Chapter Test For Exercises 1 and 2 simplify 1 3 x 7 y 2 x 3 y 5 2 5 x 6 2 x 10

Chapter test for exercises 1 and 2 simplify 1 3 x 7 y

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Chapter Test For Exercises 1 and 2, simplify. 1. 3 x 7 y 2 x 3 y 5 2. 5( x 6) 2 x 10 For Exercises 3 and 4, evaluate. 3. 3 x 2 2 x 6 when x 5 4. E 0.2381 I 2 Rt when I 30, R 5, and t 80 For Exercises 5 and 6, solve the equation. 5. 3 x 5(2 x 10) 59 6. 2( y 6) 7 4( y 16) 7. Solve: F mv 2 r for r 8. Solve for y : 3 x 2 y 10
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344 Chapter 6 Topics in Algebra For Exercises 9 and 10, solve the inequality. 9. 4 3xx1010. 2(y3) 5y12For Exercises 11 and 12, solve the proportion.11. x_916_3612. 3_715_For Exercises 13 and 14, find the product.13. (x8)(2x3)14. (3x5)(4x7)For Exercises 15–17, solve by factoring.15. x214x51 16. t212t40 17. 6x2x12For Exercises 18 and 19, solve using the quadratic formula.18. 3x2x1 19. 5y22y320. A person has invested part of $5,000 in stocks paying a 4% dividend and the rest in stocks paying a 6% dividend. If the total of the dividends was $270, how much did the person invest in each stock?21. A person invested part of $3,000 at 6% interest and the rest at 8% interest. If the interest was $190, how much money was invested at each rate?22. Ava purchased two jump drives for $57. How many jump drives can be purchased for $228?23. If you can bike 2 miles in 12 12minutes, how many hours will it take to bike 210 miles without counting rest stops?24. The number of vibrations per second of a metal string varies directly with the square root of the tension when all other factors remain unchanged. Find the number of vibrations per second of a string under a tension of 64 pounds when a string under a tension of 25 pounds makes 125 vibrations per second.25. The number of hours it takes to do a certain job varies inversely with the number of people working on the job. If it takes 12 people 8 hours to build a front porch on a Habitat for Humanity house, how many hours will it take 8 people to build a porch?26. The product of two consecutive even numbers is 624. Find the numbers. (Hint:Consecutive even numbers can be represented by xand x2.)27. A board game is played on a rectangular board whose area is 96 square inches. If the length is 4 inches longer than the width, find its dimensions.Projects1. We studied two methods for solving quadratic equations in Chapter 6: factoring and the quadratic formula. The biggest advantage of the quadratic formula is that it works on everyquadratic equation, not just the ones that factor. But is it always the best choice?(a) Solve the equation x2x6 0 using factoring. Use a stopwatch or timer to time how long it takes, then check your solution.(b) Solve the same equation, this time using the quadratic formula. Again, time yourself, and note whether you got the correct solution.(c) Repeat parts aand bfor each of the equations below.x23x4 2x2x15 3x220x7 (d) Compute your average time for each method on all four equations, then calculate the percentage of problems that you got right using each method. Which method overall would you say was more efficient, and why?(e) Repeat parts (a) through (d) for the four equations below.x22x80 4x226x48 6x255x50 2x212x144 (f) Was your decision on which method is more efficient different for the second group of equations? Write a general conclusion about the value of each method based on all of your results.2. An interesting method for solving quadratic equations came from India. The steps are1. Move the constant term to the right side of the equation.2. Multiply each term in the equation by four times the coefficient of the x2term.3. Square the coefficient of the original xterm and add it to both sides of the equation. x 0 27 0 0 0 0 0 0 0 0
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