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Problem Packet for Class Practice 6.5-7.4 #1 Intermediate Algebra / MAT 135 Spring 2017 Master ( Master Templates) Student Name/ID: 1. Divide. 2 8 x + 24 x + 22 ÷ 2 x + 3 Your answer should give the quotient and the remainder. Quotient: Remainder: 2. Divide. 3 2 8 x − 14 x + 20 x + 2 ÷ 4 x + 1 Your answer should give the quotient and the remainder. Quotient: Remainder: 3. Divide. 5 x 4 + 14 x 3 − 3 x 2 − 15 x + 10 ÷ − x 2 − 2 x + 1 Write your answer in the following form: Quotient 5 x 4 + 14 x 3 − 3 x 2 − 15 x + 10 2 −x − 2 x + 1 Problem Packet for Class Practice 6.5-7.4 #1 Page 1 / 18 = + + Remainder . 2 −x − 2 x + 1 −x 2 − 2 x + 1 4 3Copyright © 2016 2 UC Regents and ALEKS Corporation 4. Use synthetic division to find the quotient and remainder when −7 x 4 − 11 x 3 + 8 x 2 + 10 x + 4 is divided by x + 2 . Specifically, complete the synthetic division table below, and write your answer in the following form: Quotient + Remainder −2 −7 x +2 −11 8 . 10 4 −7 x 4 − 11 x 3 + 8 x 2 + 10 x + 4 = x +2 5. Use the remainder theorem to find P 2 for + x +2 4 3 2 P x = −2 x + 3 x + 6 x − 5 . Specifically, give the quotient and the remainder for the associated division and the value of P 2 . 6. Solve for v . 5 v −2 = 3 4 Simplify your answer as much as possible. 7. Solve for x . 4 8 = x −4 x −5 Problem Packet for Class Practice 6.5-7.4 #1 Page 2 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 8. Solve for y . 2 3 − =1 5y y 9. Solve for w. 4 w −3 = w −4 w −4 10. Solve for x . 3 2 x − 9 x + 18 = 1 5 + x −6 x −3 11. Solve for x . −2 x = x +4 x +7 12. Solve for u+ 9 u u. =7 − 3 u Problem Packet for Class Practice 6.5-7.4 #1 Page 3 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 13. Solve for y . y +2 y +3 = −1 y −2 y +4 14. Solve for w. 6 12 w + = 2 w − 5 w − 3 w − 8 w + 15 15. Solve for u. 3u 18 =− 2 u −3 u − 10 u + 21 16. A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 159 129 pounds requires 212 milligrams of medicine. What is the amount of medicine required by a patient weighing pounds? 17. Solve for n 2. w w + =5 n1 n2 18. There are two machines that produce aluminum cans. The newer machine can produce 5400 cans in 180 270 minutes to produce that many cans. If the two machines work together, how long will it take them to produce 5400 cans? minutes. It takes the older machine Problem Packet for Class Practice 6.5-7.4 #1 Page 4 / 18 60 Copyright © 2016 UC Regents and ALEKS Corporation 19. A company has two large computers. The slower computer can send all the company's email in The faster computer can complete the same job in will it take them to do the job? 20 60 minutes. minutes. If both computers are working together, how long Do not do any rounding. 5 kilometers against the current in the same amount of time it took him to swim 15 kilometers with the current. The rate of the current was 2 kilometers per hour. How fast would Omar swim if there were no 20. Omar swam current? 21. Simplify each expression. Assume that the variables represent any real numbers. w 26 = ____ 6 = ____ z 22. Evaluate the following. (a) (b) − 4 81 = ____ 3 −64 = ____ 23. Simplify. 4 1 16 Be sure to write your answer in lowest terms. Problem Packet for Class Practice 6.5-7.4 #1 Page 5 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 24. Simplify. 5 32 w 35 Assume that the variable represents a positive real number. 25. Simplify each radical expression as much as possible. Assume that the variables represent any real numbers. (a) (b) 5 6 5 x = 5 −z ____ 6 = ____ 26. Find the domain of the function. f x = −x + 8 Write your answer using interval notation. 27. Find the domains of the functions f and f x = 4 g x = 3 g. x +7 2x +8 Write your answers using interval notation. 28. Simplify. 12 y 16 Assume that the variable y represents a positive real number. Problem Packet for Class Practice 6.5-7.4 #1 Page 6 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 29. Simplify. 63 w 15 Assume that the variable represents a positive real number. 30. Simplify. 54 t 7 u 10 Assume that all variables represent positive real numbers. 31. Write the following in simplified radical form. 4 243 32. Write the following in simplified radical form. 3 u 5 Assume that the variable represents a positive real number. 33. Write the following in simplified radical form. 4 16 w 10 Assume that the variable represents a positive real number. 34. Write the following expression in simplified radical form. 4 5 4 32 t u Assume that all of the variables in the expression represent positive real numbers. Problem Packet for Class Practice 6.5-7.4 #1 Page 7 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 35. Write the following as an exponential expression. 7 b 2 36. Evaluate. 1 4 256 = ____ = ____ 1 3 27 37. Evaluate the following. −16 (a) −27 (b) 1 2 1 3 = = 38. Simplify. 25 3 2 39. Simplify. Write your answers without exponents. 125 1 8 − 2 3 2 3 = = Problem Packet for Class Practice 6.5-7.4 #1 Page 8 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 40. Simplify. 3 1 5 u 3 ·u Assume that the variable represents a positive real number. 41. Simplify. v 1 8 3 v 4 Write your answer using only a positive exponent. Assume that the variable represents a positive real number. 42. Simplify the expression. y − 1 2 y 1 3 1 y 4 Write your answer using only positive exponents. Assume that all variables are positive real numbers. 43. Simplify. u 9 7 5 6 Write your answer without parentheses. Assume that the variable represents a positive real number. Problem Packet for Class Practice 6.5-7.4 #1 Page 9 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 44. Simplify the expression. c −2 ·a 1 5 4 5 Write your answer without using negative exponents. Assume that all variables are positive real numbers. 45. Simplify. 45 w + 20 w Assume that the variable represents a positive real number. 46. Simplify. 3 45 w + 3 w 80 w Assume that the variable represents a positive real number. 47. Simplify as much as possible. 5 8y 63 x + x 2 7x y 2 Assume that all variables represent positive real numbers. 48. Simplify. − 3 375 x 4 + 3 3 81 x 4 Assume that the variable represents a positive real number. 49. Simplify. 45 × 2 20 Problem Packet for Class Practice 6.5-7.4 #1 Page 10 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 50. Simplify. 2v9w 8v2w2 Assume that all variables represent positive real numbers. 51. Simplify. 5 4 5 8u · 12 u 3 Assume that the variable represents a positive real number. 52. Multiply and simplify. x− 2 x +5 2 x+ 2 = 2 = 53. Write in simplified radical form with at most one radical. 6 y· 4 y 3 Assume that the variable represents a positive real number. 54. Rationalize the denominator and simplify. 9 5 Problem Packet for Class Practice 6.5-7.4 #1 Page 11 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 55. Rationalize the denominator and simplify. 3 15 56. Rationalize the denominator and simplify. 9 3 3 +2 57. Rationalize the denominator and simplify. 11 + 2 11 − 2 58. Rationalize the denominator and simplify. −7 2 v +1 Assume that the variable represents a positive real number. 59. Rationalize the denominator and simplify. 5 3 2 Problem Packet for Class Practice 6.5-7.4 #1 Page 12 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 60. Rationalize the denominator and simplify. 3 3 25 u 2 x 11 Assume that all variables represent positive numbers. Problem Packet for Class Practice 6.5-7.4 #1 Page 13 / 18 Copyright © 2016 UC Regents and ALEKS Corporation Problem Packet for Class Practice 6.5-7.4 #1 Answers for class MAT 135 Spring 2017 Master 1. Quotient: 4x +6 Remainder: 4 2. Quotient: 2x2 −4x +6 Remainder: −4 3. 5 x 4 + 14 x 3 − 3 x 2 − 15 x + 10 −x 2 − 2 x + 1 = −5 x 2 − 4 x + 6 + 4. −2 −7 −7 −11 14 3 x +4 −x 2 − 2 x + 1 8 −6 2 10 −4 6 4 −12 −8 −7 x 4 − 11 x 3 + 8 x 2 + 10 x + 4 −8 = −7 x 3 + 3 x 2 + 2 x + 6 + . x +2 x +2 5. Quotient = −2 x 3 2 −x +4x +8 Remainder =11 P 2 =11 6. v = 26 3 7. x = 3 13 Problem Packet for Class Practice 6.5-7.4 #1 Page 14 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 13 5 8. y = − 9. No solution 10. No solution 11. x = −8 , 12. u = 4 , −1 3 13. y = −1 , −6 14. w = −6 15. u = 1 , 6 16. 172 milligrams 17. n 2 = n1w 5n1 −w 18. 108 minutes 19. 15 minutes 20. Rate he swam with no current: 4 kilometers/hour 21. w = w 13 26 3 z 6 = z − 4 81 = −3 3 −64 = −4 22. (a) (b) 23. 1 2 7 Problem Packet for Class Practice 6.5-7.4 #1 Page 15 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 24. 2 w 7 25. (a) (b) 5 5 x =x 6 26. 6 5 −z = 5 −z − ∞, 8 27. Domain of f: −7 , ∞ Domain of g : − ∞, ∞ 28. 2 y 8 3 7 7w 29. 3 w 30. 3 t 3 5 31. 3 4 32. u 3 3 33. 2 w u 2 2 4 34. 2 t u 35. b 6t u 4 w 2 2t 2 7 36. 1 256 27 4 1 3 =4 =3 Problem Packet for Class Practice 6.5-7.4 #1 Page 16 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 37. 1 −16 (a) 2 = −4 1 −27 (b) 3 = −3 38. 125 39. 125 2 3 − = 1 25 = 1 4 2 1 8 3 14 15 40. u 1 41. 5 8 v 1 42. 5 12 y 15 14 43. u 4 44. a 2 c 45. 5 25 5 5w 46. 15 w 2 5w Problem Packet for Class Practice 6.5-7.4 #1 Page 17 / 18 Copyright © 2016 UC Regents and ALEKS Corporation 2 y 3 3x 47. 25 x 48. 4 x 7x 49. 60 50. 4 v 5 w 5 51. 2 u vw 3u2 52. x− 2 x +5 2 53. 12 y 9 5 5 55. 5 5 27 2 = x + 10 3 − 18 23 57. 13 + 2 22 9 58. −14 v + 7 4v −1 59. 5 3 60. 2 x + 50 11 54. 56. x + 2 =x −2 3 2 4 100 u x 2x4 Problem Packet for Class Practice 6.5-7.4 #1 Page 18 / 18 Copyright © 2016 UC Regents and ALEKS Corporation