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ANSWER: Study Guide and Review - Chapter 7 6 4 36x y Simplify each expression. 3 11. x ⋅ x ⋅ x 5 3 3 2 15. [(2r t) ] SOLUTION: SOLUTION: ANSWER: x 9 ANSWER: 18 6 64r t 2 5 12. (2xy)( −3x y ) SOLUTION: 3 16. (−2u )(5u) SOLUTION: ANSWER: ANSWER: 3 6 −6x y −10u 4 4 5 2 13. (−4ab )(−5a b ) 2 3 3 3 17. (2x ) (x ) SOLUTION: SOLUTION: ANSWER: 6 6 20a b 3 2 2 14. (6x y ) ANSWER: SOLUTION: 8x 3 3 18. ANSWER: 15 (2x ) SOLUTION: 6 4 36x y 3 3 2 15. [(2r t) ] SOLUTION: ANSWER: 4x 9 eSolutions Manual - Powered by Cognero Page 1 2 19. GEOMETRY Use the formula V = πr h to find the volume of the cylinder. ANSWER: ANSWER: Study Guide and Review - Chapter 7 15 8x 45πx Simplify each expression. Assume that no denominator equals zero. 3 3 18. 4 (2x ) 20. SOLUTION: SOLUTION: ANSWER: 4x 9 2 19. GEOMETRY Use the formula V = πr h to find the volume of the cylinder. SOLUTION: ANSWER: 21. SOLUTION: ANSWER: 45πx ANSWER: 4 Simplify each expression. Assume that no denominator equals zero. 20. 22. SOLUTION: SOLUTION: ANSWER: eSolutions Manual - Powered by Cognero ANSWER: 4y −3 0 6 23. a b c Page 2 ANSWER: ANSWER: Study Guide and Review - Chapter 7 25. 22. SOLUTION: SOLUTION: ANSWER: 4y ANSWER: −3 0 6 x 23. a b c 6 SOLUTION: 26. SOLUTION: ANSWER: 24. SOLUTION: ANSWER: 1 27. ANSWER: SOLUTION: 25. SOLUTION: ANSWER: eSolutions Manual - Powered by Cognero 3 2 Page 4 28. GEOMETRY The area of a rectangle is 25x y square feet. The width of the rectangle is 5xy feet. What is the length of the rectangle? ANSWER: ANSWER: 3 Study Guide and Review - Chapter 7 2 4 28. GEOMETRY The area of a rectangle is 25x y square feet. The width of the rectangle is 5xy feet. What is the length of the rectangle? 31. SOLUTION: SOLUTION: ANSWER: 5 32. SOLUTION: 3 The length of the rectangle is 5xy ft. ANSWER: 3 5xy ft ANSWER: Simplify. 29. SOLUTION: 33. SOLUTION: ANSWER: 7 30. ANSWER: 64 SOLUTION: 34. ANSWER: 3 SOLUTION: 31. SOLUTION: ANSWER: 4 eSolutions Manual - Powered by Cognero 35. Page 4 ANSWER: Study Guide and Review - Chapter 7 64 ANSWER: Solve each equation. 34. x 37. 6 = 7776 SOLUTION: SOLUTION: Therefore, the solution is 5. ANSWER: 4 35. ANSWER: 5 4x – 1 SOLUTION: 38. 4 = 32 SOLUTION: ANSWER: 2401 Therefore, the solution is . 36. SOLUTION: ANSWER: Express each number in scientific notation. 39. 2,300,000 ANSWER: SOLUTION: 2,300,000 → 2.300000 The decimal point moved 6 places to the left, so n = 6. 6 2,300,000 = 2.3 × 10 Solve each equation. x 37. 6 = 7776 SOLUTION: Therefore, solution is 5. eSolutions Manual -the Powered by Cognero ANSWER: 5 ANSWER: 6 2.3 × 10 40. 0.0000543 SOLUTION: 0.0000543 → 5.43 The decimal point moved 5 places to the right, so n = –5. −5 0.0000543 = 5.43 × 10 ANSWER: −5 Page 5 In scientific notation, the ratio of Earth’s diameter to 6 2,300,000 = 2.3 × 10 −2 Jupiter’s diameter is about 9.1 × 10 . ANSWER: Study Guide6 and Review - Chapter 7 2.3 × 10 40. 0.0000543 SOLUTION: 0.0000543 → 5.43 The decimal point moved 5 places to the right, so n = –5. −5 0.0000543 = 5.43 × 10 ANSWER: 5.43 × 10 −5 41. ASTRONOMY Earth has a diameter of about 8000 miles. Jupiter has a diameter of about 88,000 miles. Write in scientific notation the ratio of Earth’s diameter to Jupiter’s diameter. ANSWER: −2 about 9.1 × 10 Graph each function. Find the y-intercept, and state the domain and range. x 42. y = 2 SOLUTION: Complete a table of values for –2 < x < 2. Connect the points on the graph with a smooth curve. x x y 2 2 –1 2 0 2 1 2 2 2 SOLUTION: 3 Earth: 8000 = 8.0 × 10 4 Jupiter: 88,000 = 8.8 × 10 In scientific notation, the ratio of Earth’s diameter to −2 Jupiter’s diameter is about 9.1 × 10 . ANSWER: −2 about 9.1 × 10 Graph each function. Find the y-intercept, and state the domain and range. –2 –2 –1 0 1 1 2 2 4 The graph crosses the y-axis at 1. The domain is all real numbers, and the range is all real numbers greater than 0. ANSWER: 1; D = all real numbers; R = {y| y > 0} x 42. y = 2 SOLUTION: Complete a table of values for –2 < x < 2. Connect the points on the graph with a smooth curve. x x y 2 –2 –2 2 –1 2 0 2 1 2 –1 x 43. y = 3 + 1 0 1 1 2 2 - Powered by22Cognero eSolutions Manual 4 SOLUTION: Complete a table of values for –2 < x < 2. Connect the points on the graph with a smooth curve. Page 6 x x y 3 +1 –2 –2 3 +1 Study Guide and Review - Chapter 7 x x 43. y = 3 + 1 44. y = 4 + 2 SOLUTION: Complete a table of values for –2 < x < 2. Connect the points on the graph with a smooth curve. x x y 3 +1 –2 +1 –2 4 –1 +1 –1 4 0 4 +2 1 4 +2 2 4 +2 –2 3 –1 3 0 3 +1 1 2 SOLUTION: Complete a table of values for –2 < x < 2. Connect the points on the graph with a smooth curve. x x y 4 +2 0 2 1 4 2 10 3 +1 3 +1 The graph crosses the y-axis at 2. The domain is all real numbers, and the range is all real numbers greater than 1. ANSWER: 2; D = all real numbers; R = {y| y >1} –2 –1 +2 +2 0 3 1 6 2 18 The graph crosses the y-axis at 3. The domain is all real numbers, and the range is all real numbers greater than 2. ANSWER: 3; D = all real numbers; R = {y| y > 2} x 44. y = 4 + 2 x SOLUTION: Complete a table of values for –2 < x < 2. Connect the points on the graph with a smooth curve. x x y 4 +2 –2 –2 eSolutions Manual - Powered4by Cognero +2 –1 –1 4 +2 45. y = 2 − 3 SOLUTION: Complete a table of values for –2 < x < 2. Connect the points on the graph with a smooth curve. x x 2 –3 –2 2 –2 –3 y Page 7 Study Guide and Review - Chapter 7 x 45. y = 2 − 3 SOLUTION: Complete a table of values for –2 < x < 2. Connect the points on the graph with a smooth curve. x x 2 –3 –2 2 –1 2 0 2 –3 1 2 –3 2 2 –3 –2 –3 –1 –3 y 0 –2 1 –1 2 1 46. BIOLOGY The population of bacteria in a petri dish increases according to the model p = 550(2.7) 0.008t , where t is the number of hours and t = 0 corresponds to 1:00 P.M. Use this model to estimate the number of bacteria in the dish at 5:00 P.M. SOLUTION: If t = 0 corresponds to 1:00 P.M, then t = 4 represents 5:00 P.M. There will be about 568 bacteria in the dish at 5:00 P.M. ANSWER: about 568 47. Find the final value of $2500 invested at an interest rate of 2% compounded monthly for 10 years. SOLUTION: Use the equation for compound interest, with P = 2500, r = 0.02, n = 12, and t = 10. The graph crosses the y-axis at –2. The domain is all real numbers, and the range is all real numbers greater than –3. ANSWER: −2; D = all real numbers; R = {y| y > −3} The final value of the investment is about $3053.00. ANSWER: $3053.00 46. BIOLOGY The population of bacteria in a petri dish increases according to the model p = 550(2.7) 0.008t , where t is the number of hours and t = 0 corresponds to 1:00 P.M. Use this model to estimate the number of bacteria in the dish at 5:00 P.M. 48. COMPUTERS Zita’s computer is depreciating at a rate of 3% per year. She bought the computer for $1200. a. Write an equation to represent this situation. b. What will the computer’s value be after 5 years? SOLUTION: a. Use the equation for exponential decay, with a = 1200 and r = 0.03. eSolutions Manual - Powered by Cognero SOLUTION: If t = 0 corresponds to 1:00 P.M, then t = 4 represents 5:00 P.M. Page 8 The equation that represents the depreciation of t The final value of the investment is about $3053.00. ANSWER: Study Guide and Review - Chapter 7 $3053.00 48. COMPUTERS Zita’s computer is depreciating at a rate of 3% per year. She bought the computer for $1200. a. Write an equation to represent this situation. b. What will the computer’s value be after 5 years? SOLUTION: a. Use the equation for exponential decay, with a = 1200 and r = 0.03. The equation that represents the depreciation of t Zita’s computer is y = 1200(1 − 0.03) . b. Substitute 5 for t and solve. –1. ANSWER: −1, 1, −1 50. 3, 9, 27 ... SOLUTION: Calculate the common ratio. The common ratio is 3. Multiply each term by the common ratio to find the next three terms. 27 × 3 = 81 81 × 3 = 243 243 × 3 = 729 The next three terms of the sequence are 81, 243, and 729. ANSWER: 81, 243, 729 51. 256, 128, 64, ... After 5 years, Zita’s computer value is about $1030.48. SOLUTION: Calculate the common ratio. ANSWER: t a. 1200(1 − 0.03) b. $1030.48 Find the next three terms in each geometric sequence. 49. −1, 1, −1, 1, ... SOLUTION: Calculate the common ratio. The common ratio is –1. Multiply each term by the common ratio to find the next three terms. 1 × –1 = –1 –1 × –1 = 1 1 × –1 = –1 The next three terms of the sequence are –1, 1, and –1. ANSWER: −1, 1, −1 The common ratio is . Multiply each term by the common ratio to find the next three terms. 64 × = 32 32 × = 16 16 × = 8 The next three terms of the sequence are 32, 16, and 8. ANSWER: 32, 16, 8 Write the equation for the nth term of each geometric sequence. 52. −1, 1, −1, 1, ... SOLUTION: The first term of the sequence is –1. So, a 1 = –1. Calculate the common ratio. 50. 3, 9, 27 ... SOLUTION: Calculate common ratio. eSolutions Manualthe - Powered by Cognero The common ratio is –1. So, r = –1. Page 9 The next three terms of the sequence are 32, 16, and 8. ANSWER: Study Guide and Review - Chapter 7 32, 16, 8 Write the equation for the nth term of each geometric sequence. 52. −1, 1, −1, 1, ... SOLUTION: The first term of the sequence is –1. So, a 1 = –1. Calculate the common ratio. The common ratio is –1. So, r = –1. ANSWER: n−1 a n = 3(3) 54. 256, 128, 64, ... SOLUTION: The first term of the sequence is 256. So, a 1 = 256. Calculate the common ratio. The common ratio is . So, r = . ANSWER: ANSWER: n−1 a n = −1(−1) 53. 3, 9, 27, ... SOLUTION: The first term of the sequence is 3. So, a 1 = 3. Calculate the common ratio. The common ratio is 3. So, r = 3. ANSWER: n−1 a n = 3(3) 54. 256, 128, 64, ... SOLUTION: The first term of the sequence is 256. So, a 1 = 256. Calculate the common ratio. The common ratio is . So, r = eSolutions Manual - Powered by Cognero ANSWER: . Page 10