Practice Lesson 11-1 Practice Algebra 1 Chapter 11 "256 "32 "96. "65 "2a "13. "48n. "6n 3 "180. "25x 2 "48 "10 "60 "12. "8x 6 y 7.

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1 Practice 11-1 Simplifying Radicals Simplify each radical epression. 1. "32 2. "22? "8 3. " "a 2 b 5 Ä " "80 8. " "6 "32 "7 " " " "15? "6 "12 Ä 225 " " Q3"2R " "2a " " "48s " "15? "35 Ä 225 "48n 26. " " "3 "6n 3 Ä 256 " "m 3 n "18? " Q10"3R 2 "9 Å " " " " "48 " Å 9 Å 64 "8 " " " "49a " " " "3 Å 49 "12 "3 "8 56. "4 " "50y "45 2 y Ä 9 " " "ab "a 5 b " "12? " Q7"5R "14? "8 69. Q5"5R "16a 3? "5a "8? "7 73. "3? " "3? 2" "3? 7" " "12 3" "20 "27 " " "2 Q2"3R 2 "8 6 y 7 2"5? 2"5 "9 "2 4"5 "8y 2 Lesson 11-1 Practice Algebra 1 Chapter 11

2 Practice 11-2 Operations With Radical Epressions Simplify each epression "7 + 5" "4 - " "45 + 2" "11 + 7" "28 + " "6-8" "18 - " "2 + 2" "2Q2 1 2"3R "2Q2"3 2 4"2R "3Q"6 2 "12R 13" " Q8"3 2 7R 14. 8Q2"5 1 5"2R "21-12" "6Q7 1 3"3R 17. 8Q4 2 3"2R "12 + 6" "3 + " " " "10Q3 2 2"6R 22. 9"2 - " "13-7" "6-4" "7 + " "13-12" "40 + 6" "3Q"6 1 "3R "29-15" "6-2" "3 - " "6Q2"3 1 "6R "35 + 2" "19 + 4" "9-4"9 36. "8Q"2 2 7R "2 2 "3 "7 2 "3 " Q" R 2 Q3"5 1 "5R 2 "2 2 " "6 2"3 2 " "6 " "3 1 2"6 Solve each eercise by using the golden ratio Q1 1 "5R : The ratio of the height ; width of a window is equal to the golden ratio. The width of the door is 36 in. Find the height of the door. Epress your answer in simplest radical form and in inches. 47. The ratio of the length ; width of a flower garden is equal to the golden ratio. The width of the garden is 14 ft. Find the length of the garden. Epress your answer is simplest radical form and in feet. 48. The ratio of the width ; height of the front side of a building is equal to the golden ratio. The height of the building is 40 ft. Find the width of the building. Epress your answer in simplest radical form and in feet. Algebra 1 Chapter 11 Lesson 11-2 Practice 3

3 Practice 11-3 Solving Radical Equations Solve each radical equation. Check your solutions. If there is no solution, write no solution. 1. " + 3 = " 1 2 = " = " "4-7 = 1 5. " = " = " " = = " = " "3 1 5 = " " 1 3 = "6 2 4 = " = " = " "4 1 2 = " " + 8 = = " "3 1 8 = " "2 1 3 = " = " = " "3-5 = "3 1 4 = "5 24. = " " = = " = "6 28. = " " 1 14 = " "5 2 7 = " "2 = " 1 56 = " 1 4 = The equation d at2 gives the distance d in ft that an object travels from rest while accelerating, where a is the acceleration and t is the time. a. How far has an object traveled in 4 s when the acceleration is 5 ft/s 2? b. How long does it take an object to travel 100 ft when the acceleration is 8 ft/s 2? 35. The equation v 5 20"t relates the speed v, in m/s, to the air temperature t in Celsius degrees. a. Find the temperature when the speed of sound is 340 m/s. b. Find the temperature when the speed of sound is 320 m/s. 36. The equation V 5 Í Fr m gives the speed V in m/s of an object moving in a horizontal circle, where F is centripetal force, r is radius, and m is mass of the object. a. Find r when F = 6 N, m = 2 kg, and V = 3 m/s. b. Find F when r = 1 m, m = 3 kg, and V = 2 m/s. 4 Lesson 11-3 Practice Algebra 1 Chapter 11

4 Practice 11-4 Graphing Square Root Functions Find the domain of each function. 1. ƒ() = " ƒ() = " y = " y = " ƒ() = " y = " y = " y = "2 9. y = "6 Make a table of values and graph each function. 10. y = " y = 3" 12. y = " y = " y = " y = " y = 2" y = " y = " + 7 Describe how to translate the graph of y Á to obtain the graph of each function. 19. y = " y = " y = " y = " y = " y = " y = " y = " y = " The number of people involved in recycling in a community is modeled by the function n = 90 "3t + 400, where t is the number of months the recycling plant has been open. a. Graph the function. b. Find the number of people recycling when the plant has been open for 6 mo. c. Find the month when about 670 people were recycling. 29. The time t, in seconds, that it takes for an object to drop a distance d, in feet, is modeled by the function t = Î. Assume no air resistance. 16 d a. Graph the function. b. Find the time it takes for an object to fall 1000 ft. c. How far does an object fall in 10 s? Algebra 1 Chapter 11 Lesson 11-4 Practice 5

5 Practice 11-5 Trigonometric Ratios Use kabc at the right. Find the value of each epression. 1. sin A 2. cos A 3. tan A 4. sin B 5. cos B 6. tan B B A 9 C Find the value of each epression. Round to the nearest ten-thousandth. 7. tan sin sin cos sin tan cos cos tan cos 58 Find the value of to the nearest tenth Use kpqr at the right. Find the value of each epression. 23. sin P 24. cos P 25. tan P 26. sin R 27. cos R 28. tan R 29. A 12-ft-long guy wire is attached to a telephone pole 10.5 ft from the top of the pole. If the wire forms a 52 angle with the ground, how high is the telephone pole? P R 16 Q 6 Lesson 11-5 Practice Algebra 1 Chapter 11

6 Practice 11-6 Angles of Elevation and Depression 1. A tree casts a shadow that is 20 ft long. The angle of elevation of the sun is 29. How tall is the tree? 2. Suppose your angle of elevation to the top of a water tower is 78. If the water tower is 145 ft tall, how far are you standing from the water tower? 3. The angle of elevation from the control tower to an airplane is 49. The airplane is flying at 5000 ft. How far away from the control tower is the plane? 4. A Boy Scout on top of a 1700-ft-tall mountain spots a campsite. If he measures the angle of depression at 35, how far is the campsite from the foot of the mountain? 5. A 100-foot kite string makes a 35 angle of elevation to the kite. How high is the kite? 6. A soccer ball is placed 12 ft away from a goal post that measures 8 ft high. You kick the ball and it hits the crossbar at the top of the goal. What was the angle of elevation of your kick? 7. You are standing 10 ft away from a tree. The angle of elevation from your foot to the top of the tree is 65. How tall is the tree? Algebra 1 Chapter 11 Lesson 11-6 Practice 7