MATH 125 ELAC SPRING 2018 TEST 3 TAKE HOME 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 3 TAKE HOME NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Write an equation of the circle with the given center and radius. 1) (-8, 2); 9 1) Find an equation of variation in which y varies inversely as x and the following is true. 2) y = 4.25, when x = ) Find the power of i. 3) (-3i) 7 3) Use the properties of exponents to simplify the expression. Write with positive exponents. 4) (3x5/2 ) 2 x -1/5 4) For the given functions f and g, find the requested function. 5) If f(x) = 7x + 8 and g(x) = 4x - 1, find (f g)(x). 5) 6) If f(x) = 4x2 + 3x + 7 and g(x) = 3x - 8, find (g f)(x). 6) Provide an appropriate response. 7) Graph y = 1 4 x ) 8) Write the expression log3 2x 3 y6 as a sum or difference of multiples of logarithms. 8) GRAPH THE graph. 9) f(x) = -x 2-4x + 5 9) Solve the equation by completing the square. 10) 16x = 3x 10) Solve the logarithmic equation for x. Give an exact solution 11) log 7 (3x - 8) = 2 11) Solve the problem. 12) Two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How long would each pipe take to fill the tank alone? 12) 13) Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 7 times as many dimes as nickels, and the value of the dimes is $6.50 more than the value of the nickels. How many nickels and dimes does Jamil have? 13) 1

2 14) Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer than Juanita to do the job alone. How long would it take Juanita alone? 14) 15) A deli sells three sizes of chicken sandwiches: the small chicken sandwich contains 5 ounces of meat and sells for $3.50; the regular chicken sandwich contains 8 ounces of meat and sells for $4.00; and the large chicken sandwich contains 10 ounces of meat and sells for $4.50. A customer requests a selection of each size for a reception. She and the manager agree on a combination of 48 sandwiches made from 21 pounds 4 ounces of chicken for a total cost of $186. How many of each size sandwich will be in this combination? (Note: 1 pound = 16 ounces) 15) 16) Anne and Nancy use a metal alloy that is 24.2% copper to make jewelry. How many ounces of an alloy that is 23% copper must be mixed with an alloy that is 25% copper to form 60 ounces of the desired alloy? 16) 17) A cruise boat traveled 60 miles downstream, with the current, in 4 hours. The return trip upstream, against the current, covered the same distance but took 12 hours. Find the average velocity of the current. 17) Solve. 18) 4x + 1 = 3 + x ) 19) Find the perimeter of the trapezoid. Simplify. 19) 3 18 in. 4 2 in. 18 in in. 20) x x = 0 20) 21) 2x 2/3-9x 1/3-56 = 0 21) 22) A ball is thrown downward with an initial velocity of 14 meters per second from a cliff that is 50 meters high. The height of the ball is given by the quadratic equation h = -4.9t 2-14t + 90 where h is in meters and t is the time in seconds since the ball was thrown. Find the time that the ball will be 40 meters from the ground. Round your answer to the nearest tenth of a second. 22) 23) (2x - 4)2-4(2x - 4) + 3 = 0 23) 24) What is the minimum product of two numbers whose difference is 42? 24) 2

3 25) Two pipes can be used to fill a pool. Working together, the two pipes can fill the pool in 8 hours. The larger pipe can fill the pool in 3 hours less time than the smaller pipe can alone. Find the time to the nearest tenth of an hour it takes for the smaller pipe working alone to fill the pool. 25) 26) Scott set up a volleyball net in his backyard. One of the poles, which forms a right angle with the ground, is 8 feet high. To secure the pole, he attached a rope from the top of the pole to a stake 10 feet from the bottom of the pole. To the nearest tenth of a foot, find the length of the rope. 26) 27) A gardener is fencing off a rectangular area with a fixed perimeter of 52 ft. What is the maximum area? 27) Solve the equation. 28) log 7 x + log 7 (x + 8) = 1 28) 29) log (2 + x) - log (x - 2) = log 3 29) Graph the solution set of the system of inequalities or indicate that the system has no solution. 30) 2x + 3y 6 x - y 3 y 2 30) Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. 31) (x - 4) 2 + (y - 2) 2 = 16 31) 32) x = 2(y + 6) ) 33) y = (x + 3)2-6 33) Perform the indicated operation. Write the result in the form a + bi. 34) 7-9i 4 + i 34) 35) (9-6i) 2 35) Solve the absolute value inequality. Write the solution set using interval notation. 36) 20-3 x ) Solve the formula for the specified variable. 37) I = ne for R 37) nr + R 3

4 Use the quadratic formula to solve the equation. 38) x x = 0 38) 39) (x - 9)(x - 1) = 20 39) Solve the system of equations using matrices. 40) 8x - y + 9z = 92-7x + 4y + 6z = -8 6x - 8y + z = 33 40) Find the center and the radius of the circle. 41) x 2 + (y - 9)2 = 25 41) Solve the inequality. Graph the solution set.write the solution set in interval and set-builder notation. 3y ) < 3 42) 4 Solve the equation. Give an approximate solution to four decimal places. 43) 5 x + 7 = 6 43) Use Cramer's rule to solve the system. 44) -3x - 5y - z = -30 x + 5y - 2z = -4x + y + z = 44) Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. 45) f(x) = (x + 2) ) 46) f(x) = 2(x - 4)2-1 46) Solve the equation. Give an exact solution. 47) e (x + 5) = 7 47) Use the discriminant to determine the number and type of solutions of the equation. 48) 4x2-4x + 1 = 0 48) Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. 49) x2 + 1 x + 49) 3 4

5 Solve the system. 50) x - 2y - z = 8 5x - 10y - 5z = 40 2x - 4y - 2z = 16 50) Graph the function. Find the vertex, y-intercept, and x-intercepts (if any). 51) F(x) = 2x 2-4x ) Use the Pythagorean theorem to find the unknown side of the right triangle. 52) 52) 9 7 Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 6x 53) 53) 5 121x 22 y 18 54) ) 5

MATH 125 FALL 2018 ELAC TEST 3 TAKE HOME Name: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

MATH 125 FALL 2018 ELAC TEST 3 TAKE HOME Name: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Determine whether the functions f and g are inverses of