Solved: Determine whether the following statements are

Solve for the indicated variable. 5x  35

Solve for the indicated variable. 4t  32

Solve for the indicated variable. 3  n  12

Solve for the indicated variable. 4  5  y

Solve for the indicated variable. 24  3x

Solve for the indicated variable. 50  5t

Solve for the indicated variable.

Solve for the indicated variable.

Solve for the indicated variable. 3x  5  7

Solve for the indicated variable. 4p  5  9

Solve for the indicated variable. 9m  7  11

Solve for the indicated variable. 2x  4  5

Solve for the indicated variable. 5t  11  18

Solve for the indicated variable. 7x  4  21  24x

Solve for the indicated variable. 3x  5  25  6x

Solve for the indicated variable. 5x  10  25  2x

Solve for the indicated variable. 20n  30  20  5n

Solve for the indicated variable. 14c  15  43  7c

Solve for the indicated variable. 4(x  3)  2(x  6)

Solve for the indicated variable. 5(2y  1)  2(4y  3)

Solve for the indicated variable. 3(4t  5)  5(6  2t)

Solve for the indicated variable. 2(3n  4)  (n  2)

Solve for the indicated variable. 2(x  1)  3  x  3(x  1)

Solve for the indicated variable. 4(y  6)  8  2y  4(y  2)

Solve for the indicated variable. 5p  6(p  7)  3(p  2)

Solve for the indicated variable. 3(z  5)  5  4z  7(z  2)

Solve for the indicated variable. .

Solve for the indicated variable.

Solve for the indicated variable.

Solve for the indicated variable.

Solve for the indicated variable. 2a  9(a  6)  6(a  3)  4a

Solve for the indicated variable. 25  [2  5y  3(y  2)] 3(2y  5)  [5(y  1)  3y  3]

Solve for the indicated variable. 32  [4  6x  5(x  4)]  4(3x  4)  [6(3x  4)  7  4x]

Solve for the indicated variable. 12  [3  4m  6(3m  2)] 7(2m  8) 3[(m  2)  3m  5]

Solve for the indicated variable. 20  4[c  3  6(2c  3)]  5(3c  2)  [2(7c  8)  4c  7]

Solve for the indicated variable. 46  [7  8y  9(6y  2)] 7(4y  7)  2[6(2y  3)  4  6y]

Involve fractions. Clear the fractions by rst multiplying by the least common denominator, and then solve the resulting linear equation.

Involve fractions. Clear the fractions by rst multiplying by the least common denominator, and then solve the resulting linear equation.

Involve fractions. Clear the fractions by rst multiplying by the least common denominator, and then solve the resulting linear equation.

Involve fractions. Clear the fractions by rst multiplying by the least common denominator, and then solve the resulting linear equation.

Involve fractions. Clear the fractions by rst multiplying by the least common denominator, and then solve the resulting linear equation.

Involve fractions. Clear the fractions by rst multiplying by the least common denominator, and then solve the resulting linear equation.

Involve fractions. Clear the fractions by rst multiplying by the least common denominator, and then solve the resulting linear equation.

Involve fractions. Clear the fractions by rst multiplying by the least common denominator, and then solve the resulting linear equation.

Involve fractions. Clear the fractions by rst multiplying by the least common denominator, and then solve the resulting linear equation.

Involve fractions. Clear the fractions by rst multiplying by the least common denominator, and then solve the resulting linear equation.

Involve fractions. Clear the fractions by rst multiplying by the least common denominator, and then solve the resulting linear equation.

Involve fractions. Clear the fractions by rst multiplying by the least common denominator, and then solve the resulting linear equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Specify any values that must be excluded from the solution set and then solve the equation.

Temperature. To calculate temperature in degrees Fahrenheit we use the formula , where F is degrees Fahrenheit and C is degrees Celsius. Find the formula to convert from Fahrenheit to Celsius.

Geometry. The perimeter P of a rectangle is related to the length L and width W of the rectangle through the equation P  2L  2W. Determine the width in terms of the perimeter and length.

Costs: Cellular Phone.Your cell phone plan charges $15 a month plus 12 cents per minute. If your monthly bill is $25.08, how many minutes did you use?

Costs: Rental Car. Becky rented a car on her Ft. Lauderdale vacation. The car was $25 a day plus 10 cents per mile. She kept the car for 5 days and her bill was $185. How many miles did she drive the car?

Costs: Internet. When traveling in London, Charlotte decided to check her e-mail at an Internet caf. There was a at charge of $2 plus a charge of 10 cents a minute. How many minutes was she logged on if her bill was $3.70?

Sales: Income. For a summer job, Dwayne decides to sell magazine subscriptions. He will be paid $20 a day plus $1 for each subscription he sells. If he works for 25 days and makes $645, how many subscriptions did he sell?

Business. The operating costs for a local business are a xed amount of $15,000 and $2500 per day. a. Find C that represents operating costs for the company which depends on the number of days open, x. b. If the business accrues $5,515,000 in annual operating costs, how many days did the business operate during the year?

Business. Negotiated contracts for a technical support provider produce monthly revenue of $5000 and $0.75 per minute per phone call. a. Find R that represents the revenue for the technical support provider which depends on the number of minutes of phone calls x. b. In one month the provider received $98,750 in revenue. How many minutes of technical support were provided?

Medications are often packaged in liquid form (known as a suspension) so that a precise dose of a drug is delivered within a volume of inert liquid; for example, 250 milligrams amoxicillin in 5 milliliters of a liquid suspension. If a patient is prescribed a dose of a drug, medical personnel must compute the volume of the liquid with a known concentration to administer. The formula denes the relationship between the dose of the drug prescribed d, the concentration of the liquid suspension c, and the amount of the liquid administered a. Medicine. Aphysician has ordered a 600-milligram dose of amoxicillin. The pharmacy has a suspension of amoxicillin with a concentration of 125 milligrams per 5 milliliters. How much liquid suspension must be administered to the patient?

Medicine. Aphysician has ordered a 600-milligram dose of amoxicillin. The pharmacy has a suspension of amoxicillin with a concentration of 125 milligrams per 5 milliliters. How much liquid suspension must be administered to the patient? Medicine.Aphysician has ordered a 600-milligram dose of carbamazepine. The pharmacy has a suspension of carbamazepine with a concentration of 100 milligrams per 5 milliliters. How much liquid suspension must be administered to the patient?

Speed of Light. The frequency f of an optical signal in hertz (Hz) is related to the wavelength  in meters (m) of a laser through the equation where c is the speed of light in a vacuum and is typically taken to be c  3.0  108 meters per second (m/s). What values must be eliminated from the wavelengths?

Optics. For an object placed near a lens, an image forms on the other side of the lens at a distinct position determined by the distance from the lens to the object. The position of the image is found using the thin lens equation: where do is the distance from the object to the lens, di is the distance from the lens to the image, and f is the focal length of the lens. Solve for the object distance do in terms of the focal length and image distance.

Explain the mistake that is made. Solve the equation 4x  3  6x  7. Solution: Subtract 4x and add 7 to the equation. 3  6x Divide by 3. x  2 This is incorrect. What mistake was made?

Explain the mistake that is made. Solve the equation 3(x  1)  2  x  3(x  1). Solution: 3x  3  2  x  3x  3 3x  5  2x  3 5x 8 This is incorrect. What mistake was made? x =8 5

Explain the mistake that is made.Solve the equation . Solution: (p  3)2  4(5p) Cross multiply. 2p  6  20p 6  18p This is incorrect. What mistake was made?

Explain the mistake that is made. Solve the equation . Solution: Multiply by the LCD, x(x  1). Simplify. (x  1)  x  1 x  1  x  1 2x  2 x  1 This is incorrect. What mistake was made?

Determine whether each of the statements is true or false. The solution to the equation is the set of all real numbers.

Determine whether each of the statements is true or false. The solution to the equation is the set of all real numbers.

Determine whether each of the statements is true or false. x 1 is a solution to the equation . x2 - 1 x - 1 = x +

Determine whether each of the statements is true or false. x  1 is a solution to the equation

Solve for x, given that a, b, and c are real numbers and : ax  b  c

Solve for x, given that a, b, and c are real numbers and : a x b x = c

Solve the equation for . Are there any restrictions given that

Solve the equation for . Does y have any restrictions?

Solve for x:.

Solve for t:.

Solve the equation for x in terms of y:

Find the number a for which y  2 is a solution of the equation y  a  y  5  3ay.

Graph the function represented by each side of the equation in the same viewing rectangle and solve for x.

Graph the function represented by each side of the equation in the same viewing rectangle and solve for x. 5(x  1)  7  10  9x

Graph the function represented by each side of the equation in the same viewing rectangle and solve for x. 2x  6  4x  2x  8  2

Graph the function represented by each side of the equation in the same viewing rectangle and solve for x. 10  20x  10x  30x  20  10

Graph the function represented by each side of the equation in the same viewing rectangle and solve for x. x(x - 1) x2 = 1

Graph the function represented by each side of the equation in the same viewing rectangle and solve for x. 2x(x + 3) x2 = 2

Graph the function represented by each side of the equation in the same viewing rectangle and solve for x. 0.035x  0.029(8706  x)  285.03

Graph the function represented by each side of the equation in the same viewing rectangle and solve for x. 0.75x 0.45 x = 1 9

Discount Price. Donna redeems a 10% off coupon at her local nursery. After buying azaleas, bougainvillea, and bags of potting soil, her checkout price before tax is $217.95. How much would she have paid without the coupon?

Discount Price. The original price of a pair of binoculars is $74. The sale price is $51.80. How much was the markdown?

Cost: FairShare. Jeff, Tom, and Chelsea order a large pizza. They decide to split the cost according to how much they will eat. Tom pays $5.16, Chelsea eats of the pizza, and Jeff eats of the pizza. How much did the pizza cost?

Event Planning. Acouple decide to analyze their monthly spending habits. The monthly bills are 50% of their take-home pay, and they invest 20% of their take-home pay. They spend $560 on groceries, and 23% goes to miscellaneous. How much is their take-home pay per month?

Discounts. Abuilder of tract homes reduced the price of a model by 15%. If the new price is $125,000, what was its original price? How much can be saved by purchasing the model?

Markups. Acollege bookstore marks up the price it pays the publisher for a book by 25%. If the selling price of a book is $79, how much did the bookstore pay for the book?

Puzzle. Angela is on her way from home in Jersey City into New York City for dinner. She walks 1 mile to the train station, takes the train of the way, and takes a taxi of the way to the restaurant. How far does Angela live from the restaurant?

Puzzle. An employee at Kennedy Space Center (KSC) lives in Daytona Beach and works in the vehicle assembly building (VAB). She carpools to work with a colleague. She drives 7 miles from her house to the park-and-ride. Then she rides with her colleague from the park-and-ride in Daytona Beach to the KSC headquarters building, and then takes the KSC shuttle from the headquarters building to the VAB. The drive from the park-and-ride to the headquarters building is of her total trip, and the shuttle ride is of her total trip. How many miles does she travel from her house to the VAB on days when her colleague drives?

Puzzle.Atypical college student spends of her waking time in class, of her waking time eating, of her waking time working out, 3 hours studying, and 2 hours doing other things. How many hours of sleep does the typical college student get?

Diet. Aparticular 1550-calories-per-day diet suggests eating breakfast, lunch, dinner, and two snacks. Dinner is twice the calories of breakfast. Lunch is 100 calories more than breakfast. The two snacks are 100 and 150 calories. How many calories are each meal?

Budget. Acompany has a total of $20,000 allocated for monthly costs. Fixed costs are $15,000 per month and variable costs are $18.50 per unit. How many units can be manufactured in a month?

Budget. Awoman decides to start a small business making monogrammed cocktail napkins. She can set aside $1870 for monthly costs. Fixed costs are $1329.50 per month and variable costs are $3.70 per set of napkins. How many sets of napkins can she afford to make per month?

Numbers. Find a number such that 10 less than the number is the number.

Numbers. Find a positive number such that 10 times the number is 16 more than twice the number.

Numbers. Find two consecutive even integers such that 4 times the smaller number is 2 more than 3 times the larger number.

Numbers. Find three consecutive integers such that the sum of the three is equal to 2 times the sum of the rst two integers.

Geometry. Find the perimeter of a triangle if one side is 11 inches, another side is the perimeter, and the third side is the perimeter.

Geometry. Find the dimensions of a rectangle whose length is a foot longer than twice its width and whose perimeter is 20 feet.

Geometry. An NFLplaying eld is a rectangle. The length of the eld (excluding the end zones) is 40 more yards than twice the width. The perimeter of the playing eld is 260 yards. What are the dimensions of the eld in yards?

Geometry. The length of a rectangle is 2 more than 3 times the width, and the perimeter is 28 inches. What are the dimensions of the rectangle?

Geometry. Consider two circles, a smaller one and a larger one. If the larger one has a radius that is 3 feet larger than that of the smaller circle and the ratio of the circumferences is 2:1, what are the radii of the two circles?

Geometry. The perimeter of a semicircle is doubled when the radius is increased by 1. Find the radius of the semicircle.

Home Improvement. Aman wants to remove a tall pine tree from his yard. Before he goes to Home Depot, he needs to know how tall an extension ladder he needs to purchase. He measures the shadow of the tree to be 225 feet long. At the same time he measures the shadow of a 4-foot stick to be 3 feet. Approximately how tall is the pine tree?

Home Improvement. The same man in Exercise 23 realizes he also wants to remove a dead oak tree. Later in the day he measuresthe shadow of the oak tree to be 880 feet long, and the 4-foot stick now has a shadow of 10 feet. Approximately how tall is the oak tree?

Biology: Alligators. It is common to see alligators in ponds, lakes, and rivers in Florida. The ratio of head size (back of the head to the end of the snout) to the full body length of an alligator is typically constant. If a -foot alligator has a head length of 6 inches, how long would you expect an alligator to be whose head length is 9 inches?

Biology: Snakes. In the African rainforest there is a snake called a Gaboon viper. The fang size of this snake is proportional to the length of the snake. A3-foot snake typically has 2-inch fangs. If a herpetologist nds Gaboon viper fangs that are 2.6-inches long, how long a snake would she expect to nd?

Investing. Ashley has $120,000 to invest and decides to put some in a CD that earns 4% interest per year and the rest in a low-risk stock that earns 7%. How much did she invest in each to earn $7800 interest in the rst year?

Investing. You inherit $13,000 and you decide to invest the money in two different investments: one paying 10% and the other paying 14%. Ayear later your investments are worth $14,580. How much did you originally invest in each account?

Investing. Wendy was awarded a volleyball scholarship to the University of Michigan, so on graduation her parents gave her the $14,000 they had saved for her college tuition. She opted to invest some money in a privately held company that pays 10% per year and evenly split the remaining money between a money market account yielding 2% and a high-risk stock that yielded 40%. At the end of the rst year she had $16,610 total. How much did she invest in each of the three?

Interest. Ahigh school student was able to save $5000 by working a part-time job every summer. He invested half the money in a money market account and half the money in a stock that paid three times as much interest as the money market account. After a year he earned $150 in interest. What were the interest rates of the money market account and the stock?

Budget: Home Improvement. When landscaping their yard, a couple budgeted $4200. The irrigation system costs $2400 and the sod costs $1500. The rest they will spend on trees and shrubs. Trees each cost $32 and shrubs each cost $4. They plant a total of 33 trees and shrubs. How many of each did they plant in their yard?

Budget: Shopping. At the deli Jennifer bought spicy turkey and provolone cheese. The turkey costs $6.32 per pound and the cheese costs $4.27 per pound. In total, she bought 3.2 pounds and the price was $17.56. How many pounds of each did she buy?

Chemistry. For a certain experiment, a student requires 100 milliliters of a solution that is 8% HCl (hydrochloric acid). The storeroom has only solutions that are 5% HCl and 15% HCl. How many milliliters of each available solution should be mixed to get 100 milliliters of 8% HCl?

Chemistry. How many gallons of pure alcohol must be mixed with 5 gallons of a solution that is 20% alcohol to make a solution that is 50% alcohol?

Automobiles.Amechanic has tested the amount of antifreeze in your radiator. He says it is only 40% antifreeze and the remainder is water. How many gallons must be drained from your 5 gallon radiator and replaced with pure antifreeze to make the mixture in your radiator 80% antifreeze?

Costs: Overhead. Aprofessor is awarded two research grants, each having different overhead rates. The research project conducted on campus has a rate of 42.5% overhead, and the project conducted in the eld, off campus, has a rate of 26% overhead. If she was awarded $1,170,000 total for the two projects with an average overhead rate of 39%, how much was the research project on campus and how much was the research project off campus?

Theater. On the way to the movies a family picks up a custom-made bag of candies. The parents like caramels ($1.50/lb) and the children like gummy bears ($2.00/lb). They bought a 1.25-pound bag of combined candies that cost $2.50. How much of each candy did they buy?

Coffee. Joy is an instructional assistant in one of the college labs. She is on a very tight budget. She loves Jamaican Blue Mountain coffee, but it costs $12 a pound. She decides to blend this with regular coffee beans that cost $4.20 a pound. If she spends $14.25 on 2 pounds of coffee, how many pounds of each did she purchase?

Communications. The speed of light is approximately 3.0  108 meters per second (670,616,629 mph). The distance from Earth to Mars varies because of the orbits of the planets around the Sun. On average, Mars is 100 million miles from Earth. If we use laser communication systems, what will be the delay between Houston and NASA astronauts on Mars?

Speed of Sound. The speed of sound is approximately 760 miles per hour in air. If a gun is red mile away, how long will it take the sound to reach you?

Business. During the month of February 2011, the average price of gasoline rose 4.7% in the United States. If the average price of gasoline at the end of February 2011 was $3.21 per gallon, what was the price of gasoline at the beginning of February?

Business. During the Christmas shopping season of 2010, the average price of a at screen television fell by 40%. A shopper purchased a 42-inch at screen television for $299 in late November 2010. How much would the shopper have paid, to the nearest dollar, for the same television if it was purchased in September 2010?

Medicine.Apatient requires an IV of 0.9% saline solution, also known as normal saline solution. How much distilled water, to the nearest milliliter, must be added to 100 milliliters of a 3% saline solution to produce normal saline?

Medicine.Apatient requires an IVof D5W, a 5% solution of Dextrose (sugar) in water. To the nearest milliliter, how much D20W, a 20% solution of Dextrose in water, must be added to 100 milliliters of distilled water to produce a D5Wsolution?

Boating. Amotorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a marina in 20 minutes. The return trip takes 15 minutes. What is the speed of the current?

Aviation. ACessna 175 can average 130 miles per hour. If a trip takes 2 hours one way and the return takes 1 hour and 15 minutes, nd the wind speed, assuming it is constant.

Exercise. Ajogger and a walker cover the same distance. The jogger nishes in 40 minutes. The walker takes an hour. How fast is each exerciser moving if the jogger runs 2 miles per hour faster than the walker?

Travel. Ahigh school student in Seattle, Washington, attended the University of Central Florida. On the way to UCF he took a southern route. After graduation he returned to Seattle via a northern trip. On both trips he had the same average speed. If the southern trek took 45 hours and the northern trek took 50 hours, and the northern trek was 300 miles longer, how long was each trip?

DistanceRateTime. College roommates leave for their rst class in the same building. One walks at 2 miles per hour and the other rides his bike at a slow 6 miles per hour pace. How long will it take each to get to class if the walker takes 12 minutes longer to get to class and they travel on the same path?

DistanceRateTime.Along-distance delivery service sends out a truck with a package at 7 A.M. At 7:30 A.M., the manager realizes there was another package going to the same location. He sends out a car to catch the truck. If the truck travels at an average speed of 50 miles per hour and the car travels at 70 miles per hour, how long will it take the car to catch the truck?

Work. Christopher can paint the interior of his house in 15 hours. If he hires Cynthia to help him, they can do the same job together in 9 hours. If he lets Cynthia work alone, how long will it take her to paint the interior of his house?

Work. Jay and Morgan work in the summer for a landscaper. It takes Jay 3 hours to complete the companys largest yard alone. If Morgan helps him, it takes only 1 hour. How much time would it take Morgan alone?

Work. Tracey and Robin deliver Coke products to local convenience stores. Tracey can complete the deliveries in 4 hours alone. Robin can do it in 6 hours alone. If they decide to work together on a Saturday, how long will it take?

Work. Joshua can deliver his newspapers in 30 minutes. Ittakes Amber 20 minutes to do the same route. How long would it take them to deliver the newspapers if they worked together?

Music. Amajor chord in music is composed of notes whose frequencies are in the ratio 4:5:6. If the rst note of a chord has a frequency of 264 hertz (middle C on the piano), nd the frequencies of the other two notes. Hint: Set up two proportions using 4:5 and 4:6.

Music. Aminor chord in music is composed of notes whose frequencies are in the ratio 10:12:15. If the rst note of a minor chord is A, with a frequency of 220 hertz, what are the frequencies of the other two notes?

Grades. Danielles test scores are 86, 80, 84, and 90. The nal exam will count as of the nal grade. What score does Danielle need on the nal in order to earn a B, which requires an average score of 80? What score does she need to earn an A, which requires an average of 90?

Grades. Sams nal exam will count as two tests. His test scores are 80, 83, 71, 61, and 95. What score does Sam need on the nal in order to have an average score of 80?

Sports. In Super Bowl XXXVII, the Tampa Bay Buccaneers scored a total of 48 points. All of their points came from eld goals and touchdowns. Field goals are worth 3 points and each touchdown was worth 7 points (Martin Gramatica was successful in every extra point attempt). They scored a total of 8 times. How many eld goals and touchdowns were scored?

Sports. Atight end can run the 100-yard dash in 12 seconds. Adefensive 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. If no other players are nearby, at what yard line will the defensive back catch up to the tight end?

Recreation. How do two children of different weights balance on a seesaw? The heavier child sits closer to the center and the lighter child sits farther away. When the product of the weight of the child and the distance from the center is equal on both sides, the seesaw should be horizontal to the ground. Suppose Max weighs 42 pounds and Maria weighs 60 pounds. If Max sits 5 feet from the center, how far should Maria sit from the center in order to balance the seesaw horizontal to the ground?

Recreation. Refer to Exercise 61. Suppose Martin, who weighs 33 pounds, sits on the side of the seesaw with Max. If their average distance to the center is 4 feet, how far should Maria sit from the center in order to balance the seesaw horizontal to the ground?

Recreation. If a seesaw has an adjustable bench, then the board can slide along the fulcrum. Maria and Max in Exercise 61 decide to sit on the very edge of the board on each side. Where should the fulcrum be placed along the board in order to balance the seesaw horizontally to the ground? Give the answer in terms of the distance from each childs end.

Recreation. Add Martin (Exercise 62) to Maxs side of the seesaw and recalculate Exercise 63.

Refer to this lens law. (See Exercise 82 in Section 1.1.) The position of the image is found using the thin lens equation: ,where do is the distance from the object to the lens, di is the distance from the lens to the image, and f is the focal length of the lens.Optics. If the focal length of a lens is 3 centimeters and the image distance is 5 centimeters from the lens, what is the distance from the object to the lens?

Refer to this lens law. (See Exercise 82 in Section 1.1.) The position of the image is found using the thin lens equation: ,where do is the distance from the object to the lens, di is the distance from the lens to the image, and f is the focal length of the lens.Optics. If the focal length of the lens is 8 centimeters and the image distance is 2 centimeters from the lens, what is the distance from the object to the lens?

Refer to this lens law. (See Exercise 82 in Section 1.1.) The position of the image is found using the thin lens equation: ,where do is the distance from the object to the lens, di is the distance from the lens to the image, and f is the focal length of the lens.Optics. The focal length of a lens is 2 centimeters. If the image distance from the lens is half the distance from the object to the lens, nd the object distance.

Refer to this lens law. (See Exercise 82 in Section 1.1.) The position of the image is found using the thin lens equation: ,where do is the distance from the object to the lens, di is the distance from the lens to the image, and f is the focal length of the lens.Optics. The focal length of a lens is 8 centimeters. If the image distance from the lens is half the distance from the object to the lens, nd the object distance.

Solve each formula for the specied variable. P  2l  2w for w

Solve each formula for the specied variable. P  2l  2w for l

Solve each formula for the specied variable. for h

Solve each formula for the specied variable. C  2pr for r

Solve each formula for the specied variable. A  lw for w

Solve each formula for the specied variable. d  rt for t

Solve each formula for the specied variable. V  lwh for h

Solve each formula for the specied variable. V  pr2h for h

Tricia and Janine are roommates and leave Houston on Interstate 10 at the same time to visit their families for a long weekend. Tricia travels west and Janine travels east. If Tricias average speed is 12 miles per hour faster than Janines, nd the speed of each if they are 320 miles apart in 2 hours and 30 minutes.

Rick and Mike are roommates and leave Gainesville on Interstate 75 at the same time to visit their girlfriends for a long weekend. Rick travels north and Mike travels south. If Mikes average speed is 8 miles per hour faster than Ricks, nd the speed of each if they are 210 miles apart in 1 hour and 30 minutes.

Suppose you bought a house for $132,500 and sold it 3 years later for $168,190. Plot these points using a graphing utility. Assuming a linear relationship, how much could you have sold the house for had you waited 2 additional years?

Suppose you bought a house for $132,500 and sold it 3 years later for $168,190. Plot these points using a graphing utility. Assuming a linear relationship, how much could you have sold the house for had you sold it 1 year after buying it?

Agolf club membership has two options. Option Ais a $300 monthly fee plus $15 cart fee every time you play. Option B has a $150 monthly fee and a $42 fee every time you play. Write a mathematical model for monthly costs for each plan and graph both in the same viewing rectangle using a graphing utility. Explain when Option Ais the better deal and when Option B is the better deal.

Aphone provider offers two calling plans. Plan Ahas a $30 monthly charge and a $0.10 per minute charge on every call. Plan B has a $50 monthly charge and a $0.03 per minute charge on every call. Explain when Plan Ais the better deal and when Plan B is the better deal.

Solve by factoring. x2  5x  6  0

Solve by factoring. v2  7v  6  0

Solve by factoring. p2  8p  15  0

Solve by factoring. u2  2u  24  0

Solve by factoring. x2  12  x

Solve by factoring. 11x  2x2  12

Solve by factoring. 16x2  8x  1

Solve by factoring.3x2  10x  8  0

Solve by factoring. 9y2  1  6y

Solve by factoring. 4x  4x2  1

Solve by factoring. 8y2  16y

Solve by factoring. 3A2 12A

Solve by factoring. 9p2  12p  4

Solve by factoring. 4u2  20u  25

Solve by factoring. x2  9  0

Solve by factoring. 16v2  25  0

Solve by factoring. x(x  4)  12

Solve by factoring. 3t2  48  0

Solve by factoring. 2p2  50  0

Solve by factoring. 5y2  45  0

Solve by factoring. 3x2  12

Solve by factoring. 7v2  28

Solve using the square root method. p2  8  0

Solve using the square root method. y2  72  0

Solve using the square root method. x2  9  0

Solve using the square root method. v2  16  0

Solve using the square root method. (x  3)2  36

Solve using the square root method. (x  1)2  25

Solve using the square root method. (2x  3)2 4

Solve using the square root method. (4x  1)2 16

Solve using the square root method. (5x  2)2  27

Solve using the square root method. (3x  8)2  12

Solve using the square root method. (1  x)2  9

Solve using the square root method. (1  x)2  9

What number should be added to complete the square of each expression? x2  6x

What number should be added to complete the square of each expression? x2  8x

What number should be added to complete the square of each expression? x2  12x

What number should be added to complete the square of each expression? x2  20x

What number should be added to complete the square of each expression? x2 - 1 2x

What number should be added to complete the square of each expression?

What number should be added to complete the square of each expression?

What number should be added to complete the square of each expression?

What number should be added to complete the square of each expression? x2  2.4x

What number should be added to complete the square of each expression? x2  1.6x

Solve by completing the square. x2  2x  3

Solve by completing the square. y2  8y  2  0

Solve by completing the square. t2  6t  5

Solve by completing the square. x2  10x 21

Solve by completing the square. y2  4y  3  0

Solve by completing the square. x2  7x  12  0

Solve by completing the square. 2p2  8p 3

Solve by completing the square. 2x2  4x  3  0

Solve by completing the square. 2x2  7x  3  0

Solve by completing the square. 3x2  5x  10  0

Solve by completing the square. x2 2 - 2x = 1 4

Solve by completing the square. t2 3 + 2t 3 + 5 6 = 0

Solve using the Quadratic Formula. t2  3t  1  0

Solve using the Quadratic Formula. t2  2t  1

Solve using the Quadratic Formula. s2  s  1  0

Solve using the Quadratic Formula. 2s2  5s 

Solve using the Quadratic Formula. 3x2  3x  4  0

Solve using the Quadratic Formula. 4x2  2x  7

Solve using the Quadratic Formula. x2  2x  17  0

Solve using the Quadratic Formula. 4m2  7m  8  0

Solve using the Quadratic Formula. 5x2  7x  3

Solve using the Quadratic Formula. 3x2  5x 11

Solve using the Quadratic Formula. .

Solve using the Quadratic Formula. 1 4x2 - 2 3x - 1 3 = 01

Determine whether the discriminant is positive, negative, or zero, and indicate the number and type of root to expect. Do not solve.x2  22x  121  0

Determine whether the discriminant is positive, negative, or zero, and indicate the number and type of root to expect. Do not solve. x2  28x  196  0

Determine whether the discriminant is positive, negative, or zero, and indicate the number and type of root to expect. Do not solve.2y2  30y  68  0

Determine whether the discriminant is positive, negative, or zero, and indicate the number and type of root to expect. Do not solve.3y2  27y  66  0

Determine whether the discriminant is positive, negative, or zero, and indicate the number and type of root to expect. Do not solve. 9x2  7x  8  0

Determine whether the discriminant is positive, negative, or zero, and indicate the number and type of root to expect. Do not solve.3x2  5x  7  0

Solve using any method. v2  8v  20

Solve using any method. v2  8v 20

Solve using any method. t2  5t  6  0

Solve using any method. t2  5t  6  0

Solve using any method. (x  3)2  16

Solve using any method. (x  3)2 16

Solve using any method. (p  2)2  4p

Solve using any method. (u  5)2  16u

Solve using any method. 8w2  2w  21  0

Solve using any method. 8w2  2w  21  0

Solve using any method. 3p2  9p  1  0

Solve using any method. 3p2  9p  1  0

Solve using any method. 2 3 t2 + 4 3 t = 1 5

Solve using any method. 1 2 x2 + 2 3 x =

Solve using any method.

Solve using any method.

Solve using any method. 5 y + 4 = 4 + 3 y - 2 4(x - 2) x - 3 + 3 x = -3 x(x - 3)

Solve using any method. 5 y + 4 = 4 + 3 y - 2

Solve using any method. x2  0.1x  0.12

Solve using any method. y2  0.5y 0.06

Stock Value. From June 2003 until April 2004 JetBlue airlines stock (JBLU) was approximately worth P  4t2  80t  360, where P denotes the price of the stock in dollars and t corresponds to months, with t  1 corresponding to January 2003. During what months was the stock equal to $24?

Stock Value. From November 2003 until March 2004, Wal-Mart stock (WMT) was approximately worth P  2t2  12t  70, where P denotes the price of the stock in dollars and t corresponds to months, with t  1 corresponding to November 2003. During what months was the stock equal to $60?Research indicates that monthly prot for Widgets R Us is modeled by the function where P is prot measured in millions of dollars and q is the quantity of widgets produced measured in thousands.

Business. Find the break-even point for a month to the nearest unit.

Business. Find the production level that produces a monthly prot of $40 million.

In response to economic conditions, a local business explores the effect of a price increase on weekly prot. The function models the effect that a price increase of x dollars on a bottle of wine will have on the prot P measured in dollars. Business/Economics. What is the smallest price increase that will produce a weekly prot of $460?

In response to economic conditions, a local business explores the effect of a price increase on weekly prot. The function models the effect that a price increase of x dollars on a bottle of wine will have on the prot P measured in dollars. Business/Economics. What is the smallest price increase that will produce a weekly prot of $630?

An epidemiological study of the spread of the u in a small city nds that the total number P of people who contracted the u t days into an outbreak is modeled by the function. Health/Medicine. After approximately how many days will 160 people have contracted the u?

An epidemiological study of the spread of the u in a small city nds that the total number P of people who contracted the u t days into an outbreak is modeled by the functionHealth/Medicine.After approximately how many days will 172 people have contracted the u?

Environment: Reduce Your Margins, Save a Tree. Lets dene the usable area of an 8.5-inch by 11-inch piece of paper as the rectangular space between the margins of that piece of paper. Assume the default margins in a word processor in a colleges computer lab are set up to be 1.25 inches wide (top and bottom) and 1 inch wide (left and right). Answer the following questions using this information. a. Determine the amount of usable space, in square inches, on one side of an 8.5-inch by 11-inch piece of paper with the default margins of 1.25-inch and 1-inch. b. The Green Falcons, a campus environmental club, has convinced their colleges computer lab to reduce the default margins in their word-processing software by x inches. Create and simplify the quadratic expression that represents the new usable area, in square inches, of one side of an 8.5-inch by 11-inch piece of paper if the default margins at the computer lab are each reduced by x inches. c. Subtract the usable space in part (a) from the expression in part (b). Explain what this difference represents. d. If 10 pages are printed using the new margins and as a result the computer lab saved one whole sheet of paper, then by how much did the computer lab reduce the margins? Round to the nearest tenth of an inch.

Environment: Reduce Your Margins, Save a Tree. Repeat Exercise 103 assuming the computer labs default margins are 1 inch all the way around (left, right, top, and bottom). If 15 pages are printed using the new margins and as a result the computer lab saved one whole sheet of paper, then by how much did the computer lab reduce the margins? Round to the nearest tenth of an inch.

Television.Astandard 32-inch television has a 32-inch diagonal and a 25-inch width. What is the height of the 32-inch television?

Television.A42-inch LCD television has a 42-inch diagonal and a 20-inch height. What is the width of the 42-inch LCD television?

Numbers. Find two consecutive numbers such that their sum is 35 and their product is 306.

Numbers. Find two consecutive odd integers such that their sum is 24 and their product is 143.

Geometry. The area of a rectangle is 135 square feet. The width is 6 feet less than the length. Find the dimensions of the rectangle.

Geometry. Arectangle has an area of 31.5 square meters. If the length is 2 more than twice the width, nd the dimensions of the rectangle.

Geometry. Atriangle has a height that is 2 more than 3 times the base and an area of 60 square units. Find the base and height.

Geometry. Asquares side is increased by 3 yards, which corresponds to an increase in the area by 69 square yards. How many yards is the side of the initial square?

Falling Objects. If a person drops a water balloon off the rooftop of a 100-foot building, the height of the water balloon is given by the equation h 16t2  100, where t is in seconds. When will the water balloon hit the ground?

Falling Objects. If the person in Exercise 113 throws the water balloon downward with a speed of 5 feet per second, the height of the water balloon is given by the equation h 16t2  5t  100, where t is in seconds. When will the water balloon hit the ground?

Gardening. Asquare garden has an area of 900 square feet. If a sprinkler (with a circular pattern) is placed in the center of the garden, what is the minimum radius of spray the sprinkler would need in order to water all of the garden?

Sports. Abaseball diamond is a square. The distance from base to base is 90 feet. What is the distance from home plate to second base?

Volume. Aat square piece of cardboard is used to construct an open box. Cutting a 1-foot by 1-foot square off of each corner and folding up the edges will yield an open box (assuming these edges are taped together). If the desired volume of the box is 9 cubic feet, what are the dimensions of the original square piece of cardboard?

Volume. Arectangular piece of cardboard whose length is twice its width is used to construct an open box. Cutting a 1-foot by 1-foot square off of each corner and folding up the edges will yield an open box. If the desired volume is 12 cubic feet, what are the dimensions of the original rectangular piece of cardboard?

Gardening. Alandscaper has planted a rectangular garden that measures 8 feet by 5 feet. He has ordered 1 cubic yard (27 cubic feet) of stones for a border along the outside of the garden. If the border needs to be 4 inches deep and he wants to use all of the stones, how wide should the border be?

Gardening. Agardener has planted a semicircular rose garden with a radius of 6 feet, and 2 cubic yards of mulch (1 cubic yard  27 cubic feet) are being delivered. Assuming she uses all of the mulch, how deep will the layer of mulch be?

Work. Lindsay and Kimmie, working together, can balance the nancials for the Kappa Kappa Gamma sorority in 6 days. Lindsay by herself can complete the job in 5 days less than Kimmie. How long will it take Lindsay to complete the job by herself?

Work. When Jack cleans the house, it takes him 4 hours. When Ryan cleans the house, it takes him 6 hours. How long would it take both of them if they worked together?

Explain the mistake that is made.

Explain the mistake that is made.

Explain the mistake that is made.

Explain the mistake that is made.

Determine whether the following statements are true or false. The equation (3x  1)2  16 has the same solution set as the equation 3x  1  4.

Determine whether the following statements are true or false. The quadratic equation ax2  bx  c  0 can be solved by the square root method only if b  0.

Determine whether the following statements are true or false. All quadratic equations can be solved exactly.

Determine whether the following statements are true or false. The Quadratic Formula can be used to solve any quadratic equation.

Write a quadratic equation in general form that has x  a as a repeated real root.

Write a quadratic equation in general form that has x  bi as a root.

Write a quadratic equation in general form that has the solution set {2, 5}.

Write a quadratic equation in general form that has the solution set {3, 0}.

Solve for the indicated variable in terms of other variables. Solve for t.

Solve for the indicated variable in terms of other variables. Solve A  P(1  r)2 for r.

Solve for the indicated variable in terms of other variables. Solve a2  b2  c2 for c.

Solve for the indicated variable in terms of other variables. Solve P  EI  RI2 for I.

Solve the equation by factoring: x4  4x2  0.

Solve the equation by factoring: 3x  6x2  0.

Solve the equation using factoring by grouping: x3  x2  4x  4  0.

Solve the equation using factoring by grouping: x3  2x2  x  2  0.

Show that the sum of the roots of a quadratic equation is equal to

Show that the product of the roots of a quadratic equation is equal to .

Write a quadratic equation in general form whose solution set is

Write a quadratic equation in general form whose solution set is {2  i, 2  i}.

Aviation.An airplane takes 1 hour longer to go a distance of 600 miles ying against a headwind than on the return trip with a tailwind. If the speed of the wind is 50 miles per hour, nd the speed of the plane in still air.

Boating. Aspeedboat takes 1 hour longer to go 24 miles up a river than to return. If the boat cruises at 10 miles per hour in still water, what is the rate of the current?

Find a quadratic equation whose two distinct real roots are the negatives of the two distinct real roots of the equation ax2  bx  c  0.

Find a quadratic equation whose two distinct real roots are the reciprocals of the two distinct real roots of the equation ax2  bx  c  0.

Asmall jet and a 757 leave Atlanta at 1 P.M. The small jet is traveling due west. The 757 is traveling due south. The speed of the 757 is 100 miles per hour faster than the small jet. At 3 P.M. the planes are 1000 miles apart. Find the average speed of each plane.

Two boats leave Key West at noon. The smaller boat is traveling due west. The larger boat is traveling due south. The speed of the larger boat is 10 miles per hour faster than the speed of the smaller boat. At 3 P.M. the boats are 150 miles apart. Find the average speed of each boat.

Solve the equation x2  x  2 by rst writing it in standard form and then factoring. Now plot both sides of the equation in the same viewing screen (y1  x2  x and y2  2). At what x-values do these two graphs intersect? Do those points agree with the solution set you found?

Solve the equation x2  2x 2 by rst writing it in standard form and then using the quadratic formula. Now plot both sides of the equation in the same viewing screen (y1  x2  2xand y2 2). Do these graphs intersect? Does this agree with the solution set you found?

a. Solve the equation x2  2x  b, b  8 by rst writing it in standard form. Now plot both sides of the equation in the same viewing screen (y1  x2  2x and y2  b). At what x values do these two graphs intersect? Do those points agree with the solution set you found? b. Repeat part (a) for b 3, 1, 0, and 5.

a. Solve the equation x2  2x  b, b  8 by rst writing it in standard form. Now plot both sides of the equation in the same viewing screen (y1  x2  2x and y2  b). At what x values do these two graphs intersect? Do those points agree with the solution set you found? b. Repeat part (a) for b 3, 1, 0, and 5.

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the radical equation for the given variable

Solve the equations by introducing a substitution that transforms these equations to quadratic form. x2/3  2x1/3  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. x1/2  2x1/4  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. x4  3x2  2  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. x4  8x2  16  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. 2x4  7x2  6  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. x8  17x4  16  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. (2x  1)2  5(2x  1)  4  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. (x  3)2  6(x  3)  8  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. 4(t  1)2  9(t  1)  2

Solve the equations by introducing a substitution that transforms these equations to quadratic form. 2(1  y)2  5(1  y)  12  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. x8  17x4  16  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. 2u2  5u1  12  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. 3y2  y1  4  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. 5a2  11a1  2  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. z2/5  2z1/5  1  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. 2x1/2  x1/4  1  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. (x  3)5/3  32

Solve the equations by introducing a substitution that transforms these equations to quadratic form. (x  2)4/3  16

Solve the equations by introducing a substitution that transforms these equations to quadratic form. (x  1)2/3  4

Solve the equations by introducing a substitution that transforms these equations to quadratic form. (x  7)4/3  81

Solve the equations by introducing a substitution that transforms these equations to quadratic form. 6t2/3  t1/3  1  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form. t2/3  t1/3  6  0

Solve the equations by introducing a substitution that transforms these equations to quadratic form.

Solve the equations by introducing a substitution that transforms these equations to quadratic form.

Solve the equations by introducing a substitution that transforms these equations to quadratic form.

Solve the equations by introducing a substitution that transforms these equations to quadratic form.

Solve the equations by introducing a substitution that transforms these equations to quadratic form. u4/3  5u2/3 4

Solve the equations by introducing a substitution that transforms these equations to quadratic form. u4/3  5u2/3 4

Solve the equations by introducing a substitution that transforms these equations to quadratic form.

Solve the equations by introducing a substitution that transforms these equations to quadratic form.

Solve by factoring. x3  x2  12x  0

Solve by factoring. 2y3  11y2  12y  0

Solve by factoring. 4p3  9p  0

Solve by factoring. 25x3  4x

Solve by factoring. u5  16u  0

Solve by factoring. t5  81t  0

Solve by factoring. x3  5x2  9x  45  0

Solve by factoring. 2p3  3p2  8p  12  0

Solve by factoring. y(y  5)3  14(y  5)2  0

Solve by factoring. v(v 3)3 40(v 3)2 0

Solve by factoring. x9/4  2x5/4  3x1/4  0

Solve by factoring. u7/3  u4/3  20u1/3  0

Solve by factoring. t5/3  25t1/3  0

Solve by factoring. 4x9/5  9x1/5  0

Solve by factoring. y3/2  5y1/2  6y1/2  0

Solve by factoring. 4p5/3  5p2/3  6p1/3  0

An analysis of sales indicates that demand for a product during a calendar year is modeled by where d is demand in millions of units and t is the month of the year where t  0 represents January. Economics. During which month(s) is demand 3 million units?

An analysis of sales indicates that demand for a product during a calendar year is modeled by where d is demand in millions of units and t is the month of the year where t  0 represents January. Economics. During which month(s) is demand 4 million units?

Body Surface Area (BSA) is used in physiology and medicine for many clinical purposes. BSAcan be modeled by the function where w is weight in kilograms and h is height in centimeters. Health. The BSAof a 72 kilogram female is 1.8. Find the height of the female to the nearest centimeter.

Body Surface Area (BSA) is used in physiology and medicine for many clinical purposes. BSAcan be modeled by the function where w is weight in kilograms and h is height in centimeters. Health. The BSAof a 177 centimeter tall male is 2.1. Find the weight of the male to the nearest kilogram.

Insurance: Health. Cost for health insurance with a private policy is given by where C is the cost per day and a is the insureds age in years. Health insurance for a 6-year-old, a  6, is $4 a day (or $1460 per year). At what age would someone be paying $9 a day (or $3285 per year)?

Insurance: Life. Cost for life insurance is given by where C is the cost per day and a is the C = 15a + 1, C = 110 + a, BSA = A wh 3600 d = 31t + 1 - 0.75t insureds age in years. Life insurance for a newborn, a  0, is $1 a day (or $365 per year). At what age would someone be paying $20 a day (or $7300 per year)?

Stock Value.The stock price of MGI Pharmaceutical (MOGN) from March 2004 to June 2004 can be approximately modeled by the equation where P is the price of P = 52t2 + 1 + 50, the stock in dollars and t is the month with t  0 corresponding to March 2004. Assuming this trend continues, when would the stock be worth $85

Grades. The average combined math and verbal SAT score of incoming freshmen at a university is given by the equation where tis in years and t 0 corresponds to 1990. What year will the incoming class have an average SAT score of 1230?

Speed of Sound.Aman buys a house with an old well but does not know how deep the well is. To get an estimate he decides to drop a rock in the opening of the well and time how long it takes until he hears the splash. The total elapsed time T given by T  t1  t2, is the sum of the time it takes for the rock to reach the water, t1, and the time it takes for the sound of the splash to travel to the top of the well, t2. The time (seconds) that it takes for the rock to reach the water is given by , where d is the depth of the well in feet. Since the speed of sound is 1100 ft/s, the time (seconds) it takes for the sound to reach the top of the well is Ifthesplashisheardafter3seconds,howdeepisthe well?

Speed of Sound. If the owner of the house in Exercise 91 forgot to account for the speed of sound, what would he have calculated the depth of the well to be?

Physics: Pendulum.The period (T) of a pendulum is related to the length (L) of the pendulum and acceleration due to gravity (g) by the formula . If gravity is 9.8 m/s2 and the period is 1 second, nd the approximate length of the pendulum. Round to the nearest centimeter. Note: 100 cm  1 m.

Physics: Pendulum. The period (T) of a pendulum is related to the length (L) of the pendulum and acceleration due to gravity (g) by the formula . If gravity is 32 ft/s2 and the period is 1 second, nd the approximate length of the pendulum. Round to the nearest inch. Note: 12 in.  1 ft.

Einsteins special theory of relativity states that time is relative: Time speeds up or slows down, depending on how fast one object is moving with respect to another. For example, a space probe traveling at a velocity vnear the speed of light cwill have clocked a time thours, but for a stationary observer on Earth that corresponds to a time t0. The formula governing this relativity is given by Physics: Special Theory of Relativity. If the time elapsed on a space probe mission is 18 years but the time elapsed on Earth during that mission is 30 years, how fast is the space probe traveling? Give your answer relative to the speed of light.

Einsteins special theory of relativity states that time is relative: Time speeds up or slows down, depending on how fast one object is moving with respect to another. For example, a space probe traveling at a velocity vnear the speed of light cwill have clocked a time thours, but for a stationary observer on Earth that corresponds to a time t0. The formula governing this relativity is given by Physics: Special Theory of Relativity. If the time elapsed on a space probe mission is 5 years but the time elapsed on Earth during that mission is 30 years, how fast is the space probe traveling? Give your answer relative to the speed of light.

Explain the mistake that is made. Solve the equation Solution: This is incorrect. What mistake was made?

Explain the mistake that is made. Solve the equation Solution: This is incorrect. What mistake was made?

Explain the mistake that is made. Solve the equation x2/3  x1/3  20  0. Solution: u  x1/3 u2  u  20  0 (u  5)(u  4)  0 x  5, x 4 This is incorrect. What mistake was made?

Explain the mistake that is made. Solve the equation x4  2x2  3. Solution: x4  2x2  3  0 u  x2 u2  2u  3  0 (u  3)(u  1)  0 u 1, u  3 u  x2 x2 1, x2  3 x  ;1, x  ;3 This is incorrect. What mistake was made?

Determine whethereach statement is true orfalse. The equation (2x  1)6  4(2x  1)3  3  0 is quadratic in form.

Determine whethereach statement is true orfalse. The equation t25  2t5  1  0 is quadratic in form.

Determine whethereach statement is true orfalse. If two solutions are found and one does not check, then the other does not check.

Determine whethereach statement is true orfalse. Squaring both sides of leads to x  2  x  x  5.

Solve .

Solve .

Solve the equation without squaring both sides.

Solve the equation 3x7/12  x5/6  2x1/3  0.

Solve the equation

Solve the equation . 3 4 2x2 3

Solve the equation Plot both sides of the equation in the same viewing screen, and and zoom in on the x-coordinate of the point of intersection. Does the graph agree with your solution?

Solve the equation Plot both sides of the equation in the same viewing screen, and and zoom in on the x-coordinate of the points of intersection. Does the graph agree with your solution?

Solve the equation Plot both sides of the equationin the same viewing screen, y1 4 and Does the graph agree or disagree with your solution?

Solve the equation x1/4  4x1/2  21. Plot both sides of the equation in the same viewing screen, y1  x1/4 and y2 4x1/2  21. Does the point(s) of intersection agree with your solution?

Solve the equation Plot both sides of the equation in the same viewing screen, and Does the point(s) of intersection agree with your solution?

Solve the equation Plot both sides of the equation in the same viewing screen, and Does the point(s) of intersection agree with your solution?

Solve the equation Plot both sides of the equation in the same viewing screen, and Does the point(s) of intersection agree with your solution?

Rewrite in interval notation and graph. x 3

Rewrite in interval notation and graph.x 2

Rewrite in interval notation and graph.x  5

Rewrite in interval notation and graph.x 7

Rewrite in interval notation and graph.2  x  3

Rewrite in interval notation and graph.4  x 1

Rewrite in interval notation and graph.3  x  5

Rewrite in interval notation and graph. 0  x  6

Rewrite in interval notation and graph. 0  x  0

Rewrite in interval notation and graph.7  x 7

Rewrite in interval notation and graph. x  6 and x 4

Rewrite in interval notation and graph.x 3 and x  2

Rewrite in interval notation and graph. x 6 and x 8

Rewrite in interval notation and graph. x  8 and x  2

Rewrite in interval notation and graph.x 4 and x  2

Rewrite in interval notation and graph. x 5 and x  6

Rewrite in set notation. [0, 2)

Rewrite in set notation. (0, 3]

Rewrite in set notation. (7, 2)

Rewrite in set notation. [3, 2]

Rewrite in set notation. (, 6]

Rewrite in set notation. (5, )

Rewrite in set notation. (, )

Rewrite in set notation. [4, 4]

Write in inequality and interval notation.

Write in inequality and interval notation.

Write in inequality and interval notation.

Write in inequality and interval notation.

Write in inequality and interval notation.

Write in inequality and interval notation.

Write in inequality and interval notation.

Write in inequality and interval notation.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Graph the indicated set and write as a single interval, if possible.

Write in interval notation.

Write in interval notation.

Write in interval notation.

Write in interval notation.

Write in interval notation.

Write in interval notation.

Write in interval notation.

Write in interval notation.

Solve and express the solution in interval notation. x  3  7

Solve and express the solution in interval notation. x  4 9

Solve and express the solution in interval notation. . 3x  2  4

Solve and express the solution in interval notation. 3x  7  8

Solve and express the solution in interval notation. 5p 10

Solve and express the solution in interval notation. 4u  12

Solve and express the solution in interval notation. 3  2x  7

Solve and express the solution in interval notation. 4  3x 17

Solve and express the solution in interval notation. 1.8x  2.5 3.4

Solve and express the solution in interval notation. 2.7x  1.3  6.8

Solve and express the solution in interval notation. 3(t  1) 2t

Solve and express the solution in interval notation. 2(y  5)  3(y  4)

Solve and express the solution in interval notation. 7 2(1 x) 5 3(x2)

Solve and express the solution in interval notation. 4  3(2  x)  5

Solve and express the solution in interval notation.

Solve and express the solution in interval notation. y - 3 5 - 2 y 4

Solve and express the solution in interval notation.

Solve and express the solution in interval notation.

Solve and express the solution in interval notation.

Solve and express the solution in interval notation.

Solve and express the solution in interval notation. 2  x  3  5

Solve and express the solution in interval notation. 1  x  6  12

Solve and express the solution in interval notation. 8  4  2x  8

Solve and express the solution in interval notation. 0  2  x  5

Solve and express the solution in interval notation. 3  1  x  9

Solve and express the solution in interval notation. 3 2  5x  13

Solve and express the solution in interval notation.

Solve and express the solution in interval notation.

Solve and express the solution in interval notation. 1 2 1 + y 3 3 4

Solve and express the solution in interval notation.

Solve and express the solution in interval notation. 0.7  0.4x  1.1  1.3

Solve and express the solution in interval notation.7.1 4.7  1.2x 1.1

Weight. A healthy weight range for a woman is given by the following formula: 110 pounds for the rst 5 feet (tall) 26 pounds per inch for every inch above 5 feet Write an inequality representing a healthy weight, w, for a 5 foot 9 inch woman.

Weight. NASA has more stringent weight allowances for its astronauts. Write an inequality representing allowable weight for a female 5 foot 9 inch mission specialist given 105 pounds for the rst 5 feet, and 15 pounds per inch for every additional inch.

Prot. A seamstress decides to open a dress shop. Her xed costs are $4000 per month, and it costs her $20 to make each dress. If the price of each dress is $100, how many dresses does she have to sell per month to make a prot?

Prot. Labrador retrievers that compete in eld trials typically cost $2000 at birth. Professional trainers charge $400 to $1000 per month to train the dogs. If the dog is a champion by age 2, it sells for $30,000. What is the range of prot for a champion at age 2?

The annual revenue for a small company is modeled by where x is hundreds of units sold and R is revenue in thousands of dollars. Business. Find the number of units (to the nearest 100) that must be sold to generate at least $10 million in revenue.

The annual revenue for a small company is modeled by where x is hundreds of units sold and R is revenue in thousands of dollars. Business. Find the number of units (to the nearest 100) that must be sold to generate at least $7.5 million in revenue.

The Target or Training Heart Rate (THR) is a range of heart rate (measured in beats per minute) that enables a persons heart and lungs to benet the most from an aerobic workout. THR can be modeled by the formula where HRmax is the maximum heart rate that is deemed safe for the individual, HRrest is the resting heart rate, and I is the intensity of the workout that is reported as a percentage. Health. A female with a resting heart rate of 65 beats per minute has a maximum safe heart rate of 170 beats per minute. If her target heart rate is between 100 and 140 beats per minute, what percent intensities of workout can she consider?

The Target or Training Heart Rate (THR) is a range of heart rate (measured in beats per minute) that enables a persons heart and lungs to benet the most from an aerobic workout. THR can be modeled by the formula where HRmax is the maximum heart rate that is deemed safe for the individual, HRrest is the resting heart rate, and I is the intensity of the workout that is reported as a percentage. Health. A male with a resting heart rate of 75 beats per minute has a maximum safe heart rate of 175 beats per minute. If his target heart rate is between 110 and 150 beats per minute, what percent intensities of workout can he consider?

Cost: Cell Phones. A cell phone company charges $50 for an 800-minute monthly plan, plus an additional $0.22 per minute for every minute over 800. If a customers bill ranged from a low of $67.16 to a high of $96.86 over a 6-month period, what were the most minutes used in a single month? What were the least?

Cost: Internet. An Internet provider charges $30 per month for 1000 minutes of DSL service plus $0.08 for each additional minute. In a one-year period the customers bill ranged from $36.40 to $47.20. What were the most and least minutes used?

Grades. In your general biology class, your rst three test scores are 67, 77, and 84. What is the lowest score you can get on the fourth test to earn at least a B for the course? Assume that each test is of equal weight and the minimum score required to earn a B is an 80.

Grades. In your Economics I class there are four tests and a nal exam, all of which count equally. Your four test grades are 96, 87, 79, and 89. What grade on your nal exam is needed to earn between 80 and 90 for the course?

Markups. Typical markup on new cars is 1530%. If the sticker price is $27,999, write an inequality that gives the range of the invoice price (what the dealer paid the manufacturer for the car).

Markups. Repeat Exercise 103 with a sticker price of $42,599.

Lasers. A circular laser beam with a radius rT is transmitted from one tower to another tower. If the received beam radius rR uctuates 10% from the transmitted beam radius due to atmospheric turbulence, write an inequality representing the received beam radius.

Electronics: Communications. Communication systems are often evaluated based on their signal-to-noise ratio (SNR), which is the ratio of the average power of received signal, S, to average power of noise, N, in the system. If the SNR is required to be at least 2 at all times, write an inequality representing the received signal power if the noise can uctuate 10%.

Real Estate. The Aguileras are listing their house with a real estate agent. They are trying to determine a listing price, L, for the house. Their realtor advises them that most buyers traditionally offer a buying price, B, that is 8595% of the listing price. Write an inequality that relates the buying price to the listing price.

Humidity. The National Oceanic and Atmospheric Administration (NOAA) has stations on buoys in the oceans to measure atmosphere and ocean characteristics such as temperature, humidity, and wind. The humidity sensors have an error of 5%. Write an inequality relating the measured humidity hm, and the true humidity ht.

Recreation: Golf. Two friends enjoy playing golf. Their favorite course charges $40 for greens fees (to play the course) and a $15 cart rental (per person), so it currently costs each of them $55 every time they play. The membership offered at that course is $160 per month. The membership allows them to play as much as they want (no greens fees), but does still charge a cart rental fee of $10 every time they play. What is the least number of times they should play a month in order for the membership to be the better deal?

Recreation: Golf. The same friends in Exercise 109 have a second favorite course. That golf course charges $30 for greens fees (to play the course) and a $10 cart rental (per person), so it currently costs each of them $40 every time they play. The membership offered at that course is $125 per month. The membership allows them to play as much as they want (no greens fees), but does still charge a cart rental fee of $10. What is the least number of times they should play a month in order for the membership to be the better deal?

Federal Income Tax. What is the range of federal income taxes a person in tax bracket III will pay the IRS?

Federal Income Tax. What is the range of federal income taxes a person in tax bracket IV will pay the IRS?

Explain the mistake that is made. Rewrite in interval notation.This is incorrect. What mistake was made?

Explain the mistake that is made. Graph the indicated set and write as a single interval if possible. This is incorrect. What mistake was made?

Explain the mistake that is made. Solve the inequality 2  3p 4 and express the solution in interval notation. Solution: This is incorrect. What mistake was made?

Explain the mistake that is made. Solve the inequality 3  2x  7 and express the solution in interval notation. Solution: This is incorrect. What mistake was made?

Determine whether each statement is true or false.If x  a, then a x.

Determine whether each statement is true or false.If x a, then x a.

Select any of the statements a  d that could be true. a. m 0 and n 0 b. m  0 and n  0 c. m 0 and n  0 d. m  0 and n 0 .mn 0

Select any of the statements a  d that could be true. a. m 0 and n 0 b. m  0 and n  0 c. m 0 and n  0 d. m  0 and n 1. mn  0

Select any of the statements a  d that could be true. a. m 0 and n 0 b. m  0 and n  0 c. m 0 and n  0 d. m  0 and n 2.

Select any of the statements a  d that could be true. a. m 0 and n 0 b. m  0 and n  0 c. m 0 and n  0 d. m  0 and n 3.m n 6 0

Select any of the statements a  c that could be true. a. n  0 b. n 0 c. n  0 . m  n  m  n

Select any of the statements a  c that could be true. a. n  0 b. n 0 c. n  1 . m  n m  n

Solve the inequality x  x mentally (without doing any algebraic manipulation).

Solve the inequality x

Solve the inequality ax  b  ax  c, where 0  b  c.

Solve the inequality ax  b ax  c, where 0  b  c.

a. Solve the inequality 2.7x  3.1  9.4x 2.5. b. Graph each side of the inequality in the same viewing screen. Find the range of x-values when the graph of the left side lies below the graph of the right side. c. Do (a) and (b) agree?

a. Solve the inequality 0.5x  2.7

a. Solve the inequality x  3  2x  1  x  4. b. Graph all three expressions of the inequality in the same viewing screen. Find the range of x-values when the graph of the middle expression lies above the graph of the left side and below the graph of the right side. c. Do (a) and (b) agree?

a. Solve the inequality x  2  3x  4  2x  6. b. Graph all three expressions of the inequality in the same viewing screen. Find the range of x-values when the graph of the middle expression lies above the graph of the left side and on top of and below the graph of the right side. c. Do (a) and (b) agree?

a. Solve the inequality x  3  x  5. b. Graph each side of the inequality in the same viewing screen. Find the range of x-values when the graph of the left side lies below the graph of the right side. c. Do (a) and (b) agree?

a. Solve the inequality . b. Graph each side of the inequality in the same viewing screen. Find the range of x-values when the graph of the left side lies above the graph of the right side. c. Do (a) and (b) agree?

Solve the polynomial inequality and express the solution set in interval notation. x2  3x  10 0

Solve the polynomial inequality and express the solution set in interval notation.x2  2x  3  0

Solve the polynomial inequality and express the solution set in interval notation. u2  5u  6  0

Solve the polynomial inequality and express the solution set in interval notation.u2  6u  40 0

Solve the polynomial inequality and express the solution set in interval notation. p2  4p 3

Solve the polynomial inequality and express the solution set in interval notation. p2  2p 15

Solve the polynomial inequality and express the solution set in interval notation.2t2  3  t

Solve the polynomial inequality and express the solution set in interval notation.3t2 5t  2

Solve the polynomial inequality and express the solution set in interval notation.5v  1 6v2

Solve the polynomial inequality and express the solution set in interval notation.12t2  37t  10

Solve the polynomial inequality and express the solution set in interval notation.2s2  5s 3

Solve the polynomial inequality and express the solution set in interval notation. 8s  12  s2

Solve the polynomial inequality and express the solution set in interval notation. y2  2y 4

Solve the polynomial inequality and express the solution set in interval notation. y2  3y  1

Solve the polynomial inequality and express the solution set in interval notation. x2  4x  6

Solve the polynomial inequality and express the solution set in interval notation.x2  2x 5

Solve the polynomial inequality and express the solution set in interval notation. u2 3u

Solve the polynomial inequality and express the solution set in interval notation.u2  4u

Solve the polynomial inequality and express the solution set in interval notation.

Solve the polynomial inequality and express the solution set in interval notation.

Solve the polynomial inequality and express the solution set in interval notation.x2 9

Solve the polynomial inequality and express the solution set in interval notation.x2 16

Solve the polynomial inequality and express the solution set in interval notation.t2  81

Solve the polynomial inequality and express the solution set in interval notation.t2  49

Solve the polynomial inequality and express the solution set in interval notation. z2 16

Solve the polynomial inequality and express the solution set in interval notation.z2  2

Solve the polynomial inequality and express the solution set in interval notation.

Solve the polynomial inequality and express the solution set in interval notation.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Solve the rational inequality and graph the solution on the real number line.

Prot. A Web-based embroidery company makes monogrammed napkins. The prot associated with producing x orders of napkins is governed by the equation Determine the range of orders the company should accept in order to make a prot.

Prot. Repeat Exercise 59 using P  x2  130x  3600.

Car Value. The term upside down on car payments refers to owing more than a car is worth. Assume you buy a new car and nance 100% over 5 years. The difference between the value of the car and what is owed on the car is governed by the expression where t is age (in years) of the car. Determine the time period when the car is worth more than you owe . When do you owe more than its worth

Car Value. Repeat Exercise 61 using the expression

Bullet Speed. A .22-caliber gun res a bullet at a speed of 1200 feet per second. If a .22-caliber gun is red straight upward into the sky, the height of the bullet in feet is given by the equation h 16t2  1200t, where t is the time in seconds with t  0 corresponding to the instant the gun is red. How long is the bullet in the air?

Bullet Speed. A .38-caliber gun res a bullet at a speed of 600 feet per second. If a .38-caliber gun is red straight upward into the sky, the height of the bullet in feet is given by the equation h 16t2  600t. How many seconds is the bullet in the air?

Geometry. A rectangular area is fenced in with 100 feet of fence. If the minimum area enclosed is to be 600 square feet, what is the range of feet allowed for the length of the rectangle?

Stock Value. From June 2003 until April 2004, JetBlue airlines stock (JBLU) was approximately worth P 4t2 80t 360, where Pdenotes the price of the stock in dollars and t corresponds to months, with t  1 corresponding to January 2003. During what months was the stock value at least $36?

In response to economic conditions, a local business explores the effect of a price increase on weekly prot. The function models the effect that a price increase of x dollars on a bottle of wine will have on the prot P measured in dollars. Economics. What price increase will lead to a weekly prot of less than $460?

In response to economic conditions, a local business explores the effect of a price increase on weekly prot. The function models the effect that a price increase of x dollars on a bottle of wine will have on the prot P measured in dollars. Economics. What price increases will lead to a weekly prot of more than $550?

Real Estate. A woman is selling a piece of land that she advertises as 400 acres ( 7 acres) for $1.36 million. If you pay that price, what is the range of dollars per acre you have paid? Round to the nearest dollar.

Real Estate. A woman is selling a piece of land that she advertises as 1000 acres ( 10 acres) for $1 million. If you pay that price, what is the range of dollars per acre you have paid? Round to the nearest dollar.

Explain the mistake that is made.Solve the inequality 3x  x2. Solution: Divide by x.3  x Write the solution in interval notation. (3, ) This is incorrect. What mistake was made?

Explain the mistake that is made. Solve the inequality u2  25. Solution: Take the square root of both sides. u  5 Write the solution in interval notation. (, 5) This is incorrect. What mistake was made?

Explain the mistake that is made. Solve the inequality Solution: Factor the numerator and denominator. Cancel the (x  2) common factor. x  2 0 Solve. x 2 This is incorrect. What mistake was made?

Explain the mistake that is made. Solve the inequality Solution: Cross multiply. 3(x  4) 1(x) Eliminate the parentheses. 3x  12 x Combine like terms. 4x 12 Divide both sides by 4. x 3 This is incorrect. What mistake was made?

Determine whether each statement is true or false. Assume that a is a positive real number.If x  a2, then the solution is (, a).

Determine whether each statement is true or false. Assume that a is a positive real number.If x a2, then the solution is [a, ).

Assume the quadratic inequality ax2  bx  c  0 is true. If b2  4ac  0, then describe the solution.

Assume the quadratic inequality ax2  bx  c

Solve for x given that a and b are both positive real numbers.x2  a2

Solve for x given that a and b are both positive real numbers.x2 - b2 x + b 6 0

Solve for x given that a and b are both positive real numbers.

Solve for x given that a and b are both positive real numbers.

Plot the left side and the right side of each inequality in the same screen and use the zoom feature to determine the range of values for which the inequality is true. 1.4x2  7.2x  5.3 8.6x  3.7

Plot the left side and the right side of each inequality in the same screen and use the zoom feature to determine the range of values for which the inequality is true. 17x2  50x  19  9x2  2

Plot the left side and the right side of each inequality in the same screen and use the zoom feature to determine the range of values for which the inequality is true. 11x2  8x  16

Plot the left side and the right side of each inequality in the same screen and use the zoom feature to determine the range of values for which the inequality is true. 0.1x  7.3 0.3x2  4.1

Plot the left side and the right side of each inequality in the same screen and use the zoom feature to determine the range of values for which the inequality is true. x  x2  3x  6  2x

Plot the left side and the right side of each inequality in the same screen and use the zoom feature to determine the range of values for which the inequality is true. x2  3x  5  x2  2x  10

Plot the left side and the right side of each inequality in the same screen and use the zoom feature to determine the range of values for which the inequality is true. 2p 5 - p 7 1

Plot the left side and the right side of each inequality in the same screen and use the zoom feature to determine the range of values for which the inequality is true. 3p 4 - p 6 1

Solve the equation. |x|  3

Solve the equation. |x|  2

Solve the equation. |x| 4

Solve the equation. |x| 2

Solve the equation. |t  3|  2

Solve the equation. |t  3|  2

Solve the equation. |p  7|  3

Solve the equation. |p  7|  3

Solve the equation. |4  y|  1

Solve the equation. |2  y|  11

Solve the equation. |3x|  9

Solve the equation. |5x|  50

Solve the equation. |2x  7|  9

Solve the equation. |2x  5|  7

Solve the equation. |3t  9|  3

Solve the equation. |4t  2|  2

Solve the equation. |7  2x|  9

Solve the equation. |6  3y|  12

Solve the equation. |1  3y|  1

Solve the equation. |5  x|  2

Solve the equation. |4.7  2.1x|  3.3

Solve the equation. |5.2x  3.7|  2.4

Solve the equation.

Solve the equation.

Solve the equation. |x  5|  4  12

Solve the equation. |x  3|  9  2

Solve the equation. 3|x  2|  1  19

Solve the equation. 2|1  x|  4  2

Solve the equation. 5  7  |2  x|

Solve the equation. 1  3  |x  3|

Solve the equation. 2 |p  3|  15  5

Solve the equation. 8  3 |p  4|  2

Solve the equation. 5|y  2|  10  4|y  2|  3

Solve the equation. 3  |y  9|  11  3 |y  9|

Solve the equation. |4  x2|  1

Solve the equation. |7  x2|  3

Solve the equation. |x2  1|  5

Solve the equation. |x2  1|  5

Solve the inequality and express the solution in interval notation. |x|  7

Solve the inequality and express the solution in interval notation. |y|  9

Solve the inequality and express the solution in interval notation. |y| 5

Solve the inequality and express the solution in interval notation. |x| 2

Solve the inequality and express the solution in interval notation. |x  3|  7

Solve the inequality and express the solution in interval notation. |x  2|  4

Solve the inequality and express the solution in interval notation. |x  4| 2

Solve the inequality and express the solution in interval notation. |x  1|  3

Solve the inequality and express the solution in interval notation. |4  x|  1

Solve the inequality and express the solution in interval notation. |1  y|  3

Solve the inequality and express the solution in interval notation. |2x| 

Solve the inequality and express the solution in interval notation. |2t  3|  5

Solve the inequality and express the solution in interval notation. |3t  5| 1

Solve the inequality and express the solution in interval notation. |7  2y| 3

Solve the inequality and express the solution in interval notation. 6  5y|  1

Solve the inequality and express the solution in interval notation. |4  3x| 0

Solve the inequality and express the solution in interval notation. |4  3x| 1

Solve the inequality and express the solution in interval notation. 2|4x|  9 3

Solve the inequality and express the solution in interval notation. 5|x 1|  2  7

Solve the inequality and express the solution in interval notation. 2|x  1|  37

Solve the inequality and express the solution in interval notation. 3|x  1|  5 4

Solve the inequality and express the solution in interval notation. 3  2|x 4|  5

Solve the inequality and express the solution in interval notation. 7  3|x  2| 14

Solve the inequality and express the solution in interval notation. 9  |2x|  3

Solve the inequality and express the solution in interval notation. 4  |x  1| 1

Solve the inequality and express the solution in interval notation. 4  |x  1| 1

Solve the inequality and express the solution in interval notation.

Solve the inequality and express the solution in interval notation.

Solve the inequality and express the solution in interval notation. |2.6x  5.4|  1.8

Solve the inequality and express the solution in interval notation. |3.7  5.5x| 4.3

Solve the inequality and express the solution in interval notation. |x2  1|  8

Solve the inequality and express the solution in interval notation. |x2  1|  8

Write an inequality that ts the description. Any real numbers less than seven units from 2.

Write an inequality that ts the description. Any real numbers more than three units from 2

Write an inequality that ts the description. Any real numbers at least unit from .

Write an inequality that ts the description. Any real number no more than units from .

Write an inequality that ts the description. Any real numbers no more than two units from a.

Write an inequality that ts the description. Any real number at least a units from 3

Temperature. If the average temperature in Hawaii is 83 ( write an absolute value inequality representing the temperature in Hawaii.

Temperature. If the average temperature of a human is 97.8 (1.2), write an absolute value inequality describing normal human body temperature.

Sports. Two women tee off the green of a par-3 hole on a golf course. They are playing closest to the pin. If the rst woman tees off and lands exactly 4 feet from the hole, write an inequality that describes where the second woman must land in order to win the hole. What equation would suggest a tie? Let d  the distance from where the second woman lands to the tee.

Electronics. A band-pass lter in electronics allows certain frequencies within a range (or band) to pass through to the receiver and eliminates all other frequencies. Write an absolute value inequality that allows any frequency f within 15 Hertz of the carrier frequency fc to pass.

A company is reviewing revenue for the prior sales year. The model for projected revenue and the model for actual revenue are Rprojected  200  5x Ractual  210  4.8x where x represents the number of units sold and R represents the revenue in thousands of dollars. Since the two revenue models are not identical, an error in projected revenue occurred. This error is represented by E  |Rprojected  Ractual| Business. For what number of units sold was the error in projected revenue less than $5000?

A company is reviewing revenue for the prior sales year. The model for projected revenue and the model for actual revenue are Rprojected  200  5x Ractual  210  4.8x where x represents the number of units sold and R represents the revenue in thousands of dollars. Since the two revenue models are not identical, an error in projected revenue occurred. This error is represented by E  |Rprojected  Ractual| Business. For what number of units sold was the error in projected revenue less than $3000?

Explain the mistake that is made. Solve the absolute value equation |x  3|  7. Solution: Eliminate the absolute value symbols. x  3  7 Add 3 to both sides. x  10 Check. |10  3|  7 This is incorrect. What mistake was made?

Explain the mistake that is made. Solve the inequality |x  3|  7. Solution: Eliminate the absolute x  3 7 orx  3 7 value symbols. Add 3 to both sides. x  4 x 10 The solution is . This is incorrect. What mistake was made?

Explain the mistake that is made. Solve the inequality |5  2x|  1. Solution: Eliminate the absolute value symbols. 1  5  2x  1 Subtract 5. 6  2x 4 Divide by 2. 3  x  2 Write the solution in interval notation. This is incorrect. What mistake was made?

Explain the mistake that is made. Solve the equation |5  2x| 1. Solution: or The solution is {2, 3}. This is incorrect. What mistake was made?

Determine whether each statement is true or false. |m|  m  |m|

Determine whether each statement is true or false. |n2|  n2

Determine whether each statement is true or false. |m  n|  |m|  |n| is true only when m and n are both nonnegative.

Determine whether each statement is true or false. For what values of x does the absolute value equation |x  7|  x  7 hold?

Assuming a and b are real positive numbers, solve the equation or inequality and express the solution in interval notation. |x  a|  b

Assuming a and b are real positive numbers, solve the equation or inequality and express the solution in interval notation. |a  x| b

Assuming a and b are real positive numbers, solve the equation or inequality and express the solution in interval notation. |x| a

Assuming a and b are real positive numbers, solve the equation or inequality and express the solution in interval notation. |x| b

Assuming a and b are real positive numbers, solve the equation or inequality and express the solution in interval notation. |x  a|  b

Assuming a and b are real positive numbers, solve the equation or inequality and express the solution in interval notation. |x  a| b

For what values of xdoes the absolute value equation |x  1|  4  |x  2| hold?

Solve the inequality |3x2  7x  2|8

Graph y1  |x  7| and y2  x  7 in the same screen. Do the x-values where these two graphs coincide agree with your result in Exercise 90?

Graph y1  |x  1| and y2  |x  2|  4 in the same screen. Do the x-values where these two graphs coincide agree with your result in Exercise 97?

Graph y1  |3x2  7x  2| and y2  8 in the same screen. Do the x-values where y1 lies above y2 agree with your result in Exercise 98?

Solve the inequality |2.7x2  7.9x  5|  |5.3x2  9.2| by graphing both sides of the inequality and identify which x-values make this statement true.

Solve the inequality by graphing both sides of the inequality, and identify which x-values make this statement true.

Solve the inequality by graphing both sides of the inequality, and identify which x-values make this statement true.

Solve for the variable. 7x  4  12

Solve for the variable. 13d  12  7d  6

Solve for the variable. 20p  14  6  5p

Solve for the variable. 4(x  7)  4  4

Solve for the variable. 3(x  7)  2  4(x  2)

Solve for the variable. 7c  3(c  5)  2(c  3)  14

Solve for the variable. 14 - [-3(y - 4) + 9] = [4(2y + 3) - 6] + 4

Solve for the variable. [6 - 4x + 2(x - 7)] - 52 = 3(2x - 4) + 6[3(2x - 3) + 6]

Solve for the variable.

Solve for the variable.

Solve for the variable.

Solve for the variable.

Specify any values that must be excluded from the solution set and then solve.

Specify any values that must be excluded from the solution set and then solve.

Specify any values that must be excluded from the solution set and then solve.

Specify any values that must be excluded from the solution set and then solve.

Specify any values that must be excluded from the solution set and then solve.

Specify any values that must be excluded from the solution set and then solve.

Specify any values that must be excluded from the solution set and then solve.

Specify any values that must be excluded from the solution set and then solve.

Solve for the specied variable. Solve for x in terms of y: 3x  2[(y  4)3  7]  y  2x  6(x  3)

Solve for the specied variable. If , nd in terms of x.

Transportation. Maria is on her way from her home near Orlando to the Sundome in Tampa for a rock concert. She drives 16 miles to the Orlando park-n-ride, takes a bus of 3 4

Diet. A particular 2000 calorie per day diet suggests eating breakfast, lunch, dinner, and four snacks. Each snack is the calories of lunch. Lunch has 100 calories less than dinner. Dinner has 1.5 times as many calories as breakfast. How many calories are in each meal and snack?

Numbers. Find a number such that 12 more than the number is the number.

Numbers. Find four consecutive odd integers such that the sum of the four numbers is equal to three more than three times the fourth integer.

Geometry. The length of a rectangle is one more than two times the width, and the perimeter is 20 inches. What are the dimensions of the rectangle?

Geometry. Find the perimeter of a triangle if one side is 10 inches, another side is of the perimeter, and the third side is of the perimeter.

Investments. You win $25,000 and you decide to invest the money in two different investments: one paying 20% and the other paying 8%. A year later you have $27,600 total. How much did you originally invest in each account?

Investments. A college student on summer vacation was able to make $5000 by working a full-time job every summer. He invested half the money in a mutual fund and half the money in a stock that yielded four times as much interest as the mutual fund. After a year he earned $250 in interest. What were the interest rates of the mutual fund and the stock?

Chemistry. For an experiment, a student requires 150 milliliters of a solution that is 8% NaCl (sodium chloride). The storeroom has only solutions that are 10% NaCl and 5% NaCl. How many milliliters of each available solution should be mixed to get 150 milliliters of 8% NaCl?

Chemistry. A mixture containing 8% salt is to be mixed with 4 ounces of a mixture that is 20% salt, in order to obtain a solution that is 12% salt. How much of the rst solution must be used

Grades. Going into the College Algebra nal exam, which will count as two tests, Danny has test scores of 95, 82, 90, and 77. If his nal exam is higher than his lowest test score, then it will count for the nal exam and replace the lowest test score. What score does Danny need on the nal in order to have an average score of at least 90?

Car Value. A car salesperson reduced the price of a model car by 20%. If the new price is $25,000, what was its original price? How much can be saved by purchasing the model?

Solve by factoring. b2  4b  21

Solve by factoring. x(x  3)  54

Solve by factoring. x2  8

Solve by factoring. 6y2  7y  5  0

Solve by the square root method. q2  169  0

Solve by the square root method. c2  36  0

Solve by the square root method. (2x  4)2 64

Solve by the square root method. (d  7)2 4  0

Solve by completing the square. x2  4x  12  0

Solve by completing the square. 2x2  5x  7  0

Solve by completing the square.

Solve by completing the square. 8m  m2  15

Solve by the Quadratic Formula. 3t2  4t  7

Solve by the Quadratic Formula. 4x2  5x  7  0

Solve by the Quadratic Formula.

Solve by the Quadratic Formula. x2 6x  6

Solve by any method.

Solve by any method.

Solve by any method.

Solve by any method.

Solve by any method.

Solve by any method.

Solve for the indicated variable.

Solve for the indicated variable.