Solution: In Exercises 2836, use an equation or a system of

In Exercises 17, solve each equation, inequality, or system of equations. 2 4(x 2) 5 3(2x 1) (Section 2.3, Example 3)

In Exercises 17, solve each equation, inequality, or system of equations. x 2 3 x 5 (Section 2.3, Example 4)

In Exercises 17, solve each equation, inequality, or system of equations. 3x 9 5(x 1) (Section 2.7, Example 7)

In Exercises 17, solve each equation, inequality, or system of equations. 2x 3y 6 x 2y 5 (Section 4.3, Example 2)

In Exercises 17, solve each equation, inequality, or system of equations. 3x 2y 1 y 10 2x (Section 4.2, Example 1)

In Exercises 17, solve each equation, inequality, or system of equations. 3 x 5 1 4 x 2x 10 (Section 7.6, Example 4)

In Exercises 17, solve each equation, inequality, or system of equations. x 6 x 5 (Section 7.6, Example 3) In Exercises 816, perform the indicated operations. If possible, simplify the answer.

In Exercises 816, perform the indicated operations. If possible, simplify the answer. 12x3 3x12 (Section 5.7, Example 4)

In Exercises 816, perform the indicated operations. If possible, simplify the answer. 4 6 2 3 (5) (Section 1.8, Example 4)

In Exercises 816, perform the indicated operations. If possible, simplify the answer. (6x2 8x 3) (4x2 x 1) (Section 5.1, Example 3)

In Exercises 816, perform the indicated operations. If possible, simplify the answer. (7x 4)(3x 5) (Section 5.3, Example 2)

In Exercises 816, perform the indicated operations. If possible, simplify the answer. (5x 2)2 (Section 5.3, Example 6)

In Exercises 816, perform the indicated operations. If possible, simplify the answer. (x y)(x2 xy y2) (Section 5.4, Example 8)

In Exercises 816, perform the indicated operations. If possible, simplify the answer. x2 6x 8 x2 (3x2 6x) (Section 7.2, Example 7)

In Exercises 816, perform the indicated operations. If possible, simplify the answer. x x2 2x 3 x x2 5x 4 (Section 7.4, Example 7)

In Exercises 816, perform the indicated operations. If possible, simplify the answer. x 1 5 5 1 x (Section 7.5, Examples 2 and 5) In Exercises 1722, factor completely.

In Exercises 1722, factor completely. 4x2 49 (Section 6.4, Example 1)

In Exercises 1722, factor completely. x3 3x2 x 3 (Section 6.5, Example 4)

In Exercises 1722, factor completely. 2x2 8x 42 (Section 6.5, Example 2)

In Exercises 1722, factor completely. x5 16x (Section 6.4, Example 4)

In Exercises 1722, factor completely. x3 10x2 25x (Section 6.4, Example 5)

In Exercises 1722, factor completely. x3 8 (Section 6.4, Example 8)

In Exercises 2325, graph each equation in a rectangular coordinate system. y 1 3 x 1 (Section 3.4, Example 3)

In Exercises 2325, graph each equation in a rectangular coordinate system. 3x 2y 6 (Section 3.2, Example 4)

In Exercises 2325, graph each equation in a rectangular coordinate system. y 2 (Section 3.2, Example 7)

Find the slope of the line passing through the points (1, 3) and (2, 3). (Section 3.3, Example 1)

Write the point-slope form of the equation of the line passing through the points (1, 2) and (3, 6). Then use the point-slope form of the equation to write the slope-intercept form of the lines equation. (Section 3.5, Example 2)

In Exercises 2836, use an equation or a system of equations to solve each problem. Seven subtracted from five times a number is 208. Find the number. (Section 2.5, Example 1)

In Exercises 2836, use an equation or a system of equations to solve each problem. After a 20% reduction, a digital camera sold for $256. What was the price before the reduction? (Section 2.5, Example 6)

In Exercises 2836, use an equation or a system of equations to solve each problem. A rectangular field is three times as long as it is wide. If the perimeter of the field is 400 yards, what are the fields dimensions? (Section 2.5, Example 5)

In Exercises 2836, use an equation or a system of equations to solve each problem. You invested $20,000 in two accounts paying 7% and 9% annual interest. If the total interest earned for the year was $1550, how much was invested at each rate? (Section 4.4, Example 5)

In Exercises 2836, use an equation or a system of equations to solve each problem. A chemist needs to mix a 40% acid solution with a 70% acid solution to obtain 12 liters of a 50% acid solution. How many liters of each solution should be used? (Section 4.4, Example 6)

In Exercises 2836, use an equation or a system of equations to solve each problem. A sailboat has a triangular sail with an area of 120 square feet and a base that is 15 feet long. Find the height of the sail. (Section 2.6, Example 1)

In Exercises 2836, use an equation or a system of equations to solve each problem. In a triangle, the measure of the first angle is 10 more than the measure of the second angle. The measure of the third angle is 20 more than four times that of the second angle. What is the measure of each angle? (Section 2.6, Example 6)

In Exercises 2836, use an equation or a system of equations to solve each problem. A salesperson works in the TV and stereo department of an electronics store. One day she sold 3 TVs and 4 stereos for $2530. The next day, she sold 4 of the same TVs and 3 of the same stereos for $2510. Find the price of a TV and a stereo. (Section 4.4, Example 2)

In Exercises 2836, use an equation or a system of equations to solve each problem. The length of a rectangle is 6 meters more than the width. The area is 55 square meters. Find the rectangles dimensions. (Section 6.6, Example 8)

In Exercises 3242, add or subtract as indicated. Simplify the result, if possible. x y y x y x

In Exercises 3242, add or subtract as indicated. Simplify the result, if possible. 2x x2 2x 1 x x2 1

In Exercises 3242, add or subtract as indicated. Simplify the result, if possible. 5x x 1 2x 1 x2

In Exercises 3242, add or subtract as indicated. Simplify the result, if possible. 4 x2 x 6 4 x2 4

In Exercises 3242, add or subtract as indicated. Simplify the result, if possible. 7 x 3 2

In Exercises 3242, add or subtract as indicated. Simplify the result, if possible. 2y 5 6y 9 4 2y2 3y

In Exercises 4347, simplify each complex rational expression. 1 2 3 8 3 4 1 2

In Exercises 4347, simplify each complex rational expression. 1 x 1 1 x

In Exercises 4347, simplify each complex rational expression. 1 x 1 y 1 xy

In Exercises 4347, simplify each complex rational expression. 1 x 1 2 1 3 x 6

In Exercises 4347, simplify each complex rational expression. 3 12 x 1 16 x2

In Exercises 4855, solve each rational equation. 3 x 1 6 1 x

In Exercises 4855, solve each rational equation. 3 4x 1 x 1 4

In Exercises 4855, solve each rational equation. x 5 6 x

In Exercises 4855, solve each rational equation. 4 x x 5 5 x 5

In Exercises 4855, solve each rational equation. 2 x 3 4 x 3 8 x2 9

In Exercises 4855, solve each rational equation. 2 x 2 3 x 6

In Exercises 4855, solve each rational equation. 13 y 1 3 1 y 1

In Exercises 4855, solve each rational equation. 1 x 3 1 x 1 x 1 x2 2x 3

Park rangers introduce 50 elk into a wildlife preserve. The formula P 250(3t 5) t 25 models the elk population, P, after t years. How many years will it take for the population to increase to 125 elk?

The formula S C 1 r describes the selling price, S, of a product in terms of its cost to the retailer, C, and its markup, r, usually expressed as a percent. A small television cost a retailer $140 and was sold for $200. Find the markup. Express the answer as a percent.

In Exercises 5862, solve each formula for the specified variable. P R C n for C

In Exercises 5862, solve each formula for the specified variable. P1V1 T1 P2V2 T2 for T1

In Exercises 5862, solve each formula for the specified variable. T A P Pr for P

In Exercises 5862, solve each formula for the specified variable. 1 R 1 R1 1 R2 for R

In Exercises 5862, solve each formula for the specified variable. I nE R nr for n

In still water, a paddle boat averages 20 miles per hour. It takes the boat the same amount of time to travel 72 miles downstream, with the current, as 48 miles upstream, against the current. What is the rate of the waters current?

A car travels 60 miles in the same time that a car traveling 10 miles per hour faster travels 90 miles. What is the rate

each car? 65. A painter can paint a fence around a house in 6 hours. Working alone, the painters apprentice can paint the same fence in 12 hours. How many hours would it take them to do the job if they worked together?

If a school board determines that there should be 3 teachers for every 50 students, how many teachers are needed for an enrollment of 5400 students?

To determine the number of trout in a lake, a conservationist catches 112 trout, tags them, and returns them to the lake. Later, 82 trout are caught, and 32 of them are found to be tagged. How many trout are in the lake?

The triangles shown in the figure are similar. Find the length of the side marked with an x. 8 ft 10 ft 4 ft x D

Find the height of the lamppost in the figure. 6 ft 9 ft 5 ft ft

A companys profit varies directly as the number of products it sells. The company makes a profit of $1175 on the sale of 25 products. What is the companys profit when it sells 105 products?

The distance that a body falls from rest varies directly as the square of the time of the fall. If skydivers fall 144 feet in 3 seconds, how far will they fall in 10 seconds?

The pitch of a musical tone varies inversely as its wavelength. A tone has a pitch of 660 vibrations per second and a wavelength of 1.6 feet.What is the pitch of a tone that has a wavelength of 2.4 feet?

The loudness of a stereo speaker, measured in decibels, varies inversely as the square of your distance from the speaker. When you are 8 feet from the speaker, the loudness is 28 decibels. What is the loudness when you are 4 feet from the speaker?

The time required to assemble computers varies directly as the number of computers assembled and inversely as the number of workers. If 30 computers can be assembled by 6 workers in 10 hours, how long would it take 5 workers to assemble 40 computers?

The volume of a pyramid varies jointly as its height and the area of its base. A pyramid with a height of 15 feet and a base with an area of 35 square feet has a volume of 175 cubic feet. Find the volume of a pyramid with a height of 20 feet and a base with an area of 120 square feet.

In Exercises 14, find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. 5x 6x 24

In Exercises 14, find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. x 3 (x 2)(x 5)

In Exercises 14, find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. x2 3 x2 3x 2

In Exercises 14, find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. 7 x2 81

In Exercises 512, simplify each rational expression. If the rational expression cannot be simplified, so state. 16x2 12x

In Exercises 512, simplify each rational expression. If the rational expression cannot be simplified, so state. x2 4 x 2

In Exercises 512, simplify each rational expression. If the rational expression cannot be simplified, so state. x3 2x2 x 2

In Exercises 512, simplify each rational expression. If the rational expression cannot be simplified, so state. x2 3x 18 x2 36

In Exercises 512, simplify each rational expression. If the rational expression cannot be simplified, so state. x2 4x 5 x2 8x 7

In Exercises 512, simplify each rational expression. If the rational expression cannot be simplified, so state. y2 2y y2 4y 4

In Exercises 512, simplify each rational expression. If the rational expression cannot be simplified, so state. x2 x2 4

In Exercises 512, simplify each rational expression. If the rational expression cannot be simplified, so state. 2x2 18y2 3y x

In Exercises 1317, multiply as indicated x2 4 12x 3x x 2

In Exercises 1317, multiply as indicated 5x 5 6 3x x2 x

In Exercises 1317, multiply as indicated x2 6x 9 x2 4 x 2 x 3

In Exercises 1317, multiply as indicated y2 2y 1 y2 1 2y2 y 1 5y 5

In Exercises 1317, multiply as indicated 2y2 y 3 4y2 9 3y 3 5y 5y2

In Exercises 1822, divide as indicated. x2 x 2 10 2x 4 5

In Exercises 1822, divide as indicated. 6x 2 x2 1 3x2 x x 1

In Exercises 1822, divide as indicated. 1 y2 8y 15 7 y 5

In Exercises 1822, divide as indicated. y2 y 42 y 3 y 7 (y 3)2

In Exercises 1822, divide as indicated. 8x 8y x2 x2 y2 x2

In Exercises 2328, add or subtract as indicated. Simplify the result, if possible. 4x x 5 20 x 5

In Exercises 2328, add or subtract as indicated. Simplify the result, if possible. 8x 5 3x 1 4x 1 3x 1

In Exercises 2328, add or subtract as indicated. Simplify the result, if possible. 3x2 2x x 1 10x 5 x 1

In Exercises 2328, add or subtract as indicated. Simplify the result, if possible. 6y2 4y 2y 3 12 3y 2y 3

In Exercises 2328, add or subtract as indicated. Simplify the result, if possible. x x 2 x 4 2 x

In Exercises 2328, add or subtract as indicated. Simplify the result, if possible. x 5 x 3 x 3 x

In Exercises 2931, find the least common denominator of the rational expressions. 7 9x3 and 5 12x

In Exercises 2931, find the least common denominator of the rational expressions. 3 x2(x 1) and 11 x(x 1)2

In Exercises 2931, find the least common denominator of the rational expressions. x x2 4x 3 and 17 x2 10x 21

In Exercises 3242, add or subtract as indicated. Simplify the result, if possible. 7 3x 5 2x2

In Exercises 3242, add or subtract as indicated. Simplify the result, if possible. 5 x 1 2 x

In Exercises 3242, add or subtract as indicated. Simplify the result, if possible. 7 x 3 4 (x 3)2

In Exercises 3242, add or subtract as indicated. Simplify the result, if possible. 6y y2 4 3 y 2

In Exercises 3242, add or subtract as indicated. Simplify the result, if possible. y 1 y2 2y 1 y 1 y 1

Find all numbers for which x 7 x2 5x 36 is undefined.

In Exercises 23, simplify each rational expression. x2 2x 3 x2 3x 2

In Exercises 23, simplify each rational expression. 4x2 20x x2 4x 5

In Exercises 416, perform the indicated operations. Simplify the result, if possible. x2 16 10 5 x 4

In Exercises 416, perform the indicated operations. Simplify the result, if possible. x2 7x 12 x2 4x x2 x2 9 CHAPTER 7 TEST

In Exercises 416, perform the indicated operations. Simplify the result, if possible. 2x 8 x 3 x2 5x 4 x2 9

In Exercises 416, perform the indicated operations. Simplify the result, if possible. 5y 5 (y 3)2 y2 1 y 3

In Exercises 416, perform the indicated operations. Simplify the result, if possible. 2y2 5 y 3 6y 5 y 3

In Exercises 416, perform the indicated operations. Simplify the result, if possible. y2 2y 3 y2 7y 12 y2 4y 5 y2 7y 12

In Exercises 416, perform the indicated operations. Simplify the result, if possible. x x 3 5 x 3

In Exercises 416, perform the indicated operations. Simplify the result, if possible. 2 x2 4x 3 6 x2 x 2

In Exercises 416, perform the indicated operations. Simplify the result, if possible. 4 x 3 x 5 3 x

In Exercises 416, perform the indicated operations. Simplify the result, if possible. 1 3 x 1

In Exercises 416, perform the indicated operations. Simplify the result, if possible. 2x 3 x2 7x 12 2 x 3

In Exercises 416, perform the indicated operations. Simplify the result, if possible. 8y y2 16 4 y 4

In Exercises 416, perform the indicated operations. Simplify the result, if possible. (x y)2 x y x2 xy 3x 3y

In Exercises 1718, simplify each complex rational expression. 5 5 x 2 1 x

In Exercises 1718, simplify each complex rational expression. 1 x 1 y 1 x

In Exercises 1921, solve each rational equation. 5 x 2 3 2 2 x 1 6

In Exercises 1921, solve each rational equation. 3 y 5 1 4 y 2y 10

In Exercises 1921, solve each rational equation. 2 x 1 3 x2 1 1

Solve for a: R as a s .

In still water, a boat averages 30 miles per hour. It takes the boat the same amount of time to travel 16 miles downstream, with the current, as 14 miles upstream, against the current. What is the rate of the waters current?

One pipe can fill a hot tub in 20 minutes and a second pipe can fill it in 30 minutes. If the hot tub is empty, how long will it take both pipes to fill it?

Park rangers catch, tag, and release 200 tule elk back into a wildlife refuge. Two weeks later they observe a sample of 150 elk, of which 5 are tagged. Assuming that the ratio of tagged elk in the sample holds for all elk in the refuge, how many elk are there in the park?

The triangles in the figure are similar. Find the length of the side marked with an x. 10 in. 4 in. 8 in. x A CD F E B

The amount of current flowing in an electrical circuit varies inversely as the resistance in the circuit. When the resistance in a particular circuit is 5 ohms, the current is 42 amperes. What is the current when the resistance is 4 ohms?

In Exercises 16, solve each equation, inequality, or system of equations. 2(x 3) 5x 8(x 1)

In Exercises 16, solve each equation, inequality, or system of equations. 3(2x 4) 2(6x 12)

In Exercises 16, solve each equation, inequality, or system of equations. x2 3x 18

In Exercises 16, solve each equation, inequality, or system of equations. 2x x2 4 1 x 2 2 x 2

In Exercises 16, solve each equation, inequality, or system of equations. y 2x 3 x 2y 9

In Exercises 16, solve each equation, inequality, or system of equations. 3x 2y 2 4x 5y 18

In Exercises 79, graph each equation in a rectangular coordinate system. 3x 2y

In Exercises 79, graph each equation in a rectangular coordinate system. . y 2x 3

In Exercises 79, graph each equation in a rectangular coordinate system. y 3

In Exercises 1012, simplify each expression. 21 16 3(2 8)

In Exercises 1012, simplify each expression. 4x5 2x2 3

In Exercises 1012, simplify each expression. 1 x 2 4 1 x CUMULATIVE REVIEW EXERCISES (CHAPTERS 17)

In Exercises 1315, factor completely. 4x2 13x 3

In Exercises 1315, factor completely. 4x2 20x 25

In Exercises 1315, factor completely. 3x2 75

In Exercises 1618, perform the indicated operations. (4x2 3x 2) (5x2 7x 6)

In Exercises 1618, perform the indicated operations. 8x6 12x4 4x2 4x2

In Exercises 1618, perform the indicated operations. x 6 x 2 2x 1 x 3

You invested $4000, part at 5% and the remainder at 9% annual interest. At the end of the year, the total interest from these investments was $311. How much was invested at each rate?

A 68-inch board is to be cut into two pieces. If one piece must be three times as long as the other, find the length of each piece.