104 CHAPTER R Review of Basic Concepts 12. Identify each property illustrated. Let a, b, and c represent any real numbers. (a) a + 1b + c2 = 1a + b2 + c (b) a + 1c + b2 = a + 1b + c2 (c) a1b + c2 = ab + ac (d) a + 3b + 1-b24 = a + 0 Perform the indicated operations. 13. 1x2 - 3x + 22 - 1x - 4x22 14. 16r - 522 15. 1t + 2213t2 - t + 42 16. 2x3 - 11x2 + 28 x - 5 (Modeling) Adjusted Poverty Threshold The adjusted poverty threshold for a single person between the years 2000 and 2017 can be approximated by the formula y = -4.529x2 + 301.7x + 8660, where x = 0 corresponds to 2000, x = 1 corresponds to 2001, and so on, and the adjusted poverty threshold amount, y, is in dollars. According to this model, what was the adjusted poverty threshold, to the nearest dollar, in each given year? (Data from U.S. Census Bureau.) 17. 2010 18. 2017 Factor completely. 19. 6x2 - 17x + 7 20. x4 - 16 21. 24m3 - 14m2 - 24m 22. x3y2 - 9x3 - 8y2 + 72 23. 1a - b22 + 21a - b2 24. 1 - 27x6 Perform the indicated operations. 25. 5x2 - 9x - 2 30x3 + 6x2 , x4 - 3x2 - 4 2x8 + 6x7 + 4x6 26. x x2 + 3x + 2 + 2x 2x2 - x - 3 27. a + b 2a - 3 - a - b 3 - 2a 28. y - 2 y - 4 y Simplify or evaluate as appropriate. Assume all variables represent positive real numbers. 29. 218x5y8 30. 232x + 22x - 218x 31. A 2x - 2y B A 2x + 2y B 32. 14 211 - 27 33. a x-2y-1/3 x-5/3y-2/3b 3 34. a- 64 27b -2/3 35. (Modeling) Period of a Pendulum The period t, in seconds, of the swing of a pendulum is given by the formula t = 2p BL 32 , where L is the length of the pendulum in feet. Find the period of a pendulum 3.5 ft long. Round the answer to the nearest tenth. L
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