MATH 125 ELAC FALL 2017 TEST 2 REVIEW SHEET SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Write the system of linear equations represented by the augmented matrix. Use x, y, z, and, if necessary, w for the variables. 1) 1) 9 6 5-2 7 0 6 7 5 0 2 Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. 2) 5x + 2y + z = -11 2) 2x - 3y - z = 17 7x - y = 12 Use Cramer's rule to solve the system. 3) -5x + 6y - z = -21 x - y - 8z = -8 5x + y + z = 9 3) Use Cramer's rule to determine if the system is inconsistent system or contains dependent equations. ) x + z = 1 2x - 2y = -2 y + z = ) Use Cramer's rule to solve the system. 5) 11x + 3y= 1 5x + 2y = 5) Solve the system. 6) x + y + z = -5 x - y + 3z = -5 2x + y + z = - 6) Evaluate the determinant. 1 1 8 9-11 5 6 Solve the system of equations. 8) 3x + 3y + z = -1 x - y - z = -15 5x + y + 5z = - 8) 9) One number is less than a second number. Twice the second number is 1 less than 3 times the first. Find the two numbers. 9) 1
Find the root. Assume that all variables represent nonnegative real numbers. 10) 256x y 16 10) Find the cube root. 11) - 3-8x 30 y 2 11) 12) 3 x12 125y 6 12) Find the square root. Assume that all variables represent positive real numbers. 13) 576 13) 1) 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 10 ounces of meat and sells for $.00; and the large chicken sandwich contains 12 ounces of meat and sells for $.50. A customer requests a selection of each size for a reception. She and the manager agree on a combination of 50 sandwiches made from 26 pounds 2 ounces of chicken for a total cost of $196. How many of each size sandwich will be in this combination? (Note: 1 pound = 16 ounces) 1) 15) A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 5 hot dogs, 2 bags of potato chips, and soft drinks for $16.50. The price of a hot dog is $2.00 more than the price of a bag of potato chips. The cost of a soft drink is $.25 less than the price of two hot dogs. Find the cost of each item. 15) 16) 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 6 times as many dimes as nickels, and the value of the dimes is $.95 more than the value of the nickels. How many nickels and dimes does Jamil have? 16) Solve the system of equations using matrices. 1-3x - y - 7z = -78 5x + 7y + 8z = 122-2x - 7y + z = -32 1 18) A cruise boat traveled 72 miles downstream, with the current, in 3 hours. The return trip upstream, against the current, covered the same distance but took 12 hours. Find the average velocity of the current. 18) 19) Anne and Nancy use a metal alloy that is 1.5% copper to make jewelry. How many ounces of an alloy that is 12% copper must be mixed with an alloy that is 18% copper to form 72 ounces of the desired alloy? 19) 2
Solve the system. 20) x - 3y - z = - 5x - 15y - 5z = -20 3x - 9y - 3z = -12 20) Determine if the given ordered triple is a solution of the system. 21) (-2, -, 0) x - y + 5z = -6 x + z = -2 x + 2y + z = -10 21) Write the augmented matrix for the system of equations. 22) 9x + 11y - z + w = -2 2y + z = 7 x - y - 10z = 2 6x - 6y + 12z = - 22) Use the properties of exponents to simplify the expression. Write with positive exponents. 23) (-5p 3/5 + 3p /5 )(-5p 3/5 + 3p /5 ) 23) Use rational exponents to simplify the following. 2) 25 y 10 z 25 2) Use the properties of exponents to simplify the expression. Write with positive exponents. 25) (5x3/2 ) 2 x 1/6 25) Factor the given factor from the expression. 26) m -1/2 ; 8m 5/ - 7m -1/2 26) Solve the system of equations using matrices. 2 x + y + z = 3 x - y + 5z = -11 2x + y + z = 8 2 Use radical notation to write the expression. Simplify if possible. 28) (125x 15 ) 1/3 28) 29) (-6) /3 29) Use rational exponents to write as a single radical expression. 3 y 30) 30) y 3
Write with positive exponents. Simplify if possible. 31) 36-3/2 31) Evaluate. 32) If f(x) = 3 x + 16, find the value of f(-8). 32)
Answer Key Testname: MATH125TEST2REVIEWSHEET 1) 9x + 6y + 5z = -2 7x + 6z = 7x + 5y = 2 2) 3) {(8,, 5)} ) system is inconsistent 5) {(- 10 7, 39 7 )} 6) (1, -3, -3) 59 1 8) {(-, 1, -5)} 9) 9 and 13 10) x y 11) 2x 10 y 8 x 12) 5y 2 13) 2 1) 22 small sandwiches, 1 medium sandwiches, 1 large sandwiches. 15) $2.50 for a hot dog; $0.50 for a bag of potato chips; $0.75 for a soft drink 16) 9 nickels and 5 dimes 1 {(6,, 8)} 18) 9 mph 19) 2 ounces 20) {(x, y, z) x - 3y - z = -} 21) not a solution 22) 9 11-1 -2 0 2 1 0 7 1-1 -10 0 2 6-6 12 0-23) 25p 6/5-30p 7/5 + 9p 8/5 2) y 2/5 z 25) 25x 17/6 26) m -1/2 ( 8m 7/ - 2 {(5, 1, -3)} 28) 5x 5 29) 256 30) 12 y 1 31) 216 32) 2 5