When an anvil is dropped into a gorge, the speed withwhich

(6.1) Find the domain for each rational function. f 1x2 = 3 - 5x 7

(6.1) Find the domain for each rational function. g1x2 = 2x + 4 11

(6.1) Find the domain for each rational function. F1x2 = -3x2 x - 5

(6.1) Find the domain for each rational function. h1x2 = 4x 3x - 12

(6.1) Find the domain for each rational function. f 1x2 = x3 + 2 x2 + 8x

(6.1) Find the domain for each rational function. G1x2 = 20 3x2 - 48

Write each rational expression in lowest terms. x - 12 12 - x

Write each rational expression in lowest terms. 5x - 15 25x - 75

Write each rational expression in lowest terms. 2x 2x2 - 2x

Write each rational expression in lowest terms. x + 7 x2 - 49

Write each rational expression in lowest terms. 2x2 + 4x - 30 x2 + x - 20

The average cost (per bookcase) of manufacturing x bookcases is given by the rational function. C1x2 = 35x + 4200 x a. Find the average cost per bookcase of manufacturing 50 bookcases. b. Find the average cost per bookcase of manufacturing 100 bookcases. c. As the number of bookcases increases, does the average cost per bookcase increase or decrease? (See parts (a) and (b).)

Perform each indicated operation. Write your answers in lowest terms 4 - x 5 # 15 2x - 8

Perform each indicated operation. Write your answers in lowest terms x2 - 6x + 9 2x2 - 18 # 4x + 12 5x - 15

Perform each indicated operation. Write your answers in lowest terms a - 4b a2 + ab # b2 - a2 8b - 2a

Perform each indicated operation. Write your answers in lowest terms x2 - x - 12 2x2 - 32 # x2 + 8x + 16 3x2 + 21x + 36

Perform each indicated operation. Write your answers in lowest terms 4x + 8y 3 , 5x + 10y 9

Perform each indicated operation. Write your answers in lowest terms x2 - 25 3 , x2 - 10x + 25 x2 - x - 20

Perform each indicated operation. Write your answers in lowest terms a - 4b a2 + ab , 20b - 5a b2 - a2

Perform each indicated operation. Write your answers in lowest terms 3x + 3 x - 1 , x2 - 6x - 7 x2 - 1

Perform each indicated operation. Write your answers in lowest terms 2x - x2 x3 - 8 , x2 x2 + 2x + 4

Perform each indicated operation. Write your answers in lowest terms 5x - 15 3 - x # x + 2 10x + 20 # x2 - 9 x2 - x - 6

(6.2) Find the LCD of the rational expressions in each list 5 4x2 y5 , 3 10x2 y4, x 6y4

(6.2) Find the LCD of the rational expressions in each list 5 2x , 7 x - 2

(6.2) Find the LCD of the rational expressions in each list 3 5x , 2 x - 5

(6.2) Find the LCD of the rational expressions in each list 1 5x3, 4 x2 + 3x - 28, 11 10x2 - 30x

Perform each indicated operation. Write your answers in lowest terms. 4 x - 4 + x x - 4

Perform each indicated operation. Write your answers in lowest terms. 4 3x2 + 2 3x2

Perform each indicated operation. Write your answers in lowest terms. 1 x - 2 - 1 4 - 2x

Perform each indicated operation. Write your answers in lowest terms. 1 10 - x + x - 1 x - 10

Perform each indicated operation. Write your answers in lowest terms. x 9 - x2 - 2 5x - 15

Perform each indicated operation. Write your answers in lowest terms. 2x + 1 - 1 x - 3

Perform each indicated operation. Write your answers in lowest terms. 2 a2 - 2a + 1 + 3 a2 - 1

Perform each indicated operation. Write your answers in lowest terms. x 9x2 + 12x + 16 - 3x + 4 27x3 - 64

Perform each indicated operation. Write your answers in lowest terms. 2 x - 1 - 3x 3x - 3 + 1 2x - 2

Perform each indicated operation. Write your answers in lowest terms. Find the perimeter of the heptagon (a polygon with seven sides).

(6.3) Simplify each complex fraction. 1 - 3x 4 2 + x 4

(6.3) Simplify each complex fraction. x2 15 x + 1 5x

(6.3) Simplify each complex fraction. 2 - 3 2x x - 2 5x

(6.3) Simplify each complex fraction. 1 + x y x2 y2 - 1

(6.3) Simplify each complex fraction. 5 x + 1 xy 3 x2

(6.3) Simplify each complex fraction. x 3 - 3 x 1 + 3 x

(6.3) Simplify each complex fraction. 1 x - 1 + 1 1 x + 1 - 1

(6.3) Simplify each complex fraction. x - 3 x + 3 + x + 3 x - 3 x - 3 x + 3 - x + 3 x - 3

If f 1x2 = 3 x , x 0, find each of the following. f 1a + h2

If f 1x2 = 3 x , x 0, find each of the following. f 1a2

If f 1x2 = 3 x , x 0, find each of the following. Use Exercises 45 and 46 to find f 1a + h2 - f 1a2 h

If f 1x2 = 3 x , x 0, find each of the following. Simplify the results of Exercise 47.

14xy + 2x2 - 92 , 4xy

Divide 12xb2 + 16xb4 by 4xb3 .

13x4 - 25x2 - 202 , 1x - 32

1 -x2 + 2x4 + 5x - 122 , 1x + 22

12x3 + 3x2 - 2x + 22 , 12x + 32

13x4 + 5x3 + 7x2 + 3x - 22 , 1x2 + x + 22

Use synthetic division to find each quotient. 13x3 + 12x - 42 , 1x - 22

Use synthetic division to find each quotient. 1x5 - 12 , 1x + 12

Use synthetic division to find each quotient. 1x3 - 812 , 1x - 32

Use synthetic division to find each quotient. 13x4 - 2x2 + 102 , 1x + 22

If P1x2 = 3x5 - 9x + 7, use the remainder theorem to find the following. P142

If P1x2 = 3x5 - 9x + 7, use the remainder theorem to find the following. P1 -52

If P1x2 = 3x5 - 9x + 7, use the remainder theorem to find the following. Pa - 1 2 b

If the area of the rectangle is 1x4 - x3 - 6x2 - 6x + 182 square miles and its width is 1x - 32 miles, find the length.

Solve each equation. 3 x + 1 3 = 5 x

Solve each equation. 2x + 3 5x - 9 = 3 2

Solve each equation. 1 x - 2 - 3x x2 - 4 = 2 x + 2

Solve each equation. 7x - x7 = 0

Solve each equation or perform each indicated operation. Simplify. 5 x2 - 7x + 4 2x - 14

Solve each equation or perform each indicated operation. Simplify. 4 3 - x - 7 2x - 6 + 5 x

Solve each equation or perform each indicated operation. Simplify. 3 - 5 x - 2 x2 = 0

Solve each equation or perform each indicated operation. Simplify. 2 + 15 x2 = 13 x

(6.6) Solve each equation for the specified variable. A = h1a + b2 2 for a

(6.6) Solve each equation for the specified variable. 1 R = 1 R1 + 1 R2 for R2

(6.6) Solve each equation for the specified variable. I = E R + r for R

(6.6) Solve each equation for the specified variable. A = P + Prt for r

(6.6) Solve each equation for the specified variable. 1 x = 1 y - 1 z for x

(6.6) Solve each equation for the specified variable. H = kA1T1 - T22 L for A

Solve. The sum of a number and twice its reciprocal is 3. Find the number(s).

Solve. If a number is added to the numerator of 3 7 , and twice that number is added to the denominator of 3 7 , the result is equivalent to 10 21. Find the number.

Solve. Three boys can paint a fence in 4 hours, 5 hours, and 6 hours, respectively. Find how long it will take all three boys to paint the fence working together.

Solve. If Sue Katz can type a certain number of mailing labels in 6 hours and Tom Neilson and Sue working together can type the same number of mailing labels in 4 hours, find how long it takes Tom alone to type the mailing labels.

Solve. The speed of a Ranger boat in still water is 32 mph. If the boat travels 72 miles upstream in the same time that it takes to travel 120 miles downstream, find the current of the stream.

Solve. The speed of a jogger is 3 mph faster than the speed of a walker. If the jogger travels 14 miles in the same amount of time that the walker travels 8 miles, find the speed of the walker.

(6.7) Solve each variation problem A is directly proportional to B. If A = 6 when B = 14, find A when B = 21.

(6.7) Solve each variation problem According to Boyles law, the pressure exerted by a gas is inversely proportional to the volume as long as the temperature stays the same. If a gas exerts a pressure of 1250 kilopascals when the volume is 2 cubic meters, find the volume when the pressure is 800 kilopascals.

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. 22x + 8 11x + 4

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. xy - 3x + 2y - 6 x2 + 4x + 4

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. 2 5x , 4 - 18x 6 - 27x

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. 7x + 28 2x + 4 , x2 + 2x - 8 x2 - 2x - 8

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. 5a2 - 20 a3 + 2a2 + a + 2 , 7a a3 + a

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. 4a + 8 5a2 - 20 # 3a2 - 6a a + 3 , 2a2 5a + 15

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. 7 2x + 5 6x

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. x - 2 x + 1 - x - 3 x - 1

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. 2x + 1 x2 + x - 6 + 2 - x x2 + x - 6

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. 2 x2 - 16 - 3x x2 + 8x + 16 + 3 x + 4

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. 1 x - 2 3x 5 2x - 1 3

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. 2 1 - 2 x

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. x2 + 5x - 6 4x + 3 1x + 622 8x + 6

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. 3 x - 1 - 2 1 - x 2 x - 1 - 2 x

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. 4 + 8 x = 8

For expressions, perform the indicated operation and/or simplify. For equations, solve the equation for the unknown variable. x - 2 x2 - 7x + 10 = 1 5x - 10 - 1 x - 5

The denominator of a fraction is 2 more than the numerator. If the numerator is decreased by 3 and the denominator is increased by 5, the resulting fraction is equivalent to 2 3 . Find the fraction.

The sum of the reciprocals of two consecutive even integers is - 9 40. Find the two integers.

The inlet pipe of a water tank can fill the tank in 2 hours and 30 minutes. The outlet pipe can empty the tank in 2 hours. Find how long it takes to empty a full tank if both pipes are open.

Timmy Garnica drove 210 miles in the same amount of time that it took a DC-10 jet to travel 1715 miles. The speed of the jet was 430 mph faster than the speed of the car. Find the speed of the jet.

Two Amtrak trains traveling on parallel tracks leave Tucson at the same time. In 6 hours, the faster train is 382 miles from Tucson and the trains are 112 miles apart. Find how fast each train is traveling.

The surface area of a sphere varies directly as the square of its radius. If the surface area is 36p square inches when the radius is 3 inches, find the surface area when the radius is 4 inches.

In 2013, it is predicted that 3 out of 4 U.S. citizens will own MP3-capable phones. At this rate, how many MP3-capable phones would you predict to be owned in a community with a 2013 population of 43,560?

Currently, 8 out of 25 U.S. Internet users purchase digital music. At this rate, how many Internet users purchase digital music in a group of 2000 Internet users?

Divide 1x3 - x2 + 3x4 - 22 by 1x - 42.

C is inversely proportional to D. If C = 12 when D = 8, find C when D = 24.

Find the domain of each rational function f 1x2 = 5x2 1 - x

Find the domain of each rational function g1x2 = 9x2 - 9 x2 + 4x + 3

Write each rational expression in lowest terms. 7x - 21 24 - 8x

Write each rational expression in lowest terms. x2 - 4x x2 + 5x - 36

Write each rational expression in lowest terms. x3 - 8 x - 2

Perform the indicated operation. If possible, simplify your answer. 2x3 + 16 6x2 + 12x # 5 x2 - 2x + 4

Perform the indicated operation. If possible, simplify your answer. 5 4x3 + 7 4x3

Perform the indicated operation. If possible, simplify your answer. 3x2 - 12 x2 + 2x - 8 , 6x + 18 x + 4

Perform the indicated operation. If possible, simplify your answer. x - 12 2x - 9 , 3 - x 4x2 - 81 # x + 3 5x + 15

Perform the indicated operation. If possible, simplify your answer. 3 + 2x 10 - x + 13 + x x - 10

Perform the indicated operation. If possible, simplify your answer. 2x2 + 7 2x4 - 18x2 - 6x + 7 2x4 - 18x2

Perform the indicated operation. If possible, simplify your answer. 3 x2 - x - 6 + 2 x2 - 5x + 6

Perform the indicated operation. If possible, simplify your answer. 5 x - 7 - 2x 3x - 21 + x 2x - 14

Perform the indicated operation. If possible, simplify your answer. 3x 5 # a 5 x - 5 2x b

Simplify each complex fraction. 5 x - 7 3x 9 8x - 1 x

Simplify each complex fraction. x2 - 5x + 6 x + 3 x2 - 4x + 4 x2 - 9

Divide. 14x2 y + 9x + 3xz2 , 3xz

Divide. 14x3 - 5x2 , 12x + 12

Use synthetic division to divide 14x4 - 3x3 - x - 12 by 1x + 32 .

If P1x2 = 4x4 + 7x2 - 2x - 5, use the remainder theorem to find P1 -22 .

Solve each equation for x. 5x + 3 3x - 7 = 19 7

Solve each equation for x. x x - 4 = 3 - 4 x - 4

Solve each equation for x. 3 x + 2 - 1 5x = 2 5x2 + 10x

Solve each equation for x. x2 + 8 x - 1 = 21x + 42 x

Solve for x: x + b a = 4x - 7a b

The product of one more than a number and twice the reciprocal of the number is 12 5 . Find the number.

If Jan can weed the garden in 2 hours and her husband can weed it in 1 hour and 30 minutes, find how long it takes them to weed the garden together.

Suppose that W is inversely proportional to V. If W = 20 when V = 12, find W when V = 15.

Suppose that Q is jointly proportional to R and the square of S. If Q = 24 when R = 3 and S = 4, find Q when R = 2 and S = 3.

When an anvil is dropped into a gorge, the speed with which it strikes the ground is directly proportional to the square root of the distance it falls. An anvil that falls 400 feet hits the ground at a speed of 160 feet per second. Find the height of a cliff over the gorge if a dropped anvil hits the ground at a speed of 128 feet per second.

Translate each phrase to an algebraic expression. Use the variable x to represent each unknown number. a. Eight times a number b. Three more than eight times a number c. The quotient of a number and -7 d. One and six-tenths subtracted from twice a number e. Six less than a number f. Twice the sum of four and a number

Translate each phrase to an algebraic expression. Use the variable x to represent each unknown number. a. One third subtracted from a number b. Six less than five times a number c. Three more than eight times a number d. The quotient of seven and the difference of two and a number

Solve for y: y 3 - y 4 = 1 6

Solve x 7 + x 5 = 12 5 .

In the United States, the annual consumption of cigarettes is declining. The consumption c in billions of cigarettes per year since the year 2000 can be approximated by the formula c = -9.4t + 431 where t is the number of years after 2000. Use this formula to predict the years that the consumption of cigarettes will be less than 200 billion per year.

Olivia has scores of 78, 65, 82, and 79 on her algebra tests. Use an inequality to find the minimum score she can make on her final exam to pass the course with a 78 average or higher, given that the final exam counts as two tests.

Solve: ` 3x + 1 2 ` = -2

Solve: ` 2x - 1 3 ` + 6 = 3

Solve for x: ` 21x + 12 3 ` 0

Solve for x: ` 31x - 12 4 ` 2

Graph the equation y = -2x + 3.

Graph the equation y = -x + 3.

Determine whether the following relations are also functions. a. 51 -2, 52, 12, 72, 1 -3, 52, 19, 926 b. c. Input Correspondence Output People in a certain city Each persons age The set of nonegative integers

If f 1x2 = -x2 + 3x - 2, find a. f(0) b. f 1 -32 c. f a 1 3 b

Find the intercepts and graph: 3x + 4y = -12.

Find the intercepts and graph: 3x - y = 6.

Find an equation of the line with slope -3 containing the point 11, -52 . Write the equation in slopeintercept form y = mx + b.

Find an equation of the line with slope 1 2 containing the point 1 -1, 32 . Use function notation to write the equation.

Graph the intersection of x 1 and y 2x - 1.

Graph the union of 2x + y 4 or y 7 2.

Use the elimination method to solve the system. e 3x - 2y = 10 4x - 3y = 15

Use the substitution method to solve the system. e -2x + 3y = 6 3x - y = 5

Solve the system. 2x - 4y + 8z = 2 -x - 3y + z = 11 x - 2y + 4z = 0

Solve the system. 2x - 2y + 4z = 6 -4x - y + z = -8 3x - y + z = 6

The measure of the largest angle of a triangle is 80 more than the measure of the smallest angle, and the measure of the remaining angle is 10 more than the measure of the smallest angle. Find the measure of each angle.

Kernersville office supply sold three reams of paper and two boxes of manila folders for $21.90. Also, five reams of paper and one box of manila folders cost $24.25. Find the price of a ream of paper and a box of manila folders.

Use matrices to solve the system. x + 2y + z = 2 -2x - y + 2z = 5 x + 3y - 2z = -8

Use matrices to solve the system. x + y + z = 9 2x - 2y + 3z = 2 -3x + y - z = 1

Evaluate the following. a. 70 b. -70 c. 12x + 520 d. 2x0

Simplify the following. Write answers with positive exponents. a. 2-2 + 3-1 b. -6a0 c. x-5 x-2

Simplify each expression. Assume that a and b are integers and that x and y are not 0. a. x-b 12xb22 b. 1y3a 22 ya-6

Simplify each expression. Assume that a and b are integers and that x and y are not 0. a. 3x4a 14x-a 22 b. 1y4b23 y2b-3

Find the degree of each term. a. 3x2 b. -23 x5 c. y d. 12x2 yz3 e. 5.27

Subtract 12x - 72 from 2x2 + 8x - 3

Multiply 33 + 12a + b242 .

Multiply 34 + 13x - y242 .

Factor ab - 6a + 2b - 12.

Factor xy + 2x - 5y - 10.

Factor 2n2 - 38n + 80.

Factor 6x2 - x - 35

Factor x2 + 4x + 4 - y2 .

Factor 4x2 - 4x + 1 - 9y2 .

Solve 1x + 221x - 62 = 0.

Solve 2x13x + 121x - 32 = 0.

Simplify each rational expression. a. 2x2 10x3 - 2x2 b. 9x2 + 13x + 4 8x2 + x - 7

For the graph of f(x), answer the following: a. Find the domain and range. b. List the x- and y-intercepts. c. Find the coordinates of the point with the greatest y-value. d. Find the coordinates of the point with the least y-value. e. List the x-values whose y-values are equal to 0. f. List the x-values whose y-values are less than 0. g. Find the solutions of f 1x2 = 0.

Subtract 5k k2 - 4 - 2 k2 + k - 2

Subtract 5a a2 - 4 - 3 2 - a

Solve 3 x - x + 21 3x = 5 3

Solve 3 x - x + 21 3x = 5 3