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solving = x + 5, you would have 2x + 4 = x + 10x + 25. The statement is true. ANSWER: true Study Guide and Review - Chapter 10 State whether each sentence is true or false . If false , replace the underlined word, phrase, expression, or number to make a true sentence. 2. The expressions and are equivalent. 10. The range of the function is . SOLUTION: The range of the function the statement is false. is {y|y ≥ 0}. So, SOLUTION: ANSWER: false; false; ANSWER: Graph each function. Compare to the parent graph. State the domain and range. false; 12. y = 4. In the expression −5 2 , the radicand is 2. SOLUTION: The expression under the radical sign is called the radicand. In the expression , the radicand is 2. The statement is true. ANSWER: true + 2 SOLUTION: Make a table. x 0 0.5 y 2 ≈ 2.7 1 3 2 ≈ 3.4 3 ≈ 3.7 4 4 Plot the points on a coordinate system and draw a smooth curve that connects then. 6. The cosine of an angle is found by dividing the measure of the side opposite to the angle by the hypotenuse. SOLUTION: The sine of an angle is found by dividing the measure of the side opposite of the angle by the hypotenuse. So, the statement is false. The cosine of an angle is found by dividing the measure of the side adjacent to the angle by the hypotenuse. ANSWER: false; adjacent 8. After the first step in solving = x + 5, you 2 would have 2x + 4 = x + 10x + 25. SOLUTION: To solve = x + 5, you first need to square each side of the equation. After the first step in 2 solving = x + 5, you would have 2x + 4 = x + 10x + 25. The statement is true. The value 2 is being added to the parent function , so the graph is translated up 2 units from the parent graph . Another way to identify the translation is to note that the y-values in the table are 2 greater than the corresponding y-values for the parent function. The domain is {x|x ≥ 0} and the range is {y|y ≥ 2}. ANSWER: translated up 2; D = {x|x ≥ 0}, R = {y|y ≥ 2} ANSWER: true 10. The range of the function is . eSolutions Manual - Powered by Cognero SOLUTION: The range of the function the statement is false. Page 1 is {y|y ≥ 0}. So, the statement is false. ANSWER: Study Guide and Review - Chapter 10 false; Graph each function. Compare to the parent graph. State the domain and range. 12. y = − 6 SOLUTION: x 0 0.5 y –6 ≈ – 5.3 + 2 SOLUTION: Make a table. x 0 0.5 y 2 ≈ 2.7 14. y = 1 3 2 ≈ 3.4 3 ≈ 3.7 1 –5 2 ≈ – 4.6 3 ≈ – 4.3 4 –4 4 4 Plot the points on a coordinate system and draw a smooth curve that connects then. The value 6 is being subtracted from the parent function , so the graph is translated down 6 The value 2 is being added to the parent function , so the graph is translated up 2 units from the parent graph . Another way to identify the translation is to note that the y-values in the table are 2 greater than the corresponding y-values for the parent function. The domain is {x|x ≥ 0} and the range is {y|y ≥ 2}. units from the parent graph . Another way to identify the translation is to note that the y-values in the table are 6 less than the corresponding y-values for the parent function. The domain is {x|x ≥ 0} and the range is {y|y ≥ –6}. ANSWER: translated down 6; D = {x|x ≥ 0}, R = {y|y ≥ –6} ANSWER: translated up 2; D = {x|x ≥ 0}, R = {y|y ≥ 2} 16. y = + 5 SOLUTION: x 0 0.5 y 5 ≈ 5.7 14. y = 1 6 2 ≈ 6.4 3 ≈ 6.7 4 7 − 6 SOLUTION: x 0 0.5 y –6 ≈ – 5.3 1 –5 eSolutions Manual - Powered by Cognero 2 ≈ – 4.6 3 ≈ – 4.3 4 –4 The value 5 is being added to the parent function Page 2 , so the graph is translated up 5 units from the parent graph . Another way to identify ANSWER: Study Guide and Review - Chapter 10 16. y = + 5 SOLUTION: x 0 0.5 y 5 ≈ 5.7 20. SOLUTION: 1 6 2 ≈ 6.4 3 ≈ 6.7 4 7 ANSWER: 22. SOLUTION: The value 5 is being added to the parent function , so the graph is translated up 5 units from the parent graph . Another way to identify the translation is to note that the y-values in the table are 5 greater than the corresponding y-values for the parent function. The domain is {x|x ≥ 0} and the range is {y|y ≥ 5}. ANSWER: ANSWER: translated up 5; D = {x|x ≥ 0}, R = {y|y ≥ 5} 24. SOLUTION: Simplify. 18. SOLUTION: ANSWER: ANSWER: 26. SOLUTION: 20. eSolutions Manual - Powered by Cognero SOLUTION: Page 3 0.15 = 9, 2.15 hours is equal to 2 hours and 9 minutes. ANSWER: ANSWER: about 2.15 hours or 2 hours and 9 minutes Study Guide and Review - Chapter 10 Simplify each expression. 26. 30. SOLUTION: SOLUTION: ANSWER: 32. SOLUTION: ANSWER: −6 − 3 ANSWER: 28. WEATHER To estimate how long a thunderstorm will last, use , where t is the time in hours and d is the diameter of the storm in miles. A storm is 10 miles in diameter. How long will it last? 34. SOLUTION: SOLUTION: Substitution 10 for d. ANSWER: The storm will last about 2.15 hours. To convert 2.15 hours to hours and minutes, multiply the number of minutes in an hour by the decimal part. Because 60 • 0.15 = 9, 2.15 hours is equal to 2 hours and 9 minutes. ANSWER: about 2.15 hours or 2 hours and 9 minutes Simplify each expression. 36. MOTION The velocity of a dropped object when it hits the ground can be found using , where v is the velocity in feet per second, g is the acceleration due to gravity, and d is the distance in feet the object drops. Find the speed of a penny when it hits the ground, after being dropped from 984 feet. Use 32 feet per second squared for g. SOLUTION: Substitute 32 for g and 984 for d. 30. SOLUTION: eSolutions Manual - Powered by Cognero Page 4 ANSWER: −41 ANSWER: Study Guide and Review - Chapter 10 36. MOTION The velocity of a dropped object when it 40. hits the ground can be found using , where v is the velocity in feet per second, g is the acceleration due to gravity, and d is the distance in feet the object drops. Find the speed of a penny when it hits the ground, after being dropped from 984 feet. Use 32 feet per second squared for g. SOLUTION: SOLUTION: Substitute 32 for g and 984 for d. Check: The speed of the penny when it hits the ground is about 250.95 feet per second. ANSWER: ANSWER: about 250.95 ft/s Solve each equation. Check your solution. 42. 38. SOLUTION: SOLUTION: Check: Check: Because 10 does not satisfy the original equation, 5 is the only solution. ANSWER: −41 eSolutions Manual - Powered by Cognero 40. SOLUTION: ANSWER: 5 Determine whether each set of measures can be lengths of the sides of a right triangle. Page 5 44. 6, 8, 10 SOLUTION: Because 10 does not satisfy the original equation, 5 is the only solution. ANSWER: Study Guide and Review - Chapter 10 5 2 2 ANSWER: no Determine whether each set of measures can be lengths of the sides of a right triangle. 44. 6, 8, 10 SOLUTION: Since the measure of the longest side is 10, let c = 2 10, a = 6, and b = 8. Then determine whether c = 2 2 a +b . 48. 2, 3, 4 SOLUTION: Since the measure of the longest side is 4, let c = 4, a 2 2 2 2 No, because c ≠ a + b , a triangle with side lengths 2, 3, and 4 is not a right triangle. 2 Yes, because c = a + b , a triangle with side lengths 6, 8, and 10 is a right triangle. ANSWER: no ANSWER: yes 50. 5, 12, 13 46. 12, 16, 21 SOLUTION: Since the measure of the longest side is 21, let c = 2 21, a = 12, and b = 16. Then determine whether c = 2 2 = 2, and b = 3. Then determine whether c = a + 2 b . 2 2 2 No, because c ≠ a + b , a triangle with side lengths 12, 16, and 21 is not a right triangle. SOLUTION: Since the measure of the longest side is 13, let c = 2 13, a = 5, and b = 12. Then determine whether c = 2 2 a +b . 2 a +b . 2 2 2 Yes, because c = a + b , a triangle with side lengths 5, 12, and 13 is a right triangle. 2 2 2 No, because c ≠ a + b , a triangle with side lengths 12, 16, and 21 is not a right triangle. ANSWER: no ANSWER: yes 52. LADDER A ladder is leaning on a building. The base of the ladder is 10 feet from the building, and the ladder reaches up 15 feet on the building. How long is the ladder? 48. 2, 3, 4 SOLUTION: Since the measure of the longest side is 4, let c = 4, a 2 2 = 2, and b = 3. Then determine whether c = a + 2 b . SOLUTION: Use the Pythagorean Theorem, substituting 10 for a and 15 for b. 2 2by Cognero 2 eSolutions Manual - Powered No, because c ≠ a + b , a triangle with side lengths 2, 3, and 4 is not a right triangle. Page 6 The ladder is approximately 18.0 feet long. ANSWER: 2 2 2 Yes, because c = a + b , a triangle with side lengths 5, 12, and 13 is a right triangle. ANSWER: Study Guide and Review - Chapter 10 yes 52. LADDER A ladder is leaning on a building. The base of the ladder is 10 feet from the building, and the ladder reaches up 15 feet on the building. How long is the ladder? SOLUTION: Use the Pythagorean Theorem, substituting 10 for a and 15 for b. The ladder is approximately 18.0 feet long. ANSWER: 18.0 ft Find the values of the three trigonometric ratios for angle A . 54. SOLUTION: ANSWER: eSolutions Manual - Powered by Cognero Page 7