MATH 125 ELAC SPRING 2018 TEST 2 REVIEW SHEET NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 MATH 125 ELAC SPRING 2018 TEST 2 REVIEW SHEET NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve. 1) 5x = 12 1) 2) 3 5x = 0 2) 3) 16x - 16 = x + 3 3) 4) x 2-2 = 7 4) 5) 3 11x - 6 = 3 x ) 6) 5x + 4 = 3x ) 7) 2x + 3 = 1 + x + 1 7) Use the Pythagorean theorem to find the unknown side of the right triangle. 8) 8) ) 9) 9 12 Multiply, and then simplify if possible. Assume all variables represent positive real numbers. 10) ( 3x - 5-5) 2 10) 11) ( 3 x + -3)( 3 x + 2 x + 9) 11) 12) ( )(4-3 3) 12) Graph the inequality. 13) -7x - 6y > 0 13) 1

2 List the elements of the set. 14) If A = {-5, -4, -3, 0} and B = {-7, -5, -4, -2}, list the elements of A B. 14) Graph the solution set of the system of inequalities or indicate that the system has no solution. 15) x + y 9 y 9x - 3 x 0 y 0 15) Graph the solution of the system of linear inequalities. 16) y < 1x + 4 y > 1x ) Graph the solution set of the system of inequalities or indicate that the system has no solution. 17) 2x + 3y 6 x - y 3 y 2 17) Graph the inequality. 18) 1 5 x - 1 y -1 18) 7 Solve the compound inequality. Graph the solution set. 19) -5x or 6x ) 20) x - 5 < 1 20) Solve and graph. Write the solution set in interval notation. 21) 4x and 2x ) Solve the absolute value inequality. Write the solution set using interval notation. 22) 20-3 x ) For the compound inequality, give the solution set in both interval and graph forms. 23) 2x or 2x ) 2

3 Solve the absolute value inequality. Write the solution set using interval notation. 5-4x 24) 3 24) 7 Solve the equation. 1 25) 2 n + 2 = 3 4 n ) 26) x = 2 26) Write the domain of f in interval notation. 27) f(x) = 8-7x 27) Solve the inequality. Graph the solution set. 7y ) < 7 28) 3 Graph the solution of the system of linear inequalities. 29) y + 4x 9 3x - 4y 16 29) Solve the compound inequality. Graph the solution set. 30) -4x > 8 and x + 4 > 1 30) Determine whether the ordered pair given is a solution of the linear inequality in two variables. 31) x + 2y > -6; (6, -5) 31) List the elements of the set. 32) If A = {29, 30, 31, 34} and B = {27, 29, 30, 32}, list the elements of A B. 32) Solve the inequality. Graph the solution set. 9y ) > 9 33) 4 Use rational exponents to write as a single radical expression. 34) 3 y 2 5 y 34) 3

4 Solve the inequality. Graph the solution set. 35) 4k ) Use rational exponents to write as a single radical expression. 36) 12 x 3 x 2 36) Factor the given factor from the expression. 37) s-6/7; 14s5/7-14s-6/7 37) Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 38) ) Use the properties of exponents to simplify the expression. Write with positive exponents. 39) (5x3/2 ) 2 x 1/6 39) Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. a 40) 40) a + t Identify the domain and then graph the function. 41) f(x) = 3 x - 5; use the following table. x f(x) ) Use the properties of exponents to simplify the expression. Write with positive exponents. 42) y 5/9 (y 2/9-9y 3/9 ) 42) Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 2x 43) 43) x 17 y 13 Multiply, and then simplify if possible. Assume all variables represent positive real numbers. 44) ( )( ) 44) 4

5 Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 7 45) 45) 3 25x 2 46) x 11 46) Use the Pythagorean theorem to find the unknown side of the right triangle. 47) 47) 7 2 Add or subtract. Assume all variables represent positive real numbers. 48) 2x x x 2 48) Solve. 49) Find the perimeter of the trapezoid. Simplify. 49) 2 27 in. 4 3 in. 27 in in. Add or subtract. Assume all variables represent positive real numbers. 50) 6 3 x 3 y 7-2xy 3 8y 4 50) Simplify the radical expression. Assume that all variables represent positive real numbers. 51) x 3 y 17 51) Add or subtract. Assume all variables represent positive real numbers. 52) ) Simplify the radical expression. Assume that all variables represent positive real numbers. 56x5y6 53) 2y4 53) 5

6 Solve. 54) Scott set up a volleyball net in his backyard. One of the poles, which forms a right angle with the ground, is 6 feet high. To secure the pole, he attached a rope from the top of the pole to a stake 11 feet from the bottom of the pole. To the nearest tenth of a foot, find the length of the rope. 54) 55) A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the rope is taut while the balloon is directly above a flag pole that is 50 feet from where the rope is staked down. Find the altitude of the balloon if the rope is 120 feet long. 55) 6

7 Answer Key Testname: MATH125TEST2REVIEWSHEETSPRING2018 1) ) ) 5 4) 51, ) 8 5 6) 7) -1, 3 8) 7 2 9) 15 10) 3x x ) 2 6 x x x - 6 x ) ) 14) {-5, -4} 15) 7

8 Answer Key Testname: MATH125TEST2REVIEWSHEETSPRING ) 17) 18) 19) (-, ) 20) [5, 10) 8

9 Answer Key Testname: MATH125TEST2REVIEWSHEETSPRING ) {7} 22) [-4, 2] 23) (-, -0.5] [5.5, ) 24) - 4, ) {16, 0} 26) {-50, -30} 27) -, ) (-6, 0) 29) 30) (-3, -2) 31) Yes 32) {27, 29, 30, 31, 32, 34} 33) (-, -8) (0, ) 34) 15 y 7 35) -, , 9

10 Answer Key Testname: MATH125TEST2REVIEWSHEETSPRING ) 4 x 3 37) s-6/7(14s11/7-14) 38) ) 25x 17/6 40) a - at a - t 41) (-, ) 42) y 7/9-9y 8/9 43) x 3 y 2 11x 4 y 3 44) ) 7 3 5x 5x 46) x 3 5x 3 47) 5 48) 21x 2 49) 23 3 in. 50) 2 xy 2 3 y 51) 3y 3 5 x 3 y 2 52) ) 2x2y 7x 54) 12.5 ft 55) ft 10