 1 - ax = b, a '* 0

In Problems 69-74, solve each equation. The letters a, b, and c are constants. x x . -+ -= c a '* 0 b '* 0 a '* -b '\ a b

In Problems 69-74, solve each equation. The letters a, b, and c are constants. -+ -= c, c '* 0 x x

In Problems 69-74, solve each equation. The letters a, b, and c are constants. 1 + 1 = 2 --- x-1 x+a x-1

In Problems 69-74, solve each equation. The letters a, b, and c are constants. b+c b- c 74. --= --, c '* 0, a '* 0 x+a x-a

Find he number a for which x = 4 is a solution of the equatIOn x + 2a = 16 + ax -6a

Find the number b for which x = 2 is a solution of the equation x + 2b = x -4 + 2bx

Problems 77-82 list some formulas that occur in applications. Solve each formula for the indicated variable. EI t' 't 1 1 + 1 f R l], ec rICI Y -= - - or R RJ R2

Problems 77-82 list some formulas that occur in applications. Solve each formula for the indicated variable. Finance = A P(l + rt) for r

Problems 77-82 list some formulas that occur in applications. Solve each formula for the indicated variable. mv2 Mechanics = F R for R

Problems 77-82 list some formulas that occur in applications. Solve each formula for the indicated variable. Chemistry PV = nRT for T

Problems 77-82 list some formulas that occur in applications. Solve each formula for the indicated variable. Mathematics S = a K _ for r 1-r

Problems 77-82 list some formulas that occur in applications. Solve each formula for the indicated variable. Mechanics = v -gt + Vo for t

Finance A total of $20,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $ 3000, how much will be invested in each type of investment?

Finance A total of $10,000 is to be divided between Sean and George, with George to receive $ 3000 less than Sean. How much will each receive?

Internet Searches In November 2005, Google and Yahoo! search engines were used to conduct a total of 3.57 billion online searches. Google was used to conduct 0.5 3 billion more searches than Yahoo!. How many searches were conducted on each search engine?

Sharing the Cost of a Pizza Judy and Tom agree to share the cost of an $18 pizza based on how much each ate. If Tom 2 ate:3 the amount that Judy ate, how much should each pay? [Hint: Some pizza may be left.] Tom's portion Judy's portion

Computing Hourly Wages Sandra, who is paid time-and-ahalf for hours worked in excess of 40 hours, had gross weekly wages of $442 for 48 hours worked. What is her regular hourly rate?

Computing Hourly Wages Leigh is paid time-and-a-half for hours worked in excess of 40 hours and double-time for hours worked on Sunday. If Leigh had gross weekly wages of $342 for working 50 hours, 4 of which were on Sunday, what is her regular hourly rate?

Computing Grades Going into the final exam, which will count as two tests, Brooke has test scores of 80, 83, 71, 61, and 95. What score does Brooke need on the final in order to have an average score of 80?

Computing Grades Going into the final exam, which will count as two-thirds of the final grade, Mike has test scores of 86, 80, 84, and 90. What score does Mike need on the final in order to earn a B, which requires an average score of 80? What does he need to earn an A, which requires an average of 90?

Business: Discount Pricing A builder of tract homes reduced the price of a model by 15%. If the new price is $425,000, what was its original price? How much can be saved by purchasing the model?

Business: DiscOlmt Pricing A car dealer, at a year-end clearance, reduces the list price of last year's models by 15%. If a certain four-door model has a discounted price of $8000, what was its list price? How much can be saved by purchasing last year's model?

Business: Marking up the Price of Books A college book store marks up the price that it pays the publisher for a book by 35 %. If the selling price of a book is $92.00, how much did the bookstore pay for this book?

Personal Finance: Cost of a Car The suggested list price of a new car is $18,000. The dealer's cost is 85% of list. How much will you pay if the dealer is willing to accept $100 over cost for the car?

Business: Theater Attendance The manager of the Coral Theater wants to know whether the majority of its patrons are adults or children. One day in July, 5200 tickets were sold and the receipts totaled $29,961. The adult admission is $7.50, and the children's admission is $4.50. How many adult patrons were there?

Business: Discount Pricing A wool suit, discounted by 30% for a clearance sale, has a price tag of $399. What was the suit's original price?

Geometry The perimeter of a rectangle is 60 feet. Find its length and width if the length is 8 feet longer than the width.

Geometry The perimeter of a rectangle is 42 meters. Find its length and width if the length is twice the width.

Internet Users In March 2006, 152 million people in the United States were Internet users, which accounted for 21.9% of the world's online audience. How many people worldwide were Internet users in March 2006?

One step in the following list contains an error. Identify it and explain what is wrong. x = 2 (1) 3x - 2x = 2 (2) 3x = 2x + 2 (3) x2 + 3x = x2 + 2x + 2 (4) x2 + 3x - 10 = x2 + 2x - 8 (5) (x - 2) (x + 5) = (x - 2)( x + 4) (6) x + 5 = x + 4 (7) 1 = 0 (8)

The equation --5 8 + x x+3 + 3=-x+3 has no solution, yet when we go through the process of solving it we obtain x = -3. Write a brief paragraph to explain what causes this to happen.

Make up an equation that has no solution and give it to a fellow student to solve. Ask the fellow student to write a critique of your equation.

Factor: x2 -5x - 6 (pp. 49-55)

Factor: 2x2 -x -3 (pp. 49-55)

The solution set of the equation (x -3)(3x + 5) = 0 is _____. (p. 13)

True or False = Ixl. (pp. 23-24)

To complete the square of the expression x2 + 5x, you would_____the number _____.

The quantity b2 - 4ac is called the_____of a quadratic equation. If it is_____ , the equation has no real solution.

True or False Quadratic equations always have two real solutions.

True or False If the discriminant of a quadratic equation is positive, then the equation has two solutions that are negatives of one another.

In Problems 9-28, solve each equation by factoring. x2 -9x = 0

In Problems 9-28, solve each equation by factoring. x2 + 4x = 0

In Problems 9-28, solve each equation by factoring. x2-25=O

In Problems 9-28, solve each equation by factoring. x2 - 9 = 0

In Problems 9-28, solve each equation by factoring. Z2 + Z - 6 = 0

In Problems 9-28, solve each equation by factoring. v2 + 7v + 6 = 0

In Problems 9-28, solve each equation by factoring. 2x2 - 5x -3 = 0

In Problems 9-28, solve each equation by factoring. 3x2 + 5x + 2 = 0

In Problems 9-28, solve each equation by factoring. 3t 2 - 48 = 0

In Problems 9-28, solve each equation by factoring. 2/ - 50 = 0

In Problems 9-28, solve each equation by factoring. x(x - 8) + 12 = 0

In Problems 9-28, solve each equation by factoring. x(x + 4) = 12

In Problems 9-28, solve each equation by factoring. 4x2 + 9 = 12 x

In Problems 9-28, solve each equation by factoring. 2 5x2 + 16 = 40x

In Problems 9-28, solve each equation by factoring. 6(p2 - 1) = 5p

In Problems 9-28, solve each equation by factoring. 2(2u2 - 4u) + 3 = 0

In Problems 9-28, solve each equation by factoring. 6x - 5 = .. f'\ x

In Problems 9-28, solve each equation by factoring. x + - = 7 x

In Problems 9-28, solve each equation by factoring. 4(x -2) 3 -3 + - = --- x -3 x x(x - 3)

In Problems 9-28, solve each equation by factoring. 5 3 --x+4 = 4 +--x - 2

In Proble ms 29-34, so lve each eq uation by the Sq uare Root Method. x2 = 25

In Proble ms 29-34, so lve each eq uation by the Sq uare Root Method. x2 = 36

In Proble ms 29-34, so lve each eq uation by the Sq uare Root Method. (x - 1)2 = 4

In Proble ms 29-34, so lve each eq uation by the Sq uare Root Method. (x + 2)2 = 1

In Proble ms 29-34, so lve each eq uation by the Sq uare Root Method. (2y + 3)2 = 9

In Proble ms 29-34, so lve each eq uation by the Sq uare Root Method. (3 z - 2)2 = 4

In Problems 35-40, what number should be added to complete the square of each expre ssion? x2 - 8x

In Problems 35-40, what number should be added to complete the square of each expre ssion? x2 -4x

In Problems 35-40, what number should be added to complete the square of each expre ssion? x2 +

In Problems 35-40, what number should be added to complete the square of each expre ssion? 1 x - -x 3

In Problems 35-40, what number should be added to complete the square of each expre ssion? y2 - 2y

In Problems 35-40, what number should be added to complete the square of each expre ssion? 7 7 . 5

In Proble ms 41-46, solve each eq uatio n by co mpleti ng the sq uare. x2 + 4x = 21

In Proble ms 41-46, solve each eq uatio n by co mpleti ng the sq uare. x2 - 6x = 13

In Proble ms 41-46, solve each eq uatio n by co mpleti ng the sq uare. x2 - 1x -3 = 0

In Proble ms 41-46, solve each eq uatio n by co mpleti ng the sq uare. v- +-v -- = O > 3 " 3

In Proble ms 41-46, solve each eq uatio n by co mpleti ng the sq uare. 3x2 + x - 1 = 0

In Proble ms 41-46, solve each eq uatio n by co mpleti ng the sq uare. 2 X2 -3x - 1 = 0

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. x2 -4x + 2 = 0

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. x2 + 4x + 2 = 0

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. x2 -4x - 1 = 0

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. x2 + 6x + 1 = 0

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 2 x2 - 5x + 3 = 0

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 2X2 + 5x + 3 = 0

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 41 -y + 2 = 0

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 4t 2 + t + 1 = 0

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 4x2 = 1 - 2x

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 2X2 = 1 -2x

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 4x2 = 9x

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 5x = 4x2

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 9t 2 - 6t + 1 = 0

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 4u2 - 6u + 9 = 0

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. -x --x - - = 0 4 4 2

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 2 ? 3" x- - x -3 = 0

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 5 2 1 x - x = - .) 3

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 3 2 1 5x - x = 5

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 2x(x + 2) = 3

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 3x(x + 2) = 1

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 4 - - -1 = 0 x .x2

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 4 + - -? = 0 x .r -

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 3x 1 . --+-=4 x -2 x

In Problems 47-70, find the real solutions, if any, of each equation. Use the quadratic formula. 2x 1 --+ - = 4 x -3 x

In Problems 71-78, find the real solutions, if any, of each equatio n. Use the quadratic formula and a calculater. Express any solutions rounded to two decimal places. x2 - 4.1x + 2 .2 = 0

In Problems 71-78, find the real solutions, if any, of each equatio n. Use the quadratic formula and a calculater. Express any solutions rounded to two decimal places. x2 + 3.9x + 1.8 = 0

In Problems 71-78, find the real solutions, if any, of each equatio n. Use the quadratic formula and a calculater. Express any solutions rounded to two decimal places. x2 + V3x -3 = 0

In Problems 71-78, find the real solutions, if any, of each equatio n. Use the quadratic formula and a calculater. Express any solutions rounded to two decimal places. x2 + V2x -2 = 0

In Problems 71-78, find the real solutions, if any, of each equatio n. Use the quadratic formula and a calculater. Express any solutions rounded to two decimal places. 7TX2 - x - 7T = 0

In Problems 71-78, find the real solutions, if any, of each equatio n. Use the quadratic formula and a calculater. Express any solutions rounded to two decimal places. 7TX2 + TTX -2 = 0

In Problems 71-78, find the real solutions, if any, of each equatio n. Use the quadratic formula and a calculater. Express any solutions rounded to two decimal places. 3 x2 + 87TX + v29 = 0

In Problems 71-78, find the real solutions, if any, of each equatio n. Use the quadratic formula and a calculater. Express any solutions rounded to two decimal places. 7Tx2 - 15V2x + 20 = 0

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. x2 - 5 = 0

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. x2 - 6 = 0

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. 16x2 - 8x + 1 = 0

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. 9 x2 - 12 x + 4 = 0

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. 10x2 - 19 x - 15 = 0

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. 6x2 + 7 x - 20 = 0

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. 2 + z = 6z2

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. 2 = y + 61

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. r+ V2 x = 2

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. 1:.x2 = V2x + 1 2

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. x2 + x = 4

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. x2 + X = 1

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. x 2 7x + 1 --+ --= -:--- x - 2 x+l x2 - x -2

In Problems 79-92, find the real solutions, if any, of each equation. Use any method. 3x 1 4 - 7x --x + 2 + --x-I = ----=- -- x2 + x - 2

In Problems 93-98, use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution, or no real solution, without solving the equation. 2 x2 - 6x + 7 = 0

In Problems 93-98, use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution, or no real solution, without solving the equation. x2 + 4x + 7 = 0

In Problems 93-98, use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution, or no real solution, without solving the equation. 9 x2 -3 0x + 25 = 0

In Problems 93-98, use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution, or no real solution, without solving the equation. 2 5x2 - 2 0x + 4 = 0

In Problems 93-98, use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution, or no real solution, without solving the equation. 3 x2 + 5x - 8 = 0

In Problems 93-98, use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution, or no real solution, without solving the equation. 2 x2 - 3x - 7 = 0

College Tuition and Fees The average annual published undergraduate tuition-and-fee charges C, in dollars, for public four-year institutions from academic years 2000- 2001 through 2005- 2006 can be estimated by the equation C = 20.2x 2 + 3 14.5x + 3 467.6, where x is the number of years afer the 2000- 2001 academic year. Assuming the model will remain valid beyond 2005- 2006, in what academic year will average annual tuition-and-fee charges be $8000? Source: College Board, Trends in College P ri cing 2005

Women's Weekly Earnings The median weekly earnings E, in dollars, for full-time women wage and salary workers ages 16 years and older from 2000 through 2004 can be estimated by the equation E = 0.14x 2 + 7.8x + 5 40, where x is the n urn ber of years after 2000. Assuming the model will remain valid beyond 2004, in what year will the median weekly earnings be $63 2? Source: U.S. Department of Labor, Highlights of Women 's Ea rning s in 2004, September 2005

Dimensions of a Window The area of the opening of a rectangular window is to be 143 square feet. If the length is to be 2 feet more than the width, what are the dimensions?

Dimensions of a Window The area of a rectangular window is to be 3 06 square centimeters. If the length exceeds the width by 1 centimeter, what are the dimensions?

Geometry Find the dimensions of a rectangle whose perimeter is 26 meters and whose area is 40 square meters

Watering a Field An adjustable water sprinkler that sprays water in a circular pattern is placed at the center of a square field whose area is 1250 square feet (see the figure). What is the shortest radius setting that can be used if the field is to be completely enclosed within the circle?

Constructing a Box An open box is to be constructed from a square piece of sheet metal by removmg a square of Side 1 foot from each corner and turning up the edges. If the box is to hold 4 cubic feet, what should be the dimensions of the sheet metal?

Constructing a Box Rework Problem 105 if the piece of sheet metal is a rectangle whose length is twice its width.

Physics A ball is thrown vertically upward from the top of a building 96 feet tall with an initial velocity of 80 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s = 96 + 80t - 16r2. (a) After how many seconds does the ball strike the ground? (b) After how many seconds will the ball pass the top of the building on its way down?

Physics An object is propelled vertically upward with an initial velocity of 20 meters per second. The distance s (ill meters) of the object from the ground after t seconds is s = -4.9t 2 + 20t . (a) When will the object be 15 meters above the ground? (b) When will it strike the ground? (c) Will the object reach a height of 100 meters?

Reducing the Size of a Candy Bar A jumbo chocolate bar with a rectangular shape measures 12 centimeters in length, 7 centimeters in width, and 3 centimeters in thickness. Due to escalating costs of cocoa, management decides to reduce the volume of the bar by 10%. To accomplish this reduction, management decides that the new bar should have the same 3 centimeter thickness, but the length and width of each should be reduced an equal number of centimeters. What should be the dimensions of the new candy bar?

Reducing the Size of a Candy Bar Rework Problem 109 if the reduction is to be 20%.

Constructing a Border around a Pool A circular pool meaV\ sures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 3 inches, how wide will the border be? (1 cubic yard = 27 cubic feet) See the illustration.

Constructing a Border arollnd a Pool Rework Problem 111 if the depth of the border is 4 inches.

Constructing a Border around a Garden A landscaper, who just completed a rectangular flower garden measuring 6 feet by 10 feet, orders 1 cubic yard of premixed cement, all of which is to be used to create a border of uniform width around the garden. If the border is to have a depth of 3 inches, how wide will the border be? (1 cubic yard = 27 cubic feet)

Dimensions of a Patio A contractor orders 8 cubic yards of premixed cement, all of which is to be used to pour a patio that will be 4 inches thick. If the length of the patio is specified to be twice the width, what will be the patio dimensions? (1 cubic yard = 27 cubic feet)

Comparing TVs The screen size of a television is determined by the length of the diagonal of the rectangular screen. traditional 4:3 LCD 1 6:9 Traditional TVs come in a 4 : 3 format, meaning the ratio of the length to the width of the rectangular is 4 to 3. What is the area of a 37-inch traditional TV screen? What is the area of a 37-inch LCD TV whose screen is in a 16 : 9 format? Which screen is larger? [Hint: If x is the length of a 4 : 3 format screen, then 2 x is the width.]

Comparing TVs Refer to Problem 1 15. Find the screen area of a traditional 50-inch TV and compare it with a 50-inch Plasma TV whose screen is in a 16 : 9 format. Which screen is larger?

The sum of the consecutive integers 1, 2, 3, ... , n is given by 1 the formula "2 n (n + 1). How many consecutive integers, starting with 1, must be added to get a sum of 666?

Geometry If a polygon of n sides has n( n - 3) diagonals, how many sides will a polygon with 65 diagonals have? Is there a polygon with SO diagonals?

Show that the sum of the roots of a quadratic equation is -.

Show that the product of the roots of a quadratic equation . c lS -. a

Find k such that the equation kx2 + x + k = 0 has a repeated real solution.

Find k such that the equation x2 - kx + 4 = 0 has a repeated real solution.

Show that the real solutions of the equation ax 2 + bx + c = 0 are the negatives of the real solutions of the equation ax 2 -bx + c = O. Assume that b2 - 4ac ;:0: O.

Show that the real solutions of the equation ax 2 + bx + c = 0 are the reciprocals of the real solutions of the equation cx 2 + bx + a = O. Assume that b2 - 4ac ;:0: O.

Which of the following pairs of equations are equivalent? Explain. (a) x2 = 9; x = 3 (b) x = v9; x = 3 (c) (x - 1)(x -2) = (x - 1 f; x - 2 = x - 1

Describe three ways that you might solve a quadratic equation. State your preferred method; explain why you chose it.

Explain the benefits of evaluating the discriminant of a quadratic equation before attempting to solve it.

Create three quadratic equations: one having two distinct solutions, one having no real solution, and one having exactly one real solution.

The word quadra tic seems to imply four (quad), yet a quadratic equation is an equation that involves a polynomial of degree 2. Investigate the origin of the term quadra tic as it is used in the expression quadra tic equa tion . Write a brief essay on your findings.

Name the integers and the rational numbers in the set - -3, 0, v2, -, 1 (pp. 4-5)

True or False Rational numbers and irrational numbers are in the set of real numbers. (pp. 4 -5)

Rationalize the denominator of 3 -- 2+ V3 (p. 74 )

In the complex number 5 + 2i, the number 5 is called the _______ part; the number 2 is called the _______ part; the number i is called the _______ _______.

The equation x2 = -4 has the solution set ___ _

True or False The conjugate of 2 + 5i is -2 - 5i.

True or False All real numbers are complex numbers

True or False If 2 -3i is a solution of a quadratic equation with real coefficients, then -2 + 3i is also a solution.

In Problems 9-46, write each expression in the standard form a + bi. (2 -3i) + (6 + 8i)

In Problems 9-46, write each expression in the standard form a + bi. (4 + 5i) + (-8 + 2i)

In Problems 9-46, write each expression in the standard form a + bi. (-3 + 2i) - (4 -4i)

In Problems 9-46, write each expression in the standard form a + bi. (3 -4 i) - (-3 -4i)

In Problems 9-46, write each expression in the standard form a + bi. (2 - 5i) - (8 + 6i)

In Problems 9-46, write each expression in the standard form a + bi. ( -8 + 4i) - (2 -2i)

In Problems 9-46, write each expression in the standard form a + bi. 3 (2 - 6i)

In Problems 9-46, write each expression in the standard form a + bi. -4(2 + 8i)

In Problems 9-46, write each expression in the standard form a + bi. 2i(2 - 3i)

In Problems 9-46, write each expression in the standard form a + bi. 3i( -3 + 4i)

In Problems 9-46, write each expression in the standard form a + bi. (3 - 4i)(2 + i)

In Problems 9-46, write each expression in the standard form a + bi. (5 + 3i)(2 - i)

In Problems 9-46, write each expression in the standard form a + bi. ( -6 + i)(-6 - i)

In Problems 9-46, write each expression in the standard form a + bi. ( -3 + i)(3 + i)

In Problems 9-46, write each expression in the standard form a + bi. O 4

In Problems 9-46, write each expression in the standard form a + bi. 13_ 5 - 12i

In Problems 9-46, write each expression in the standard form a + bi. 2 7 i

In Problems 9-46, write each expression in the standard form a + bi. 2_-_i 1\ ' -2!

In Problems 9-46, write each expression in the standard form a + bi. l + i

In Problems 9-46, write each expression in the standard form a + bi. 2 + 3i 1 - !

In Problems 9-46, write each expression in the standard form a + bi. G + iy

In Problems 9-46, write each expression in the standard form a + bi. ( - iy

In Problems 9-46, write each expression in the standard form a + bi. (1 + i) 2

In Problems 9-46, write each expression in the standard form a + bi. (1 - if

In Problems 9-46, write each expression in the standard form a + bi. i23

In Problems 9-46, write each expression in the standard form a + bi. il4

In Problems 9-46, write each expression in the standard form a + bi. i-15

In Problems 9-46, write each expression in the standard form a + bi. i-23

In Problems 9-46, write each expression in the standard form a + bi. i6 - 5

In Problems 9-46, write each expression in the standard form a + bi. 4 + i3

In Problems 9-46, write each expression in the standard form a + bi. 6i3 - 4i5

In Problems 9-46, write each expression in the standard form a + bi. 4i3 - 2P + 1

In Problems 9-46, write each expression in the standard form a + bi. (1 + i)3

In Problems 9-46, write each expression in the standard form a + bi. (3i)4 + 1

In Problems 9-46, write each expression in the standard form a + bi. i7 (1 + i2)

In Problems 9-46, write each expression in the standard form a + bi. 2i4(1 + i2)

In Problems 9-46, write each expression in the standard form a + bi. i6 + i4 + P + 1

In Problems 9-46, write each expression in the standard form a + bi. P + i5 + P + i

In Problems 47-52, perform the indicated operations and express your answer in the form a + bi. V-4

In Problems 47-52, perform the indicated operations and express your answer in the form a + bi. v-9

In Problems 47-52, perform the indicated operations and express your answer in the form a + bi. V-25

In Problems 47-52, perform the indicated operations and express your answer in the form a + bi. v-64

In Problems 47-52, perform the indicated operations and express your answer in the form a + bi. Y(3 + 4i) (4i - 3)

In Problems 47-52, perform the indicated operations and express your answer in the form a + bi. r - (4-+ 3i-) (-3i-- 4)

In Problems 53-72, solve each equation in the complex number system . x2 + 4 = 0

In Problems 53-72, solve each equation in the complex number system . x2 - 4 = 0

In Problems 53-72, solve each equation in the complex number system . x2 - 16 = 0

In Problems 53-72, solve each equation in the complex number system . x2 + 25 = 0

In Problems 53-72, solve each equation in the complex number system . x2 - 6x + 13 = 0

In Problems 53-72, solve each equation in the complex number system . x2 + 4x + 8 = 0

In Problems 53-72, solve each equation in the complex number system . x2 - 6x + 10 = 0

In Problems 53-72, solve each equation in the complex number system . x2 - 2x + 5 = 0

In Problems 53-72, solve each equation in the complex number system . 8x2 - 4x + 1 = 0

In Problems 53-72, solve each equation in the complex number system . lOx2 + 6x + 1 = 0

In Problems 53-72, solve each equation in the complex number system . 5x2 + 1 = 2x

In Problems 53-72, solve each equation in the complex number system . 13x2 + 1 = 6x

In Problems 53-72, solve each equation in the complex number system . x2 + X + 1 = 0

In Problems 53-72, solve each equation in the complex number system . x2 - x + 1 = 0

In Problems 53-72, solve each equation in the complex number system . x3 - 8 = 0

In Problems 53-72, solve each equation in the complex number system . x3 + 27 = 0

In Problems 53-72, solve each equation in the complex number system . X4 = 16

In Problems 53-72, solve each equation in the complex number system . X4 = 1

In Problems 53-72, solve each equation in the complex number system . X4 + 13x2 + 36 = 0

In Problems 53-72, solve each equation in the complex number system . X4 + 3x2 - 4 = 0

In Problems 73-78, without solving, determine the character of the solutions of each equation in the complex number system. 3x2 - 3x + 4 = 0

In Problems 73-78, without solving, determine the character of the solutions of each equation in the complex number system. 2x2 - 4x + 1 = 0

In Problems 73-78, without solving, determine the character of the solutions of each equation in the complex number system. 2x2 + 3x = 4

In Problems 73-78, without solving, determine the character of the solutions of each equation in the complex number system. x2 + 6 = 2x

In Problems 73-78, without solving, determine the character of the solutions of each equation in the complex number system. 9x2 - 12x + 4 = 0

In Problems 73-78, without solving, determine the character of the solutions of each equation in the complex number system. 4x2 + 12x + 9 = 0

2 + 3i is a solution of a quadratic equation with real coefficients. Find the other solution.

4 - i is a solution of a quadratic equation with real coefficients. Find the other solution.

In Problems 81-84, z = 3 - 4i and w = 8 + 3i. Write each expression in the standard form a + bi. z + Z

In Problems 81-84, z = 3 - 4i and w = 8 + 3i. Write each expression in the standard form a + bi. w - I

In Problems 81-84, z = 3 - 4i and w = 8 + 3i. Write each expression in the standard form a + bi. zz

In Problems 81-84, z = 3 - 4i and w = 8 + 3i. Write each expression in the standard form a + bi. z - w

Electrical Circuits The impedance Z, in ohms, of a circuit element is defined as the ratio of the phasor voltage V, in volts, across the element to the phasor current I, in amperes, through the elements. That is, Z = f. If the voltage across a circuit element is 18 + i volts and the current through the element is 3 - 4i amperes, determine the impedance.

Parallel ircuits n an ac CirCUit Wit 1 two para I el pathways, the total Impedance Z, 111 ohms, satls les the formula - = - + -, Z ZI Z2 where ZI is the impedance of the first pathway and Z2 is the impedance of the second pathway. Determine the total impedance if the impedances of the two pathways are ZI = 2 + i ohms and Z2 = 4 - 3i ohms.

Use z = a + bi to show that z + z = 2a and z - z = 2bi.

Use z = a + bi to show that z = z.

Use z = a + bi and w = c + di to show that z + w = z + W.

Use z = a + bi and w = c + di to show that z w = z w.

Explain to a friend how you would add two complex numbers and how you would multiply two complex numbers. Explain any differences in the two explanations.

Write a brief paragraph that compares the method used to rationalize the denominator of a radical expression and the method used to write the quotient of two complex numbers in standard form.

True or False The principal square root of any nonnegative real number is always nonnegative. (pp. 23-24)

v-8 = _____. (pp. 72-76)

Factor 6x3 - 2X2 (pp. 49-55)

When an apparent solution does not satisfy the original equation, it is called a(n) ____ solution.

If u is an expression involving x, the equation au2 + bu + = c 0, a oF 0, is called a(n) equation ____ ____ ____ .

True or False Radical equations sometimes have extraneous solutions.

In Problems 7-40, find the real solutions of each equation. V2t=1 = 1

In Problems 7-40, find the real solutions of each equation. v3t+4 = 2

In Problems 7-40, find the real solutions of each equation. v3t+4 =-6

In Problems 7-40, find the real solutions of each equation. v5t+3 = -2

In Problems 7-40, find the real solutions of each equation. VI - 2x - 3 =

In Problems 7-40, find the real solutions of each equation. - 1 =

In Problems 7-40, find the real solutions of each equation. =2

In Problems 7-40, find the real solutions of each equation. 2x -= 3 -1

In Problems 7-40, find the real solutions of each equation. x2 + 2x = -1

In Problems 7-40, find the real solutions of each equation. \Yx2 + 16 = V

In Problems 7-40, find the real solutions of each equation. = x 8v

In Problems 7-40, find the real solutions of each equation. x 3vX

In Problems 7-40, find the real solutions of each equation. VIS - 2x = x

In Problems 7-40, find the real solutions of each equation. =x

In Problems 7-40, find the real solutions of each equation. X = 2

In Problems 7-40, find the real solutions of each equation. x 2V -x - 1

In Problems 7-40, find the real solutions of each equation. yx2 - X - 4 = x + 2

In Problems 7-40, find the real solutions of each equation. Y 3 - x + = X - 2

In Problems 7-40, find the real solutions of each equation. 3+=X

In Problems 7-40, find the real solutions of each equation. 2 + V 12 - 2x = x

In Problems 7-40, find the real solutions of each equation. -Vx+l= 1

In Problems 7-40, find the real solutions of each equation. + Vx+2=1

In Problems 7-40, find the real solutions of each equation. - = 2

In Problems 7-40, find the real solutions of each equation. V3x - 5 -Vx+7 = 2

In Problems 7-40, find the real solutions of each equation. V3 - 2VX = V

In Problems 7-40, find the real solutions of each equation. VlO + 3 VX = VX

In Problems 7-40, find the real solutions of each equation. (3x + 1)1/2 = 4

In Problems 7-40, find the real solutions of each equation. (3x - 5)1/2 = 2

In Problems 7-40, find the real solutions of each equation. (5x - 2) 1/3 = 2

In Problems 7-40, find the real solutions of each equation. (2x + 1)1/3 = -1

In Problems 7-40, find the real solutions of each equation. (x2 + 9) 1/2 = 5

In Problems 7-40, find the real solutions of each equation. (x2 - 16) 1/2 = 9

In Problems 7-40, find the real solutions of each equation. x3/2 - 3xl/2 = 0

In Problems 7-40, find the real solutions of each equation. X3/4 - 9xl/4 = 0

In Problems 41-72, find the real solutions of each equation. x4 - 5x2 + 4 = 0

In Problems 41-72, find the real solutions of each equation. X4 - 10x2 + 25 = 0

In Problems 41-72, find the real solutions of each equation. 3x4 - 2x2 - 1 = 0

In Problems 41-72, find the real solutions of each equation. 2 X4 - 5x2 - 12 = 0

In Problems 41-72, find the real solutions of each equation. x6 + 7 x3 - 8 = 0

In Problems 41-72, find the real solutions of each equation. x6 - 7x3 - 8 = 0

In Problems 41-72, find the real solutions of each equation. x + 2)2 + 7(x + 2) + 12 = 0

In Problems 41-72, find the real solutions of each equation. (2x + 5)2 - (2x + 5) - 6 = 0

In Problems 41-72, find the real solutions of each equation. (3x + 4f - 6(3x + 4) + 9 = 0

In Problems 41-72, find the real solutions of each equation. (2 - x)2 + (2 - x) - 20 = 0

In Problems 41-72, find the real solutions of each equation. 2(s + If - 5(s + 1) = 3

In Problems 41-72, find the real solutions of each equation. 3(1 - y)2 + 5(1 - y) + 2 = 0

In Problems 41-72, find the real solutions of each equation. x - 4xVX = 0

In Problems 41-72, find the real solutions of each equation. x + 8VX = 0

In Problems 41-72, find the real solutions of each equation. x + VX = 20

In Problems 41-72, find the real solutions of each equation. x + VX = 6

In Problems 41-72, find the real solutions of each equation. t l/2 - 2tl/4 + 1 = 0

In Problems 41-72, find the real solutions of each equation. ZI/2 - 4ZI /4 + 4 = 0

In Problems 41-72, find the real solutions of each equation. 4XI/2 - 9XI/4 + 4 = 0

In Problems 41-72, find the real solutions of each equation. XI/2 - 3xl/4 + 2 = 0

In Problems 41-72, find the real solutions of each equation. \Y 5x2 - 6 = x

In Problems 41-72, find the real solutions of each equation. \y 4 - 5x2 = x

In Problems 41-72, find the real solutions of each equation. x2 + 3x + Vx2 + 3x = 6

In Problems 41-72, find the real solutions of each equation. x2 - 3x - Vx2 - 3x = 2

In Problems 41-72, find the real solutions of each equation. I ? = 1_ + 2 (x + 1 )- x+1

In Problems 41-72, find the real solutions of each equation. 1 2 + -- = 12 (x - 1) x-I

In Problems 41-72, find the real solutions of each equation. 3x-2 - 7x-1 - 6 = 0

In Problems 41-72, find the real solutions of each equation. 2x-2 - 3x-1 - 4 = 0

In Problems 41-72, find the real solutions of each equation. 2x2/3 - 5xl/3 - 3 = 0

In Problems 41-72, find the real solutions of each equation. 3x4/3 + 5x2/3 - 2 = 0

In Problems 41-72, find the real solutions of each equation. V)2 2v -- +--= 8 v+1 v + 1

In Problems 41-72, find the real solutions of each equation. (-y ) 2 = 6(-Y ) + 7

In Problems 73-88, find the real solutions of each equation by factoring. x3 - 9x = 0

In Problems 73-88, find the real solutions of each equation by factoring. X4 - x2 = 0

In Problems 73-88, find the real solutions of each equation by factoring. 4x3 = 3x2

In Problems 73-88, find the real solutions of each equation by factoring. x5 - 4x3

In Problems 73-88, find the real solutions of each equation by factoring. x3 + x2 - 20x = 0

In Problems 73-88, find the real solutions of each equation by factoring. x3 + 6x2 - 7 x = 0

In Problems 73-88, find the real solutions of each equation by factoring. x3 + x2-x- 1 = 0

In Problems 73-88, find the real solutions of each equation by factoring. x3 + 4x2 - X - 4 = 0

In Problems 73-88, find the real solutions of each equation by factoring. x3 - 3x2 - 4x + 12 = 0

In Problems 73-88, find the real solutions of each equation by factoring. x3 - 3x2 - X + 3 = 0

In Problems 73-88, find the real solutions of each equation by factoring. 2x3 + 4 = x2 + 8x

In Problems 73-88, find the real solutions of each equation by factoring. 3x3 + 4x2 = 27x + 36

In Problems 73-88, find the real solutions of each equation by factoring. 5x3 + 45x = 2x2 + 18

In Problems 73-88, find the real solutions of each equation by factoring. 3x3 + 12x = 5x2 + 20

In Problems 73-88, find the real solutions of each equation by factoring. x(x2 - 3x) I/3 + 2(x2 - 3x)4/3 = 0

In Problems 73-88, find the real solutions of each equation by factoring. 3x(x2 + 2X) I/2 - 2(x2 + 2x)3/2 = 0

In Problems 89-94, find the real solutions of each equation. Use a calculator LO express any solutions rounded to two decimal places. x - 4xl/2 + 2 = 0

In Problems 89-94, find the real solutions of each equation. Use a calculator LO express any solutions rounded to two decimal places. x2/3 + 4xl/3 + 2 = 0

In Problems 89-94, find the real solutions of each equation. Use a calculator LO express any solutions rounded to two decimal places. X4 + v3x2 - 3 = 0

In Problems 89-94, find the real solutions of each equation. Use a calculator LO express any solutions rounded to two decimal places. x4 + v2x2 - 2 = 0

In Problems 89-94, find the real solutions of each equation. Use a calculator LO express any solutions rounded to two decimal places. 7T(1 + t)2 = 7T + 1 + t

In Problems 89-94, find the real solutions of each equation. Use a calculator LO express any solutions rounded to two decimal places. 7T(1 + r)2 = 2 + 7T(1 + r)

If k= x + 3 --and k - k = 12, fmd x. x-3

If k = x + 3 --and k2 - 3k = 2 8, find x.

Physics: Using Sound to Measure Distance The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the time elapsed until a sound is heard. If II is the time (measured in seconds) that it takes for the object to strike the water, then t1 will obey the equation s = 16ft, where s is the Vs distance (measured in feet). It follows that II = 4. Suppose that t 2 is the time that it takes for the sound of the impact to reach your ears. Because sound waves are known to travel at a speed of approximately 1100 feet per second, the time t 2 to travel the distance s will be s . t 11 . 2 = --. See the I ustratlOn. 1 100 Falling object: t = {S 1 "4 Sound waves: t2= IIO Now tl + tz is the total time that elapses from the moment that the object is dropped to the moment that a sound is heard. We have the equation . d Vs s Total time elapse = 4 + 1 1 00 Find the distance to the water's surface if the total time elapsed from dropping a rock to hearing it hit water is 4 seconds.

Crushing Load A civil engineer relates the thickness T, in inches, and height H, in feet, of a square wooden pillar to its crushing load L, in tons, using the model T = 1LH2 If a square wooden pillar is 4 inches thick and 1 0 feet high, what is its crushing load? 25

Foucault's Pendulum The period of a pendulum is the time it takes the pendulum to make one full swing back and forth. The IT period T, in seconds, is given by the formula T = 271" 'Y 32: where I is the length, in feet, of the pendulum. In 1 851, lean-Bernard-Leon Foucault demonstrated the axial rotation of Earth using a large pendulum that he hung in the Pantheon in Paris. The period of Foucault's pendulum was approximately 1 6.5 seconds. What was its length?

Make up a radical equation that has no solution.

Make up a radical equation that has an extraneous solution.

Discuss the step in the solving process for radical equations that leads to the possibility of extraneous solutions. Why is there no such possibility for linear and quadratic equations?

Graph the inequality: x :2:: -2. (pp. 1 7-19)

True or False -5 > -3 (pp. 1 7-19)

If each side of an inequality is multiplied by a(n) ______ number, then the sense of the inequality symbol is reversed.

A( n) _____ _____, denoted [a, b], consists of all real numbers x for which a ::; x ::; b.

The _____ _____ state that the sense, or direction, of an inequality remains the same if each side is multiplied by a positive number, while the direction is reversed if each side is multiplied by a negative number.

In Problems 6-9, assume that a < b and c < o. Tl'ue 01' False a + c < b + c

In Problems 6-9, assume that a < b and c < o. Tl'Ue or False a-c< b-c

In Problems 6-9, assume that a < b and c < o. Tl'Ue 01' False ac > bc

In Problems 6-9, assume that a < b and c < o. True or False a b -<- C C

True or False The square of any real number is always nonnegative.

In Problems II-16, express the graph shown in blue using interval notation. A lso express each as an inequality involving x. -1 0 2 3

In Problems II-16, express the graph shown in blue using interval notation. A lso express each as an inequality involving x. -2 -1 0 2

In Problems II-16, express the graph shown in blue using interval notation. A lso express each as an inequality involving x. -1 0 1 2 3

In Problems II-16, express the graph shown in blue using interval notation. A lso express each as an inequality involving x. -2 -1 0 1 2

In Problems II-16, express the graph shown in blue using interval notation. A lso express each as an inequality involving x. -1 o 1 2 3

In Problems II-16, express the graph shown in blue using interval notation. A lso express each as an inequality involving x. 1 o 1 2 3

In Problems 17-22, an inequality is given. Write the inequality obtained by: (a) Adding 3 to each side of the given inequality. (b) Subtracting 5 from each side of the given inequality. (c) Multiplying each side of the given inequality by 3. (d) Multiplying each side of the given inequality by -2. 3 < 5

In Problems 17-22, an inequality is given. Write the inequality obtained by: (a) Adding 3 to each side of the given inequality. (b) Subtracting 5 from each side of the given inequality. (c) Multiplying each side of the given inequality by 3. (d) Multiplying each side of the given inequality by -2. 2 > 1

In Problems 17-22, an inequality is given. Write the inequality obtained by: (a) Adding 3 to each side of the given inequality. (b) Subtracting 5 from each side of the given inequality. (c) Multiplying each side of the given inequality by 3. (d) Multiplying each side of the given inequality by -2. 4 > -3

In Problems 17-22, an inequality is given. Write the inequality obtained by: (a) Adding 3 to each side of the given inequality. (b) Subtracting 5 from each side of the given inequality. (c) Multiplying each side of the given inequality by 3. (d) Multiplying each side of the given inequality by -2. -3 > -5

In Problems 17-22, an inequality is given. Write the inequality obtained by: (a) Adding 3 to each side of the given inequality. (b) Subtracting 5 from each side of the given inequality. (c) Multiplying each side of the given inequality by 3. (d) Multiplying each side of the given inequality by -2. 2x + 1 < 2

In Problems 17-22, an inequality is given. Write the inequality obtained by: (a) Adding 3 to each side of the given inequality. (b) Subtracting 5 from each side of the given inequality. (c) Multiplying each side of the given inequality by 3. (d) Multiplying each side of the given inequality by -2. 1 - 2x > 5

In Problems 23-30, write each inequality using interval notation, and illustrate each inequality using the real number line. 0 ::; x ::; 4

In Problems 23-30, write each inequality using interval notation, and illustrate each inequality using the real number line. -1 < x < 5

In Problems 23-30, write each inequality using interval notation, and illustrate each inequality using the real number line. 4 ::; x < 6

In Problems 23-30, write each inequality using interval notation, and illustrate each inequality using the real number line. -2 < x < 0

In Problems 23-30, write each inequality using interval notation, and illustrate each inequality using the real number line. x :2:: 4

In Problems 23-30, write each inequality using interval notation, and illustrate each inequality using the real number line. ::; 5

In Problems 23-30, write each inequality using interval notation, and illustrate each inequality using the real number line. x < -4

In Problems 23-30, write each inequality using interval notation, and illustrate each inequality using the real number line. x > 1

In Problems 31-38, write each interval as an inequality involving x, and illustrate each inequality using the real number line. [2, 5]

In Problems 31-38, write each interval as an inequality involving x, and illustrate each inequality using the real number line. (1, 2)

In Problems 31-38, write each interval as an inequality involving x, and illustrate each inequality using the real number line. (-3 , -2)

In Problems 31-38, write each interval as an inequality involving x, and illustrate each inequality using the real number line. [0, 1)

In Problems 31-38, write each interval as an inequality involving x, and illustrate each inequality using the real number line. [4, 00)

In Problems 31-38, write each interval as an inequality involving x, and illustrate each inequality using the real number line. (-00, 2]

In Problems 31-38, write each interval as an inequality involving x, and illustrate each inequality using the real number line. (-00, -3 )

In Problems 31-38, write each interval as an inequality involving x, and illustrate each inequality using the real number line. ( -8, 00)

In Problems 39-52, fill in the blank with the correct inequality symbol. If x < 5, then x - 5 _____ 0.

In Problems 39-52, fill in the blank with the correct inequality symbol. If x < -4, then x + 4 ____ 0.

In Problems 39-52, fill in the blank with the correct inequality symbol. If x > -4, then x + 4_____ 0.

In Problems 39-52, fill in the blank with the correct inequality symbol. If x > 6, then x - 6 _____ 0.

In Problems 39-52, fill in the blank with the correct inequality symbol. If x :2:: -4, then 3x _____ - 12.

In Problems 39-52, fill in the blank with the correct inequality symbol. If x ::; 3, then 2x _____ 6.

In Problems 39-52, fill in the blank with the correct inequality symbol. If x> 6, then -2x _____ - 12.

In Problems 39-52, fill in the blank with the correct inequality symbol. If x > -2, then -4x ______ 8.

In Problems 39-52, fill in the blank with the correct inequality symbol. If x :2:: 5, then -4x _____ -20.

In Problems 39-52, fill in the blank with the correct inequality symbol. If x ::; -4, then -3x ______ 12.

In Problems 39-52, fill in the blank with the correct inequality symbol. If 2x > 6, then x _____ 3.

In Problems 39-52, fill in the blank with the correct inequality symbol. If 3x ::; 12, then x _____ 4.

In Problems 39-52, fill in the blank with the correct inequality symbol. It - "2 x ::; 3 , then x _____ -6.

In Problems 39-52, fill in the blank with the correct inequality symbol. If -"4 x > 1, then x _____ -4.

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. x + 1 < 5

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. x - 6 < 1

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 1 - 2x :::; 3

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2 - 3x :::; 5

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 3x - 7 > 2

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2x + 5 > 1

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 3x - 1 2: 3 + x

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2x - 2 2: 3 + x

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -2(x + 3) < 8

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -3(1 - x) < 12

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 4 - 3 (1 - x) :::; 3

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 8 - 4(2 - x) :::; -2x

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. "2 (x - 4) > x + 8

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 3x + 4 > 3 (x - 2)

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. :: 2: 1 - :: 2 4

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. :: 2: 2 + :: 3 6

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 0 :::; 2x - 6 :::; 4

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 4 :::; 2x + 2 :::; 10

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -5 :::; 4 - 3x :::; 2

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -3 :::; 3 - 2x :::; 9

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -3 < --< 0 4

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 3x + 2 0 < 2 < 4

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 1 < 1 - "2 x < 4

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 0 < 1 - 3 x < 1

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. (x + 2)(x - 3) > (x - 1 ) (x + 1)

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. (x - 1 )(x + 1) > (x - 3)(x + 4)

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. x(4x + 3) :::; (2x + 1)2

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. x(9x - 5) :::; (3x - 1)2

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 1 x + 1 3 - :::; -- < - 234

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 3 < -2- :::; 3

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. (4x + 2rl < 0

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. (2x - 1)- 1 > 0

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2 3 85. 0 < - < x 5

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 4 2 0 < - < - x 3

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 0 < (2x - 4rl < "

In Problems 53-88, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 0 < (3x + 6r1 < - 3

In Problems 89-98, find a and b. If -1 < x < 1, then a < x + 4 < b.

In Problems 89-98, find a and b. If -3 < x < 2, then a < x - 6 < b.

In Problems 89-98, find a and b. If 2 < x < 3, then a < -4x < b.

In Problems 89-98, find a and b. If -4 < x < 0, then a < "2 x < b.

In Problems 89-98, find a and b. If 0 < x < 4, then a < 2x + 3 < b.

In Problems 89-98, find a and b. If -3 < x < 3, then a < 1 - 2x < b.

In Problems 89-98, find a and b. If -3 < x < 0, then a < -- < b. x+4

In Problems 89-98, find a and b. If 2 < x < 4, then a < x _ 6 < b.

In Problems 89-98, find a and b. If 6 < 3x < 12 , then a < < b.

In Problems 89-98, find a and b. If 0 < 2x < 6, then a < .-? < b.

What is the domain of the variable in the expression ?

What Vs+2x is the domain of the variable in the expression ?

A young adult may be defined as someone older than 21, but less than 30 years of age. Express this statement using inequalities.

Middle-aged may be defined as being 40 or more and less than 60. Express this statement using inequalities.

Life Expectancy The Social Security Administration determined that an average 30-year-old male in 2005 couldexpect to live at least 49 .66 more years and an average 30-year-old female in 2005 could expect to live at least 53.58 more years. (a) To what age can an average 30-year-old male expect to live? Express your answer as an inequality. (b) To what age can an average 30-year-old female expect to live? Express your answer as an inequality. (c) Who can expect to live longer, a male or a female? By how many years? Source: Actuarial Study No. 120, August 2005

General Chemistry For a certain ideal gas, the volume V (in cubic centimeters) equals 20 times the temperature T (in degrees Celsius). If the temperature varies from 80 to 120 C inclusive, what is the corresponding range of the volume of the gas?

Real Estate A real estate agent agrees to sell an apartment complex according to the following commission schedule: $45,000 plus 25 % of the selling price in excess of $900,000. Assuming that the complex will sell at some price between $900,000 and $1,100,000 inclusive, over what range does the agent's commission vary? How does the commission vary as a percent of selling price?

Sales Commission A used car salesperson is paid a commission of $25 plus 40% of the selling price in excess of owner's cost. The owner claims that used cars typically sell for at least owner's cost plus $200 and at most owner's cost plus $3000. For each sale made, over what range can the salesperson expect the commission to vary?

Federal Tax Withholding The percentage method of withholding for federal income tax (2006) states that a single person whose weekly wages, after subtracting withholding allowances, are over $620, but not over $1409, shall have $78.30 plus 25% of the excess over $620 withheld. Over what range does the amount withheld vary if the weekly wages vary from $700 to $900 inclusive?

Exercising Sue wants to lose weight. For healthy weight loss, the American College of Sports Medicine (ACSM) recommends 200 to 300 minutes of exercise per week. For the first six days of the week, Sue exercised 40, 45, 0, 50, 25, and 35 minutes. How long should Sue exercise on the seventh day in order to stay within the ACSM guidelines?

Electricity Rates Commonwealth Edison Company's charge for electricity in May 2006 is 8.275 per kilowatt-hour. In addition, each monthly bill contains a customer charge of $7.58. If last year's bills ranged from a low of $63.47 to a high of $214.53, over what range did usage vary (in kilowatt-hours)? Source: Commonwealth Edison Co., Chicago, Illinois, 2006.

Water Bills The Village of Oak Lawn charges homeowners $28.84 per quarter-year plus $2.28 per 1000 gallons for water usage in excess of 12,000 gallons. In 2006 one homeowner's quarterly bill ranged from a high of $74.44 to a low of $42.52. Over what range did water usage vary? Source: Village of Oak Lawn, Illinois, April 2006.

Markup of a New Car The markup over dealer's cost of a new car ranges from 12% to 18%. If the sticker price is $18,000, over what range will the dealer's cost vary?

IQ Tests A standard intelligence test has an average score of 100. According to statistical theory, of the people who take the test, the 2.5% with the highest scores will have scores of more than 1.960' above the average, where 0' (sigma, a number called the standard deviation) depends on the nature of the test. If 0' = 12 for this test and there is (in principle) no upper limit to the score possible on the test, write the interval of possible test scores of the people in the top 2.5%.

Computing Grades In your Economics 101 class, you have scores of 68, 82, 87, and 89 on the first four of five tests. To get a grade of B, the average of the first five test scores must be greater than or equal to 80 and less than 90. (a) Solve an inequality to find the range of the score that you need on the last test to get a B. (b) What score do you need if the fifth test counts double?

"Light" Foods For food products to be labeled "light," the U.S. Food and Drug Administration requires that the altered product must either contain one-third or fewer calories than the regular product or it must contain one-half or less fat than the regular product. If a serving of Miracle Whip Light contains 20 calories and 1.5 grams of fat, then what must be true about either the number of calories or the grams of fat in a serving of regular Miracle Whip?

Arithmetic Mean If a < b, show that a < 2 < b. The a + b . number - II d h 'th f f db 2 - IS ca e t e art me IC mean a a an .

Refer to Problem 115. Show that the arithmetic mean of a and b is equidistant from a and b.

Geometric Mean If 0 < a < b, show that a < vaJj < b. The number vaJj is called the geometric mean of a and b.

Refer to Problems 115 and 1 17. Show that the geometric mean of a and b is less than the arithmetic mean of a and b.

Harmonic Mean For 0 < a < b, let h be defined by ! = ! (! + !) h 2 a b Show that a < h < b. The number h is called the harmonic mean of a and b.

Refer to Problems 1 15, 1 17, and 1 19. Show that the harmonic mean of a and b equals the geometric mean squared divided by the arithmetic mean.

Another Reciprocal PrOI)erty Prove that if 0 < a < b, then 1 1 0< - < -. b a

Make up an inequality that has no solution. Make up one that has exactly one solution.

The inequality y} + 1 < -5 has no real solution. Explain why.

Do you prefer to use inequality notation or interval notation to express the solution to an inequality? Give your reasons. Are there particular circumstances when you prefer one to the other? Cite examples.

How would you explain to a fellow student the underlying reason for the multiplication properties for inequalities (page 1 27), that is, the sense or direction of an inequality remains the same if each side is multiplied by a positive real number, whereas the direction is reversed if each side is multiplied by a negative real number.

1-21 = ____. (p. 19)

True or False Ixl 0 for any real number x. (p. 19)

The solution set of the equation Ixl == 5 is { ____ }.

The solution set of the inequality Ixl < 5 is {xl }.

True or False The equation Ixl == -2 has no solution.

True or False The inequality Ixl -2 has the set of real numbers as solution set.

In Problems 7-34, solve each equation. 12xl = 6

In Problems 7-34, solve each equation. 13xl = 12

In Problems 7-34, solve each equation. 2x + 31 = 5

In Problems 7-34, solve each equation. 13x - 11 = 2

In Problems 7-34, solve each equation. 11 - 4tl + S = 1

In Problems 7-34, solve each equation. 11 - 2z1 + 6 = 9

In Problems 7-34, solve each equation. 1-2xl = lsi

In Problems 7-34, solve each equation. I-xl = 111

In Problems 7-34, solve each equation. 1-21x = 4

In Problems 7-34, solve each equation. 131x = 9

In Problems 7-34, solve each equation. 3" lxl = 9

In Problems 7-34, solve each equation. 41xl = 9

In Problems 7-34, solve each equation. + I = 2

In Problems 7-34, solve each equation. I - I = 1

In Problems 7-34, solve each equation. u - 21 = - -2

In Problems 7-34, solve each equation. 2 - vi = -1

In Problems 7-34, solve each equation. 4 - 12xl = 3

In Problems 7-34, solve each equation. 5 - IX I =3

In Problems 7-34, solve each equation. x2 - 91 = 0

In Problems 7-34, solve each equation. Ix2 - 161 = 0

In Problems 7-34, solve each equation. x2 - 2xl = 3

In Problems 7-34, solve each equation. x2 + xl = 12

In Problems 7-34, solve each equation. Ix2 + x-II = 1

In Problems 7-34, solve each equation. x2 + 3x - 21 = 2

In Problems 7-34, solve each equation. 3X - 2 1 = 2 2x - 3

In Problems 7-34, solve each equation. 1 2x + 1 --1 = 1 3x + 4

In Problems 7-34, solve each equation. Ix2 + 3xl = Ix2 - 2x

In Problems 7-34, solve each equation. Ix2 - 2xl = Ix2 + 6xl

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 12xl < S

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 3xl < 15

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 13xl > 12

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 12xl > 6

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. Ix - 21 + 2 < 3

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. Ix + 41 + 3 < 5

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 13t - 21 :5 4

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 12u + 51 :5 7

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 12x - 31 2

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 13x + 41 2

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 1 - 4xl - 7 < -2

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 11 - 2xl - 4 < -1

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 11 - 2xl > 3

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2 - 3xl > 1

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 1-4xl + I-51 :5 1

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. I-xl - 141 :5 2

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -2xl > 1 -3

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -x - 21 1

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -12x - 11 -3

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -11 - 2xl -3

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2xl < -1

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 3xl 0

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 5xl -1

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 16xl < -2

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2x + 3 - 1

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 3 - Ix + 11 < "

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 5 + Ix - 11 > "

In Problems 35-62, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2X - 3 1 --- + - 1 > 1 2

Body Temperature "Normal" human body temperature is 9S.6F. If a temperature x that differs from normal by at least 1.5 is considered unhealthy, write the condition for an unhealthy temperature x as an inequality involving an absolute value, and solve for x.

Household Voltage In the United States, normal household voltage is 110 volts. However, it is not uncommon for actual voltage to differ from normal voltage by at most 5 volts. Express this situation as an inequality involving an absolute value. Use x as the actual voltage and solve for x.

Reading Books A Gallup poll conducted May 20-22, 2005, found that Americans read an average of 13.4 books per year. Gallup is 99% confident that the result from this poll is off by fewer than 1.35 books from the actual average x. Express this situation as an inequality involving absolute value, and solve the inequality for x to determine the interval in which the actual average is likely to fall. Note: In statistics, this interval is called a 99% confidence interval.

SI)eed of Sound According to data from the Hill Aerospace Museum (Hill Air Force Base, Utah), the speed of sound varies depending on altitude, barometric pressure, and temperature. For example, at 20,000 feet, 13.75 inches of mercury, and -12.3F, the speed of sound is about 707 miles per hour, but the speed can vary from this result by as much as 55 miles per hour as conditions change. (a) Express this situation as an inequality involving an absolute value. (b) Using x for the speed of sound, solve for x to find an interval for the speed of sound.

Express the fact that x differs from 3 by less than as an inequality involving an absolute value. Solve for x.

Express the fact that x differs from -4 by less than 1 as an inequality involving an absolute value. Solve for x.

In Problems 71-76, find a and b. If Ix - 11 < 3, then a < x + 4 < b.

In Problems 71-76, find a and b. If Ix + 21 < 5, then a < x - 2 < b

In Problems 71-76, find a and b. If Ix + 41 ::; 2, then a ::; 2x - 3 ::; b.

In Problems 71-76, find a and b. If Ix - 31 ::; 1, then a ::; 3x + 1 ::; b.

In Problems 71-76, find a and b. If Ix + 41 ::; 2, then a ::; 2x - 3 ::; b.

In Problems 71-76, find a and b. If Ix - 31 ::; 1, then a ::; 3x + 1 ::; b.

In Problems 71-76, find a and b. If Ix - 21 ::; 7, then a ::; --::; b. x - 10 x

In Problems 71-76, find a and b. If Ix + 11 ::; 3, then a ::; -- ::; b. x + 5

Show that if a > 0, b > 0, and va < Vb, then a < b. [Hint: b - a = (Vb - va)(Vb + ya)]

Show that a ::; lal.

Prove the triangle inequality la + bl ::; lal + Ibl. [Hint: Expand la + bl2 = (a + b ) 2 , and use the result of Problem 78.]

Prove that la - bl 2: lal - Ibl. [Hint: Apply the triangle inequality from Problem 79 to lal = I(a - b) + bl]

If a > 0, show that the solution set of the inequality x 2 < a consists of all numbers x for which -va < x < va

If a > 0, show that the solution set of the inequality x2 > a consists of all numbers x for which x < -va or x > v

In Problems 83-90, use the results found in Problems 81 and 82 to solve each inequality. x2 < 1

In Problems 83-90, use the results found in Problems 81 and 82 to solve each inequality. x2 < 4

In Problems 83-90, use the results found in Problems 81 and 82 to solve each inequality. x2 : 9

In Problems 83-90, use the results found in Problems 81 and 82 to solve each inequality. x2 : 9

In Problems 83-90, use the results found in Problems 81 and 82 to solve each inequality. x2 : 16

In Problems 83-90, use the results found in Problems 81 and 82 to solve each inequality. x2 : 9

In Problems 83-90, use the results found in Problems 81 and 82 to solve each inequality. x2> 4

In Problems 83-90, use the results found in Problems 81 and 82 to solve each inequality. x2 > 16

Solve 13x - 12x + 111 = 4

Solve Ix + 13x - 211 = 2.

The equation Ixl = -2 has no solution. Explain why.

The inequality /x/ > -0.5 has all real numbers as the solution. Explain why.

The inequality Ixl > 0 has as solution set {xix =F O}. Explain why.

The process of using variables to represent unknown quantities and then finding relationships that involve these variables is referred to as ____ ___ .

The money paid for the use of money is _____.

Objects that move at a constant velocity are said to be in ______.

True or False The amount charged for the use of principal for a given period of time is called the rate of interest.

True or False If an object moves at an average velocity v, the distance s covered in time t is given by the formula s = vt.

Suppose that you want to mix two coffees in order to obtain 100 pounds of the blend. If x represents the number of pounds of coffee A, write an algebraic expression that represents the number of pounds of coffee B.

In Problems 7-16, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols. Geometry The area of a circle is the product of the number 7T and the square of the radius.

In Problems 7-16, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols. Geometry The circumference of a circle is the product of the number 7T and twice the radius.

In Problems 7-16, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols. Geometry The area of a square is the square of the length of a side.

In Problems 7-16, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols. Geometry The perimeter of a square is four times the length of a side.

In Problems 7-16, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols. Physics Force equals the product of mass and acceleration.

In Problems 7-16, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols. Physics Pressure is force per unit area.

In Problems 7-16, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols. Physics Work equals force times distance.

In Problems 7-16, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols. Physics Kinetic energy is one-half the product of the mass and the square of the velocity.

In Problems 7-16, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols. Business The total variable cost of manufacturing x dishwashers is $150 per dishwasher times the number of dishwashers manufactured.

In Problems 7-16, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols. Business The total revenue derived from selling x dishwashers is $250 per dishwasher times the number of dishwashers sold.

Financial Planning Betsy, a recent retiree, requires $6000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 15% per year or in a certificate of deposit (CD) paying 7% per year. How much money should be invested in each to realize exactly $6000 in interest per year?

Financial Planning After 2 years, Betsy (see Problem 17) finds that she will now require $7000 per year. Assuming that the remaining information is the same, how should the money be reinvested?

Banking A bank loaned out $12,000, part of it at the rate of 8% per year and the rest at the rate of 18% per year. If the interest received totaled $1000, how much was loaned at 8%?

Banking Wendy, a loan officer at a bank, has $1,000,000 to lend and is required to obtain an average return of 18% per year. If she can lend at the rate of 19% or at the rate of 16%, how much can she lend at the 16% rate and still meet her requirement?

Blending Teas The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $5 per pound with some Orange Pekoe tea that sells for $3 per pound to get 100 pounds of the new blend. The selling price of the new blend is to be $4.50 per pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required?

Business: Blending Coffee A coffee manufacturer wants to market a new blend of coffee that sells for $3.90 per pound by mixing two coffees that sell for $2.75 and $5 per pound, respectively. What amounts of each coffee should be blended to obtain the desired mixture? [Hint: Assume that the total weight of the desired blend is 100 pounds.]

Business: Mixing Nuts A nut store normally sells cashews for $9.00 per pound and almonds for $3.50 per pound. But at the end of the month the almonds had not sold well, so, in order to sell 60 pounds of almonds, the manager decided to mix the 60 pounds of almonds with some cashews and sell the mixture for $7.50 per pound. How many pounds of cashews should be mixed with the almonds to ensure no change in the profit?

Business: Mixing Candy A candy store sells boxes of candy containing caramels and cremes. Each box sells for $12.50 and holds 30 pieces of candy (all pieces are the same size). If the caramels cost $0.25 to produce and the cremes cost $0.45 to produce, how many of each should be in a box to make a profit of $3?

Physics: Uniform Motion A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current? See the figure.

Physics: Uniform Motion A motorboat heads upstream on a river that has a current of 3 miles per hour. The trip upstream takes 5 hours, and the return trip takes 2.5 hours. What is the speed of the motorboat? (Assume that the motorboat maintains a constant speed relative to the water.)

Physics: Uniform Motion A motorboat maintained a constant speed of 15 miles per hour relative to the water in going 10 miles upstream and then returning. The total time for the trip was 1.5 hours. Use this information to find the speed of the current.

Physics: Uniform Motion Two cars enter the Florida Turnpike at Commercial Boulevard at 8:00 AM, each heading for Wildwood. One car' s average speed is 10 miles per hour more than the other's. The faster car arrives at Wildwood at 1 11:00 AM, 2" hour before the other car. What was the average speed of each car? How far did each travel?

Moving Walkways The speed of a moving walkway is typically about 2.5 feet per second. Walking on such a moving walkway, it takes Karen a total of 40 seconds to travel 50 feet with the movement of the walkway and then back again against the movement of the walkway. What is Karen's normal walking speed? Source: Answers. com

Moving Walkways The Gare Montparnasse train station in Paris has a high-speed version of a moving walkway. If he walks while riding this moving walkway, Jean Claude can travel 200 meters in 30 seconds less time than if he stands still on the moving walkway. If Jean Claude walks at a normal rate of 1.5 meters per second, what is the speed of the Gare Montparnasse walkway? Source: Answers. com

Tennis Anyone'! A regulation doubles tennis court has an area of 2808 square feet. If it is 6 feet longer than twice its width, determine the dimensions of the court. Source: United States Tennis Association

Laser Printers It takes an HP LaserJet 1300 laser printer 10 minutes longer to complete a 600-page print job by itself than it takes an HP LaserJet 2420 to complete the same job by itself. Together the two printers can complete the job in 12 minutes. How long does it take each printer to complete the print job alone? What is the speed of each printer? Source: Hewlett-Packard

Working Together on a Job Trent can deliver his newspapers in 30 minutes. It takes Lois 20 minutes to do the same route. How long would it take them to deliver the newspapers if they work together?

Working Together on a Job Patrice, by himself, can paint four rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her to paint four rooms?

Enclosing a Garden A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it. See the figure. (a) If the length of the garden is to be twice its width, what will be the dimensions of the garden? (b) What is the area of the garden? (c) If the length and width of the garden are to be the same, what would be the dimensions of the garden? (d) What would be the area of the square garden?

Construction A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long. (a) If the pond is square, what are its dimensions? (b) If the pond is rectangular and the length of the pond is to be three times its width, what are its dimensions? (c) If the pond is circular, what is its diameter? (d) Which pond has the most area?

Football A tight end can run the 100-yard dash in 12 seconds. A defensive back can do it in 10 seconds. The tight end catches a pass at his own 20-yard line with the defensive back at the 15-yard line. (See the figure.) If no other players are nearby, at what yard line will the defensive back catch up to the tight end? [Hint: At time t = 0, the defensive back is 5 yards behind the tight end.]

Computing Business Expense Therese, an outside salesperson, uses her car for both business and pleasure. Last year, she traveled 30,000 miles, using 900 gallons of gasoline. Her car gets 40 miles per gallon on the highway and 25 in the city. She can deduct all highway travel, but no city travel, on her taxes. How many miles should Therese be allowed as a business expense?

Mixing Water and Antifreeze How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 60% antifreeze?

Mixing Water and Antifreeze The cooling system of a certain foreign-made car has a capacity of 15 liters. If the system is filled with a mixture that is 40% antifreeze, how much of this mixture should be drained and replaced by pure antifreeze so that the system is filled with a solution that is 60% antifreeze?

Chemistry: Salt Solutions How much water must be evaporated from 32 ounces of a 4% salt solution to make a 6% salt solution?

Chemistry: Salt Solutions How much water must be evaporated from 240 gallons of a 3% salt solution to produce a 5% salt solution?

Purity of Gold The purity of gold is measured in karats, with pure gold being 24 karats. Other purities of gold are expressed as proportional parts of pure gold. Thus, IS-karat IS 12 gold is 24' or 75 % pure gold; 12-karat gold is 24 ' or 50% pure gold; and so on. How much 12-karat gold should be mixed with pure gold to obtain 60 grams of 16-karat gold?

Chemistry: Sugar Molecules A sugar molecule has twice as many atoms of hydrogen as it does oxygen and one more atom of carbon than oxygen. If a sugar molecule has a total of 45 atoms, how many are oxygen? How many are hydrogen?

Running a Race Mike can run the mile in 6 minutes, and Dan can run the mile in 9 minutes. If Mike gives Dan a head start of 1 minute, how far from the start will Mike pass Dan? How long does it take? See the figure.

Range of an Airplane An air rescue plane averages 300 miles per hour in still air. It carries enough fuel for 5 hours of flying time. If, upon takeoff, it encounters a head wind of 30 mi/hr, how far can it fly and return safely? (Assume that the wind remains constant.)

Emptying Oil Tankers An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the tanker in 9 hours. If the main pump is started at 9 AM, when should the auxiliary pump be started so that the tanker is emptied by noon?

Cement Mix A 20-pound bag of Economy brand cement mix contains 25% cement and 75% sand. How much pure cement must be added to produce a cement mix that is 40% cement?

Emptying a Tub A bathroom tub will fill in 15 minutes with both faucets open and the stopper in place. With both faucets closed and the stopper removed, the tub will empty in 20 minutes. How long will it take for the tub to fill if both faucets are open and the stopper is removed?

Using Two Pumps A 5-horsepower (hp) pump can empty a pool in 5 hours. A smaller, 2-hp pump empties the same pool in 8 hours. The pumps are used together to begin emptying this pool. After two hours, the 2-hp pump breaks down. How long will it take the larger pump to empty the pool?

A Biathlon Suppose that you have entered an 87-mile biathlon that consists of a run and a bicycle race. During your run, your average velocity is 6 miles per hour, and during your bicycle race, your average velocity is 25 miles per hour. You finish the race in 5 hours. What is the distance of the run? What is the distance of the bicycle race?

Cyclists Two cyclists leave a city at the same time, one going east and the other going west. The westbound cyclist bikes 5 mph faster than the eastbound cyclist. After 6 hours they are 246 miles apart. How fast is each cyclist riding?

COml Jaring Olympic Heroes In the 1984 Olympics, C. Lewis of the United States won the gold medal in the 100-meter race with a time of 9.99 seconds. In the 1 896 Olympics, Thomas Burke, also of the United States, won the gold medal in the 100-meter race in 12.0 seconds. If they ran in the same race repeating their respective times, by how many meters would Lewis beat Burke?

Constructing a Coffee Can A 39-ounce can of Hills Bros. coffee requires 188.5 square inches of aluminum. If its height is 7 inches, what is its radius? [Hint: The surface area S of a right cylinder is S = 271"r2 + 2m"h, where r is the radius and h is the height.] T 7 in. 1

Critical Thinking You are the manager of a clothing store and have just purchased 100 dress shirts for $20.00 each. After 1 month of selling the shirts at the regular price, you plan to have a sale giving 40% off the original selling price. However, you still want to make a profit of $4 on each shirt at the sale price. What should you price the shirts at initially to ensure this? If, instead of 40% off at the sale, you give 50% off, by how much is your profit reduced?

Critical Thinking Make up a word problem that requires solving a linear equation as part of its solution. Exchange problems with a friend. Write a critique of your friend's problem.

Critical Thinking Without solving, explain what is wrong with the following mixture problem: How many liters of 25% ethanol should be added to 20 liters of 48% ethanol to obtain a solution of 58% ethanol? Now go through an algebraic solution. What happens?

Computing Average Speed In going from Chicago to Atlanta, a car averages 45 miles per hour, and in going from Atlanta to Miami, it averages 55 miles per hour. If Atlanta is halfway between Chicago and Miami, what is the average speed from Chicago to Miami? Discuss an intuitive solution. Write a paragraph defending your intuitive solution. Then solve the problem algebraically. Is your intuitive solution the same as the algebraic one? If not, find the flaw.

Speed of a Plane On a recent flight from Phoenix to Kansas City, a distance of 919 nautical miles, the plane arrived 20 minutes early. On leaving the aircraft, I asked the captain, "What was our tail wind?" He replied, "I don't know, but our ground speed was 550 knots." How can you determine if enough information is provided to find the tail wind? If possible, find the tail wind. (1 knot = 1 nautical mile per hour)

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 2-3=8

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) x 2'4- 2=4

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) -2(5 - 3x) + 8 = 4 + 5x

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) (6 - 3x) - 2(1 + x) = 6x

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 3x x 1 5. - - - = - 4 3 12

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 4 - 2x 1 3 +"6 = 2x

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) x 6 --= - x,,= 1 x - 1 5

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 4x - 5 3 ---=2 x,,=- 3 - 7x 7

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) x( 1 - x) = 6

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) x(1 + x) = 6

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 1:. (r - 1:.) = - 2 - 3 4 6

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 1 - 3x x + 6 1 4 = 3 + 2"

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) (x - 1) (2x + 3) =

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) x(2 - x) = 3(x - 4)

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 2x + 3 = 4x2

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 1 + 6x = 4x2

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) =2

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) .=3

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) x(x + 1) + 2 =

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 3x2 - X + 1 = 0

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) x4 -5x2 + 4 = 0

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 3x4 + 4x2 + 1 = 0

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) V 2x - 3 + x = 3

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) =x- 2

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) \Y 2x + 3 = 2

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 3x + 1 = -1

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) "Vx+l + = V2x + 1

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) --Vx--=s = 3

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 2XI/2 - 3 = 0

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 3xl/4 - 2 = 0

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) x-6 - 7x-3 - 8 = 0

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 6x-1 - 5x-I/2 + 1 = 0

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) x2 + m2 = 2mx + (nxf n,,= 1, n ,,= -1

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) b2 x2 + 2ax = x2 + a2 b,,= 1, b ,,= -1

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.)

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) -- + --= - x,,= 0, x ,,= m, x ,,= n x-m x-n x

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) yx2 + 3x + 7 - yx2 - 3x + 9 + 2 = 0

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) Y x2 + 3x + 7 - yx2 + 3x + 9 =

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) [2x + 3[ =

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) [3x - 1[ = 5

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) [2 - 3x[ + 2 = 9

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) [1 - 2x[ + 1 = 4

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 2x3 = 3x2

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 5x4 = 9x3

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 2x3 + 5x2 - 8x - 20 =

In Problems 1-46, find all the real solution5; if any, of each equation. (Where they appeaJ; a, b, m, and n are positive constants.) 3x3 + 5x2 - 3x - 5 = 0

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2x - 3 x ---+ 2 :5 - 5

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 5 - x --:5 6x - 4 3

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -9 2x + 3:5 --- :5 7 -4

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2x - 2 -4 < -- < 6 3

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 3 -3x 51.2 < --< 6 12

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 5 - 3x -3 :5 --- :5 6 2

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. [3x + 4[ < 2

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. [1 - 2x[ < :

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. [2x - 5[ 9

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. [3x + 1[ 10

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2 + [2 - 3x[ :5 4

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. + [ 2X ; 1 [ :5 1

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 1 - [2 - 3x[ < -4

In Problems 47-60, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2X - 1 [ 1 - 3 <-2

In Problems 61-64, what number should be added to complete the square of each expression? x2 + 6x

In Problems 61-64, what number should be added to complete the square of each expression? x2 - lOx

In Problems 61-64, what number should be added to complete the square of each expression? x2 - i . x 3

In Problems 61-64, what number should be added to complete the square of each expression? ? 4 64 . r +-x 5

In Problems 65-74, use the complex number system and write each expression in the standard form a + bi. (6 + 3i) - (2 - 4i)

In Problems 65-74, use the complex number system and write each expression in the standard form a + bi. (8 - 3i) + ( -6 + 2i)

In Problems 65-74, use the complex number system and write each expression in the standard form a + bi. 4(3 - i) + 3( -5 + 2i)

In Problems 65-74, use the complex number system and write each expression in the standard form a + bi. 2(1 + i) - 3(2 - 3i)

In Problems 65-74, use the complex number system and write each expression in the standard form a + bi. 3 _ 3 + i

In Problems 65-74, use the complex number system and write each expression in the standard form a + bi. 4 --. 2-{

In Problems 65-74, use the complex number system and write each expression in the standard form a + bi. i50

In Problems 65-74, use the complex number system and write each expression in the standard form a + bi. i29

In Problems 65-74, use the complex number system and write each expression in the standard form a + bi. (2 + 3i)3

In Problems 65-74, use the complex number system and write each expression in the standard form a + bi. (3 - 2i)3

In Problems 75-82, solve each equation in the complex number system. x2 + x + 1 = 0

In Problems 75-82, solve each equation in the complex number system. x2 - x + 1 = 0

In Problems 75-82, solve each equation in the complex number system. 2X2 + x -2 = 0

In Problems 75-82, solve each equation in the complex number system. 3x2 - 2x - 1 = 0

In Problems 75-82, solve each equation in the complex number system. x2 + 3 = x

In Problems 75-82, solve each equation in the complex number system. 2x2 + 1 = 2x

In Problems 75-82, solve each equation in the complex number system. x(1-x)=6

In Problems 75-82, solve each equation in the complex number system. x(1 + x) = 2

Translate the following statement into a mathematical expression : The perimeter p of a rectangle is the sum of two times the length I and two times the width w.

Translate the following statement into a mathematical expression:The total cost C of manufacturing x bicycles in one day is $50,000 plus $95 times the number of bicycles manufactured.

Banking A bank lends out $9000 at 7% simple interest. At the end of 1 year, how much interest is owed on the loan?

Financial Planning Steve, a recent retiree, requires $5000 per year in extra income. He has $70,000 to invest and can invest in A-rated bonds paying 8% per year or in a certificate of deposit (CD) paying 5% per year. How much money should be invested in each to realize exactly $5000 in interest per year?

Lightning and Thunder A flash of lightning is seen, and the resulting thunderclap is heard 3 seconds later. If the speed of sound averages 1 100 feet per second, how far away is the storm?

Physics: Intensity of Light The intensity I (in candlepower) f .. . 900 a a certam lIght source obeys the equatIOn I = -? , where xx is the distance (in meters) from the light. Over what range of distances can an object be placed from this light source so that the range of intensity of light is from 1600 to 3600 candlepower, inclusive?

Extent of Search and Rescue A search plane has a cruising speed of 250 miles per hour and carries enough fuel for at most 5 hours of flying. If there is a wind that averages 30 miles per hour and the direction of the search is with the wind one way and against it the other, how far can the search plane travel before it has to turn back?

Extent of Search and Rescue If the search plane described in Problem 89 is able to add a supplementary fuel tank that allows for an additional 2 hours of flying, how much farther can the plane extend its search?

Rescue at Sea A life raft, set adrift from a sinking ship 150 miles offshore, travels directly toward a Coast Guard station at the rate of 5 miles per hour. At the time that the raft is set adrift, a rescue helicopter is dispatched from the Coast Guard station. If the helicopter's average speed is 90 miles per hour, how long will it take the helicopter to reach the life raft? 90 milhr 5 --milhr ---- 150 mi --- .. : I

Physics: Uni form Motion Two bees leave two locations 150 meters apart and fly, without stopping, back and forth between these two locations at average speeds of 3 meters per second and 5 meters per second, respectively. How long is it until the bees meet for the first time? How long is it until they meet for the second time?

Physics: Uniform Motion A Metra commuter train leaves Union Station in Chicago at 12 noon. Two hours later, an Amtrak train leaves on the same track, traveling at an average speed that is 50 miles per hour faster than the Metra train. At 3 PM the Amtrak train is 10 miles behind the commuter train. How fast is each going?

Physics An object is thrown down from the top of a building 1280 feet tall with an initial velocity of 32 feet per second. The distance s (in feet) of the object from the ground after t seconds is s = 1280 - 32t - 16t 2 (a) When will the object strike ground? (b) What is the height of the object after 4 seconds?

Working Together to Get a Job Done Clarissa and Shawna, working together, can paint the exterior of a house in 6 days. Clarissa by herself can complete this job in 5 days less than Shawna. How long will it take Clarissa to complete the job by herself?

Emptying a Tank Two pumps of different sizes, working together, can empty a fuel tank in 5 hours. The larger pump can empty this tank in 4 hours less than the smaller. lf the larger pump is out of order, how long will it take the smaller one to do the job alone?

Chemistry: Salt Solutions How much water should be added to 64 ounces of a 10% salt solution to make a 2% salt solution?

Chemistry: Salt Solutions How much water must be evaporated from 64 ounces of a 2% salt solution to make a 10% salt solution?

Geometry The hypotenuse of a right triangle measures 13 centimeters. Find the lengths of the legs if their sum is 17 centimeters.

Geometry The diagonal of a rectangle measures 10 inches. If the length is 2 inches more than the width, find the dimensions of the rectangle.

Chemistry : Mixing Acids A laboratory has 60 cubic centimeters (cm3 ) of a solution that is 40% HCI acid. How many cubic centimeters of a 15% solution of HCI acid should be mixed with the 60 cm3 of 40% acid to obtain a solution of 25% HCI? How much of the 25% solution is there?

Framing a Painting An artist has 50 inches of oak trim to frame a painting. The frame is to have a border 3 inches wide surrounding the painting. (a) If the painting is square, what are its dimensions? What are the dimensions of the frame? (b) If the painting is rectangular with a length twice its width, what are the dimensions of the painting? What are the dimensions of the frame?

Using Two Pumps An 8-horsepower (hp) pump can fill a tank in 8 hours. A smaller, 3-hp pump fills the same tank in 12 hours. The pumps are used together to begin filling this tank. After four hours, the 8-hp pump breaks down. How long will it take the smaller pump to fill the tank?

Pleasing Proportion One formula stating the relationship between the length I and width w of a rectangle of "pleasing proportion" is 1 2 = w(1 + w). How should a 4 foot by 8 foot sheet of plasterboard be cut so that the result is a rectangle of "pleasing proportion" with a width of 4 feet?

F inance An inheritance of $900,000 is to be divided among Scott, Alice, and Tricia in the following manner: Alice is to receive % of what Scott gets, while Tricia gets of what Scott gets. How much does each receive?

B us iness: Determining the Cost of a Charte r A group of 20 senior citizens can charter a bus for a one-day excursion trip for $15 per person. The charter company agrees to reduce the price of each ticket by 10 for each additional passenger in excess of 20 who goes on the trip, up to a maximum of 44 passengers (the capacity of the bus). If the final bill from the charter company was $482.40, how many seniors went on the trip, and how much did each pay?

U tilizing Copying Machines A new copying machine can do a certain job in 1 hour less than an older copier. Together they can do this job in 72 minutes. How long would it take the older copier by itself to do the job?

n a 100-meter race, Todd crosses the finish line 5 meters ahead of Scott. To even things up, Todd suggests to Scott that they race again, this time with Todd lining up 5 meters behind the start. (a) Assuming that Todd and Scott run at the same pace as before, does the second race end in a tie? (b) If not, who wins? (c) By how many meters does he win? (d) How far back should Todd start so that the race ends in a tie? After running the race a second time, Scott, to even things up, suggests to Todd that he (Scott) line up 5 meters in front of the start. (e) Assuming again that they run at the same pace as in the first race, does the third race result in a tie? (f) If not, who wins? (g) By how many meters? (h) How far ahead should Scott start so that the race ends in a tie?

Physics: Uniform Motion A man is walking at an average speed of 4 miles per hour alongside a railroad track. A freight train, going in the same direction at an average speed of 30 miles per hour, requires 5 seconds to pass the man. How long is the freight train? Give your answer in feet. 30 mi/hr t = 0 -5 sec -t = 5