Elementary Algebra Review for Exam 4

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Bryce McCormick
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1 Elementary Algebra Review for Exam 4 List all numbers for which the rational expression is undefined. 9 ) a - 7 2) 3) x2-25 x2 + 2x + 32 x2-49 x2-3x - 40 Simplify, if possible. 4) 2m 6p2 4m9p 5) 6) x x x + 2 -x Provide an appropriate response. 3) Explain why the expressions 2 - x and are opposites. x - 2 4) What is wrong with the following? 4x + = 4x + = 4x Multiply and, if possible, simplify. y - 5) y2 œ y y2-2 6) 3x 2 4 œ 2 x3 7) 2p - 2 p œ 7p2 3p - 3 7) ) b - a 3a - 3b a2-7a (a + 5)(a - 7) ) 2x 2-9 4x2-4 œ 7x - 7 4x + 9 9) m 2-6 m œ m2 m2 + 2m ) 7t t 20) 5x + 0 x - œ 3x 2-6x + 3 x2-4 0) 3x + 3 5x2 + 2x + 6 2) x - 7 (x + 3)2 œ x 2-4x - 2 (x - 7)2 ) y 2-6y - 6 y2-5y ) x 2 + 3x - 4 5x3-3x2 œ 25x 3-9x 3x - 3 2) a2-36 a2 + 0a ) k2 + k + 2 k2 + 3k + 42 œ k2 + 7k k2 + 6k + Divide and, if possible, simplify. 24) 2x 2 5 d x 3 5

2 Elementary Algebra Review for Exam 4 Page 2 25) 2x 0 2y9 d x 4 2y5 26) 9 y - x d 3 x - y 27) 3p - 3 p d 5p - 5 2p2 2) x 2-9x + 20 x2-5x + 4 d (x 2-6x + 5) 29) z 2 + 5z + 54 z2 + 6z + 63 d z2 + 6z z2 + 2z ) (y + 5) d 3y 2 + 0y - 25 y2 + y + 5 Perform the indicated operation. Simplify, if possible. 4 3) 2x + 7 2x Decide whether or not the ordered pair is a solution of the system. 39) (4, -5) 4x + y = 3x + 4y = - 40) (-3, -4) 4x + y = -6 2x = -22-4y Solve the system of equations by graphing. If there is no solution or an infinite number of solutions, state this. 4) x - 3y = 9 x + 2y = - 42) x = -y y + x = 6 43) y = 4x + 6 y = -3x ) 33) 3 q q - 9 4m m m ) y = 3 x + 2 x - 3y = 7 45) 3x - y = 5 6x = 2y ) 3a + 5 a - 5-2a + 7 a ) m 2-6m m m ) x 2-5x x x - x 2 x + 3 Provide an appropriate response. 46) Describe the graph of an inconsistent system of two linear equations in two variables. 47) Explain in your own words what it means for a system of two linear equations in two variables to be dependent. 37) 3) 3x + x2 + 2x x + 6 x2 + 2x - 24 x2-0x 9x x2 + 2x + 36 x2 + 2x + 36 Solve the system using the substitution method. If there is no solution or an infinite number of solutions, state this. 4) y = 2x - -3x + y = -2 49) x - 7y = -49-7x - 6y = -42

3 Elementary Algebra Review for Exam 4 Page 3 50) y - 3x = 3y - x = 7 5) x + y = 9 x + y = 7 52) x + y = 3 7x + 7y = 2 Solve the problem. 53) The sum of two numbers is 4 and their difference is 9. Find the numbers. 54) Two angles have a sum of 05e. Their difference is 3e. Find the angles. 55) The sum of two angles is 94e. One angle is 22e less than twice the other. Find the angles. 56) Two angles are supplementary (they sum to 0 ), and one is 40e more than three times the other. Find the smaller angle. Solve the system using the elimination method. If there is no solution or an infinite number of solutions, state this. 57) x - 4y = 9 2x - 4y = 4 5) x - 3y = -7 4y = 7x ) -5x + 5y = 0 3x + 2y = 4 60) -2x - 6y = 4-4x - 2y = 6) -4x + 5y = -2-2x + 5y = 6 Solve the problem. 62) One car rental agency offered a rental at $27.00 per day plus $0.5 per mile. A competitor offered a special rate of $.00 per day plus $0.20 per mile. For what number of miles will the two plans be equal? 63) Joe has a collection of nickels and dimes that is worth $.20. If the number of dimes were doubled and the number of nickels were increased by 5, the value of the coins would be $3.5. How many dimes does he have? 64) Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $3.00 each and Kathy selling adult tickets for $6.50 each. If their total income for 29 tickets was $25.50, how many did Ron sell? 65) Ellen wishes to mix candy worth $.52 per pound with candy worth $3.3 per pound to form 2 pounds of a mixture worth $3.2 per pound. How many pounds of the more expensive candy should she use? 66) Anne and Nancy use a metal alloy that is 9.4% copper to make jewelry. How many ounces of a % alloy must be mixed with a 23% alloy to form 0 ounces of the desired alloy? 67) In a local election, 26,76 people voted. This was an increase of 2% over the last election. How many people voted in the last election? Round to the nearest whole person if necessary. 6) If Gloria received a 9% raise and is now making $23,90 a year, what was her salary before the raise? Divide. 69) (x2 + 9x + 3 ) d (x + 4) 70) 3m m 2 m + 5 Simplify. Do not use negative exponents in your answer. 7) a) y7œ y-2 b) 3- œ 3-6

4 Elementary Algebra Review for Exam 4 Page 4 72) a) c -5 3 b) 3x-4 y-7z-2 73) a) (3x-2yz5) -4 b) (x-9yz2)(x-4y-4z6) Solve the equation. 74) (x - )(x + 9) = ) 5x2-6x = Write a slope-intercept equation for the line with the given slope that contains the given point. 76) m = 5; (3, 6) Write a point-slope equation for the line with the given slope that contains the given point. 77) m = -2; (6, 4) Write the slope-intercept equation of the line containing the given points. 7) ( -2, -6 ) and (, -) Solve the problem. 79) The length of a rectangular frame is 3 cm more than the width. The area inside the frame is 54 square cm. Find the dimensions of the frame. 0) One leg of a right triangle is 6 cm shorter than the other leg. The length of the hypotenuse is 30 cm. Find the length of each leg.

5 Answer Key Testname: EA EXAM 4 REVIEW F06 ) a = 7 2) x = - and -4 3) x = -5 and 7p 4) m3 5) 4 5 6) x - 3 2x 7) - 3 a ) a + 5 9) -7 0) 5x + 2 ) y + 2 y + 3 2) a - 6 a + 4 3) Their sum is zero. Another explanation is -( 2 - x ) = -(2 - x) = x ) You can only cancel factors, and is not a factor of 4x +. The has to be divided out of both terms, not just the last. 5) (y - )(y + 2) (y2 + 6)(y2-2) or y2 + y - 2 y4 + 4 y ) x 7) 4p 3 ) 9) 20) 2) 22) x - 7 4(x + ) m(m + 4) (m + 6) 5(x - ) x - 2 x + 3 (x + 4)(5x + 3) 3x 23) k k ) x 25) 3x 6 2y4 26) -3 6p 27) 5 2) (x - )2 29) z + 5 z 30) 3) (y + 5)(y + 3) 3y - 5 2x 2 32) q ) 4 34) a + a ) m ) ) x - 4 x - 7 3) x ) Yes 40) Yes 4) (3, -2) 42) No solution 43) (-3, 4) 44) No solution 45) Infinite number of solutions 46) The graph is a pair of parallel lines. 47) One equation can be obtained by multipling both sides of the other equation by a nonzero constant, and thus the equations are equivalent. Therefore, the graph of the system is a single line, and every point on the line is a solution of the system. This means that the system has infinitely many solutions.

6 Answer Key Testname: EA EXAM 4 REVIEW F06 4) (-6, -20) 49) (0, 7) 50) - 7, 3 5) No solution 52) Infinite number of solutions 53) and 30 54) 59e and 46e 55) 72e and 22e 56) 35e 57) (5, -) 5) (, 5) 59) (0, 2) 60) Infinite number of solutions 6) No solution 62) 0 63) 54 dimes 64) tickets 65) 6 pounds 66) 24 ounces 67) 22,336 people 6) $22, ) x x ) 2m m + 5 7) a) y5 b) 72) a) 3 5 c5 73) a) 74) -5, -3 75) - 4 5, 2 or 243 c5 x y4z20 76) y = 5x ) y - 4 = -2(x - 6) 7) y = - 2 x ) cm 0) cm and 24 cm 32 b) y 7z x3 b) 3y 7z2 x4

Elementary Algebra Review for Exam 4

Elementary Algebra Review for Eam 4 ) The length of a rectangular picture frame is 9 cm more than the width. The area inside the frame is 90 square cm. Find the dimensions of the frame. ) A 0-ft ladder