Complete the square for each expression to obtain a perfect square trinomial. Then, factor. 11) r2 10r 12) z2 12z 13) c2 5c 14) x2 x 15) a2 2 3 a 16) d 2 5 2 d Solve by completing the square. 17) p2 6p 16 0 18) w2 2w 35 0 19) n2 10n 6 20) t2 9 4t 21) f 2 3f 1 0 22) j2 7j 4 23) 3q2 7q 12 24) 6v2 15v 3 0 (10.2) Solve using the quadratic formula. 25) m2 4m 12 0 26) 3y2 10y 8 27) 10g 5 2g2 28) 20 4x 5x2 29) 1 6 t2 1 3 t 2 3 0 30) (s 3)(s 5) 9 31) (6r 1)(r 4) 2(12r 1) 32) z2 3 2 z 13 16 0 Find the value of the discriminant. Then, determine the number and type of solutions of each equation. Do not solve. 33) 3n2 2n 5 0 34) t2 3(t 2) 35) Find the value of b so that 4k2 bk 9 0 has only one rational solution. 36) A ball is thrown upward from a height of 4 ft. The height, h(t), of the ball (in feet) t sec after the ball is released is given by h(t) 16t2 52t 4. a) How long does it take the ball to reach a height of 16 ft? b) How long does it take the ball to hit the ground? (10.1–10.2) Keep in mind the four methods we have learned for solving quadratic equations: factoring, the square root property, completing the square, and the quadratic formula. Solve the equations using one of these methods. 37) 3k2 4 7k 38) n2 6n 11 0 39) 15 3 (y 8)2 40) (2a 1)(a 2) 14 41) 1 3 w2 w 5 6 42) 4t2 5 7 43) 6 p(p 10) 2(4p 15) 44) 6 2m 3m2 45) x3 x 46) 1 12 b2 9 2 1 4 b 47) Let f (x) (2x 1)2. Find all values of x so that f (x) 25. 48) Let f (x) 1 10 x2 3x and g(x) 4x 11 5 . Find all values of x such that f (x) g(x). (10.3) Solve. 49) 5k k 1 3k 4 50) 10 m 3 8 m2 51) f 17f 12 52) x 41x 5 53) n4 17n2 16 0 54) b4 5b2 14 0 55) q2/3 2q1/3 3 0 56) y 2 3y1/2 57) 2r4 7r2 2 58) 2(v 2)2 (v 2) 3 0 59) (2k 5)2 5(2k 5) 6 0 Write an equation, and solve. 60) At the end of the day, the employees at Forever Young have to put all clothes left in the dressing room back to their proper places. Working together, Lorena and Erica can put away the clothes in 1 hr 12 min. On her own, it takes Lorena 1 hr longer to put away the clothes than it takes Erica to do it by herself. How long does it take each girl to put away the clothes by herself ? (10.4) Solve for the indicated variable. 61) F mv2 r for v 62) U 1 2 kx2 for x 63) r B A p for A 64) r B V pl for V 65) kn2 ln m 0 for n 66) 2p2 t rp for p www.mhhe.com/messersmith CHAPTER 10 Review Exercises 697
messersmith_power_intermediate_algebra_1e_ch4_7_10
To see the actual publication please follow the link above