Determine whether the given lengths can be side lengths of a right triangle. 1. 6, 7, , 15, , 4, 5
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1 Algebra Test Review Name Instructor Hr/Blk Determine whether the given lengths can be side lengths of a right triangle. 1., 7, 8. 17, 1, 8.,, For the values given, a and b are legs of a right triangle. Find the length of the hypotenuse. If necessary, round to the nearest tenth.. a =, b = 8. a = 1, c = 0. a =, b = 9 7. b = 18, c = 0 8. a = 7, c = a = 7, b =. Use the Pythagorean Theorem to answer each question. 10. A 0-ft ladder is placed ft from the base of a building. How high on the building will the ladder reach? 11. A soccer field is 80 yd long and yd wide. What is the diagonal distance across the field? 1. A hiker goes six miles east and then turns south. If the hiker finishes 7. miles from the starting point, how far south did the hiker go? Find the exact distance and midpoint between the two points. 1. (, ) & (, 8) 1. (10, -7) & (, 1) 1. (-, 0) & (, -) All solutions are limited to the real numbers set. 1a. List the square roots of. 1b. Evaluate. 1c. List the square roots of -. 1d. Evaluate. 1e. List the square roots of. 1f. Evaluate. 1g. List the square roots of -. 1h. Evaluate.
2 Simplify each radical expression x 1. x. 18x. 10b. 7m n. 17a b x x 9. y 0 y x 11. c d 7c Simplify each radical expression x 8x
3 Simplify each radical expression. 7. ( 0 80) Solve. Check for extraneous solutions. 9. x 1 0. x x 1. 8x. x 0. x. x 7 x. x x x 1
4 Solve the following problems. If necessary, round answers to the nearest tenth. 8. The distance d in feet that it takes an automobile to stop if it is traveling S miles per hour is given by S 1d. Find the distance it would take an automobile traveling miles per hour to stop. 9. You can use the expression D = 1. h to approximate the visibility range D, in miles, from a height of h feet above ground. a. Estimate the visibility from a height of 900 feet. b. How far above ground is an observer whose visibility range is 8 miles? Find the domain of each function and graph. 70. y x 71. y x 7. y x 7. y x 1
5 MULTIPLE CHOICE 1. To the nearest tenth, what is the length of the missing side? A. 18. B. 1.8 C.. D..0 E..0. A right triangle has a side length that measures m and a hypotenuse that measures 8. m. What is the measure of the other side of the triangle? A. 7. m B. 8.1 m C. 9.0 m D. 9. m E. 9.8 m. What is the distance between (-1, 10) and (, -)? A. 8 B. 7 C. 8 D. 170 E. 19. Which set of lengths could be the side lengths of a right triangle? A. 0 cm, cm, 9 cm B. 1 in., 8 in., 8 in. C. 10 ft, 1 ft, 1 ft D. 7 km, km, 8 km E. yd. yd, yd. What are the real square root(s) of 0.00? A. ±0. B. ±0.0 C. ±0.8 D. ±0.08 E. no real square root
6 . What is the simplified form of 10? A. 70 B. C. 7 0 D E. 7. What is the simplified form of A. n n B. n C. n n D. n 9 E. n 8 9 8n? 8. What is the simplified form of A. B. C. 9 y x 9 xy x 9x xy D. 9 x y xy E. 9 x y x x? 81 y 9. What is the simplest form of A. x y 0x B. x y 0x C. D. x y x 7 x y E. x y x 7 x? 80 y 10. What is the simplified form of 1 1? A. 180 B. C. D. 0 9 E. 180
7 11. What is the simplified form of c 1c? A. 1c B. 1c C. c D. c E. c 7 1. What is the simplified form of 11? A. B. 11 C. 11 D. 1 E What is the simplified form of 7? A. B. C. 9 D. E What is the simplified form of A B. 0 8 C. 10 D. 10 E ? 1. What is the simplest form of 7 7? A. 9 1 B. 9 1 C. 7 D. - E. 9
8 1. Which radical expression is in simplified form? 9 7x A. B. C. 8 D. 8x E What is the simplest form of A. B ? C. 0 D. E What is the simplest form of 7x 1xy? A. x y B. x C. y x x y D. x y E. 1 xy y 19. What is the simplest form of A. 1 7 B. 1 7 C. 1 7 D E. 7? 0. Simplify A. 1 7 B C. D E. 1 7
9 1. What is the solution of A. B. 7 C. 11 D. 1 E. g 1 g?. The solution set of x 8 is the set of all real numbers x such that 1 A. x > 17 B. x > 9 C. x > D. x > 1 E. x >. What is the solution of x 7? A. B. C. 10 D. 1 E. 8. What are the solution of d 11? A., - B., - C., - D., E., -. A company invests $1,000 in an account that compounds interest annually. After two years, the account is worth $1,099.. Use the function A P 1 r, where r is the annual interest rate, P is the principal, and A is the amount of money after years. What is the interest rate of the account? A. 1.0% B..% C..% D. 7.% E. 1.%
10 . The pendulum of a cuckoo clock completes one full swing every T seconds. L The variable T is determined by the function T where L is the length in meters of the. pendulum. Each swing takes 0. seconds. How many centimeters long is the pendulum? A..1 cm B. 0. cm C. 1. cm D. 8. cm E. 0 cm 7. What is the domain of the function y x? A. (, 0] B. [-7, ) C. x < 7 D. (, ) E. x > - 8. What is the equation of the graph to the right? A. y x D. y x B. y x E. C. y x y x 9. What is the equation of the graph to the right? A. y x D. y x B. y x E. C. y x y x D 0. The function T models the time T in seconds than an object has been falling 1 after the object has fallen D feet. When will the time be more than or equal to 1 minute? A. D > 1 ft B. D > ft C. D > 90 ft D. D > 00 ft E. D > 7,00 ft
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