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All Textbook Solutions for Algebra and Trigonometry (MindTap Course List)

86E 87E 88E 89E 90E 91E 92E 93E 94E 95E 96E 97E 98E 99E 100E 101E 102E 103E 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E 20E 15-28 Linear Equations Solve the given linear equation. -3x-3=5x-3 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E 32E 33E 34E 35E 36E 37E 38E 39E 40E 41E 42E 43E 41-54 Equations Involving Fractional Expressions The given equation is either linear or equivalent to a linear equation. Solve the equation. 2x-72x+4=23 45E 46E 47E 48E 41-54 Equations Involving Fractional Expressions The given equation is either linear or equivalent to a linear equation. Solve the equation. 1z-12z-15z=10z+1 50E 51E 52E 53E 54E 55E 56E 57E 58E 59E 60E 61E 62E 63E 64E 65E 66E 67E 68E 69E 70E 71E 72E 73E 74E 75E 76E 77E 78E 79E 80E 81E 82E 83E 84E 85E 86E 87E 88E 89E 90E 91E 92E 93E 94E 95E 96E 97E 87-100 Solving for a Variable Solve the equation for the indicated variable. a2x+a-1=a+1x; for x 99E 100E Shrinkage in Concrete Beams As concrete dries, it shrinks; the higher the water content, the greater the shrinkage. If a concrete beam has a water content of w kg/m3, then it will shrink by a factor S=0.032w-2.510, 000 Where S is the fraction of the original beam length that disappear owing to shrinkage. aA beam 12.025 m long is cast in concrete that contains 250 kg/m3 water. What is the shrinkage factor S? How long will be the beam be when it has dried? bA beam is 10.014 m long when wet. The manufacturer wants it to shrink to 10.009 m, so the shrinkage factor should be S=0.00050. What water content will provide this amount of shrinkage?102E 103E Food Consumption The average daily food consumption F of a herbivorous mammal with body weight x, where both F and x are measured in pounds, is given approximately by the equation F=0.3x34. Find the weight x of an elephant that consumes 300 lb of food per day 105E DISCUSS: Proof That 0 = 1? The following steps appear to give equivalent equations, which seem to prove that 1 = 0. Find the error. x=1 Given x2=x Multiply by x x2-x=0 Subtract x xx-1 Factor x=0 Divide by x-1 1=0 Given x=1 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E SKILLS 7-20 Using Variables Express the given quantity in terms of the indicated variable. The concentrationin oz/gal of salt in a mixture of 3 gal of brine containing 25 oz of salt to which some pure water has been added; x= volume of pure water added in gal 20E 21E APPLICATIONS Cell Phone Costs A cell phone company charges a monthly fee of 10 for the first 1000 messages and 10 cents for each additional text message. Miriams bill for text messages for the month of June is 38.50. How many text messages did she send that month?APPLICATIONS Average Linh has obtained scores of 82, 75 and 71 on her midterm algebra exams. If the final exams counts twice as much as a midterm, what score must she make on her final exam to get an average score of 80? Assume that the maximum possible score on each test is 100.24E 25E 26E 27E 28E 29E 30E 31E APPLICATIONS Labor Costs A plumber and his assistant work together to replace the pipes in an old house. The plumber charges 45 an hour for his own labor and 25 an hour for his assistants labor. The plumber work twice as long as his assistant on this job, and the labor on the final bill is 4025. How long did the plumber and his assistant work in this job?33E 34E 35E 36E 37E 38E 39E 40E APPLICATIONS Geometry Find the length y in the figure if the shaded area is 120 in2.APPLICATIONS Geometry Find the length x in the figure if the shaded area is 144 cm2.43E 44E 45E APPLICATIONS Height of Tree A woodcutter determines the height of a tall tree by first measuring a smaller one 125 ft away, then moving so that his eyes are in a line of sight along the tops of the trees and measuring how far he is standing from the small treesee the figure. Suppose the small tree is 20 ft. tall, the man is 25 ft. from the small tree, and his eye level is 5 ft. above the ground. How tall the taller tree?47E 48E 49E 50E 51E APPLICATIONS Mixture Problem A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The sterilize tank contains 100 gal of a solution 2 ordinary household bleach mixed with pure distilled water. New research indicates that the concentration of bleach should be 5 for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?APPLICATIONS Mixture Problem A bottle contains 750mL of fruit punch with a concentration of 50 pure fruit juice. Jill drinks 100 mL of the punch and then refills the bottle with an equal amount of a cheaper brand of punch. If the concentration of juice in the bottle is now reduced to 48, what was the concentration in the punch that Jill added?54E 55E 56E APPLICATIONS Sharing a Job Betty and Karen have been hired to paint the houses in a new development. Working together, the women can paint a house in two-thirds the time that it takes Karen working alone. Betty takes 6 h to paint a house alone. How long does it take Karen to paint a house working alone?APPLICATIONS Sharing a Job Next-door neighbours Bob and Jim use hoses from both houses to fill Bobs swimming pool. They know that it takes 18 h using both hoses. They also know that Bobs hose, used alone, takes 20 less time than Jims hose alone. How much time is required to fill the pool by each hose alone?59E 60E 61E 62E APPLICATIONS Law of the Lever The figure shows a lever system, similar to a seesaw that you might find in a childrens playground. For the system to balance, the product of the weight and its distance from the fulcrum must be the same in the same on each side; that is, w1x1=w2x2 This equation is called the law of the lever and was the first discovered by Archimedes see page 831. A woman and her son are playing on the seesaw. The boy is at the one end, 8 ft from the fulcrum. If the son weighs 100 lb.and the mother weighs 125 lb., where should the woman sit so that the seesaw is balanced?APPLICATIONS Law of the Lever A plank 30 ft long rests on top of a flat-roofed building, with 5 ft. of the plank projecting over the edge, as shown in the figure. A worker weighing 240 lb. sits on one end of the plank. What is the largest weight that can be hung on the projecting end of the plank if it is to remain in balance? Use the law of the lever stated in Exercise 63.65E 66E APPLICATIONS Dimensions of a Structure A storage bin for corn consists of a cylindrical section of wire mesh, surmounted by a conical tin roof, as shown in the figure. The height of the roof is one-third the height of the entire structure. If the total volume of the structure is 1400 ft3 and its radius is 10 ft, what is its height? Hint: Use the volume formulas listed on the inside front cover of this book.APPLICATIONS An Ancient Chinese Problem This problem is taken from a Chinese mathematics textbook called Chui-Chang suan-shu, or Nine Chapters on the Mathematical Art, which was written about 250 B.C. A 10-ft-long stem of bamboo is broken in such a way that its tip touches the ground 3 ft from the base of the stem, as shown in the figure. What is the height of the break? Hint: Use the Pythagorean Theorem 69E 70E 1CC 2CC 3CC 4CC 5CC 6CC 7CC 8CC 9CC 10CC 11CC 12CC 13CC 14CC 15CC 16CC 17CC 18CC 19CC 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E 32E 33E 34E 35E 36E 37E 38E 39E 40E 41E 42E 43E 44E 45E 46E 47E 48E 49E 50E 51E 52E 53E 54E 55E 56E 57E 58E 59E 60E 61E 62E 63E 64E 65E 66E 67E 68E 69E 70E 71E 72E 73E 74E 75E 76E 77E 78E 79E 80E 81E 82E 83E 84E 85E 86E 87E

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