406 CHAPTER 6 Algebra, Graphs, and Functions 6.1 In Exercises 1– 4, evaluate the expression for the given value(s) of the variable. 1. x x x 10 , 3 2 + = 39 2. x x 5, 2 2 − − = − −9 3. x x x 3 2 7, 2 2 − + = 15 4. x x x x 4 7 3 1, 1 3 2 + − + = − 7 In Exercises 5 and 6, combine like terms. 5. x x 3 9 6 − + + − x4 3 6. x x x 2 3( 2) 7 + − + − x 12 6 In Exercises 7–10, solve the equation for the given variable. 7. t4 8 12 + = − −5 8. − = + + x x 4( 2) 3 5( 4) −31 9. x x 5 2 3 4 + = − −13 10. x x 2 5 1 4 + = + 3 6.2 In Exercises 11–14, use the formula to determine the value of the indicated variable for the values given. 11. F ma = Determine F when m 40 = and a 5 = (physics). 200 12. v lwh = 210 Determine v when l w h 10, 7, and 3 (geometry). = = = 13. z x n μ σ = − Determine x when z 2, 100, 3, μ σ = = = and n 16 = (statistics). 101.5 14. E mc2 = Determine m when E 400 = and c 4 (physics). = 25 In Exercises 15 and 16, solve for y. 15. x y 8 4 16 − = = − y x2 4 16. x y 2 9 17 + = y x y x 2 17 9 or 2 9 17 9 = − + = − + In Exercises 17 and 18, solve for the variable indicated. 17. A lw w , for = = w A l 18. L wh lh l 2( ), for = + = − = − l L wh h l L h w 2 2 or 2 Review Exercises CHAPTER 6 6.3 In Exercises 19 and 20, write the phrase in mathematical terms. 19. 5, increased by 3 times x + x 5 3 20. The difference between 9 divided by q and 15 − q 9 15 In Exercises 21–24, write an equation that can be used to solve the problems. Solve the equation and determine the desired value(s). 21. Three, increased by 7 times a number is 17. + = = x x 3 7 17; 2 22. The product of 3 and a number, increased by 8, is 6 less than the number. + = − = − x x x 3 8 6; 7 23. Five times the difference of a number and 4 is 45. − = = x x 5( 4) 45; 13 24. Fourteen more than 10 times a number is 8 times the sum of the number and 12. + = + = x x x 10 14 8( 12); 41 In Exercises 25–28, write the equation and then determine the solution. 25. MODELING—Investing Jim received an inheritance of $15,000. If he wants to invest twice as much money in mutual funds as in bonds, how much should he invest in mutual funds? + = x x2 15,000; bonds: $5000, mutual funds: $10,000 26. MODELING—Restaurant Profit John owns two restaurants. His profit for a year at restaurant A is $15,000 greater than his profit at restaurant B. The total profit from both restaurants is $75,000. Determine the profit at each restaurant. + + = x x( 15,000) 75,000; $30,000 for B and $45,000 for A 27. Making Oatmeal A recipe for Hot Oats Cereal calls for 2 cups of water and for 1 3 cup of dry oats. How many cups of dry oats would be used with 3 cups of water? 1 2 cup 28. Laying Blocks A mason lays 120 blocks in 1 hr 40 min. How long will it take to lay 300 blocks? 250 min, or 4 hr 10 min 6.4 In Exercises 29–32, determine the quantity indicated. 29. s is directly proportional to t. If s 60 = when t 10, = determine s when t 12. = 72 30. J is inversely proportional to the square of A. If J 25 = when A 2, = determine J when A 5. = 4 31. W is directly proportional to L and inversely proportional to A. If W 80 = when L 100 = and A 20, = determine W when L 50 = and A 40. = 20 32. z is jointly proportional to x and y and inversely proportional to the square of r. If z 12 = when x y 20, 8, = = and r 8, = determine z when x y 10, 80, = = and r 3. = ≈ 426.7 $ $
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