MAT1033 Intermediate Algebra Final Exam Review …

1 MAT1033 - Intermediate Algebra - Final Exam ReviewTextbook: beginning & Intermediate Algebra , 5th Ed., by Martin-GaySection the )9x - (3x - 1) = 22)13x + 2 = 16x + 433) + (6000 - y) = )Four times the sum of some number plus 2 isequal to 8 times the number minus 20. Findthe )The length of a rectangular room is 9 feetlonger than twice the width. If the room'sperimeter is 210 feet, what are the room'sdimensions?Section the formula for the specified )P = 2L + 2 Wfor L7)V = 13Ah for ASection If needed, round to two decimal )Robin got a 4% raise in her salary from lastyear. This year she is earning $37,440. Howmuch did she make last year?9)How much pure acid should be mixed with 6gallons of a 50% acid solution in order to getan 80% acid solution?Section )If $2000 is invested at 10% simple annualinterest, how much should be invested at 12%annual simple interest so that the total yearlyincome from both investments is $5000?

2 Section the inequality. Graph the solution set and write it ininterval )-21x - 9 -3(6x - 5)12)3 3x - 3 18 Section the ordered pair so that it is a solution of thegiven linear )6x + y = -22;(-5, ), (0, ), (1, )Section three ordered pair solutions by completing the use the ordered pairs to graph the )y = -3x + 2x y01-1 Section the linear equation by finding and plotting )-6x - 12y = 12 Graph the linear )x = -217)y = -2 Section the slope of the line that passes through the )(9, 0) and (0, -1)19)(-8, 10) and (-8, 4)1 Determine whether the pair of lines is parallel,perpendicular, or ) 3x - 4y = 16 8x + 6y = 1 Find the slope of the line and write the slope as a rate ofchange with proper )The graph shows the total cost y (in dollars) ofowning and operating a mini-van where x isthe number of miles (4000, )(8000, )x5000100001500020000y4000300020001000(4 000, )(8000, )Section the slope-intercept form to graph the )

3 Y = 12x + 5 Find an equation of the line with the given slope thatpasses through the given point. Write the equation in theform Ax + By = )m = 4; (9, 7)24)m = - 23; (5, 2)Find an equation of the line described. Write the equationin slope-intercept form if )Slope 2, through (-6, -3)26)Through (2, -26) and (-7, 46)Find an equation of the )Perpendicular to y = 10, through (-3, -1)Section the domain and the range of the ){(9, 2), (-7, 2), (-5, 2)}Determine whether the relation is also a ){(-2, 2), (2, -2), (4, -9), (8, -5), (10, -2)}Determine whether the graph is the graph of a )x-55y5-5x-55y5-5 Evaluate the )Find f(-2) when f(x) = 3x2 + 2x + the system of equations by )y=-x + 2y=2x + 833)x + y=-6x + y= -4 Sections the system of equations by the substitution oraddition )-2x + y = -1-3x - 2y = -1935)2x + y = 108x + 4y = 4036)8x + 5y=60-2x - 5y= -9037)-3x + 5y=-7-5x + 3y= -12 Section )

4 One number is 10 less than a second the second number is 59 more than 5times the first. Find the two )Devon purchased tickets to an air show for 8adults and 2 children. The total cost was $ cost of a child's ticket was $5 less than thecost of an adult's ticket. Find the price of anadult's ticket and a child's the )5x + y > - 1041)-3x - 5y 15 Graph the solution of the system of linear )y x + 3y 5 - x43)y + 2x -73x - 4y 8 Section the )3x2y2z3245)15m13n133m12n1046)-4y0 Section the indicated )(-6y + 9) + (-4y2 + 3y - 4)48)(5n6 - 19n5 + 13) - (2n6 - 7n5 + 9)Section )(3x - 12)(x + 6)50)(a - 6)(a2 + 6a - 9)Section )(9a - 7)252)(5p + 12)(5p - 12)Section the expression. Write the result using positiveexponents )4-354)(x-5y6)-355)2-9x-5y42-6x-8y8 Evaluate the expression using exponential rules.

5 Write theresult in standard ) 10-4 Section the )-40x4 + 56x3 - 40x2-8x3 Find the quotient using long )x2 + 12x + 23x + 9 Section completely. If the polynomial cannot be factored,write "prime."59)32x9y8 - 16x7y5 - 24x4y360)s(t2 + 6) - 7(t2 + 6)61)xy - 2yz + 9x - 18z3 Section completely. If the polynomial cannot be factored,write "prime."62)x2 - x - 2063)3x2 - 9xy - 12y264)x2 - x - 45 Sections completely. If the polynomial cannot be factored,write "prime."65)6y2 - 17y + 1266)12y2 + 54y - 3067)64x2 + 80x + 2568)3x2 + 2x - 8 Section completely. If the polynomial cannot be factored,write "prime."69)25x2 - 4970)x4 - 8171)x3 - 872)54x3 + 250 Section the )x2 - 5x + 6 = 074)x(3x + 16) = 1275)81x3 - x = 0 Section the domain of the rational )f(x) = 4x - 7x2 - 4 Simplify the )2x - 1435 - 5x78)2x + 210x2 + 18x + 8 Section or divide as )x2 + 9x + 20x2 + 12x + 32 x2 + 8xx2 - 3x - 4080)(x + 5)(x - 6)4x 5x + 2520x581)(x + 6)2x - 6 x2 - 366x - 36 Section the least common denominator (LCD).

6 82)1x2 + 14x + 49 , 1x2 + 7x83)7x2 - 6x + 5 , 7x2 + 3x - 4 Perform the indicated operation. Simplify if )7x + 4x2 - 2x - 63 - 6x - 3x2 - 2x - 63 Section the indicated operation. Simplify if )x2x - 3 - 38x - 1286)4x - 6 + 136 - x87)xx2 - 16 - 6x2 + 5x + 44 Section the )1 + 1x = 12x289)3y + 2 - 7y - 2 = 8y2 - 490)1x + 7 + 2x + 3 = -4x2 + 10x + 21 Section )If three times a number added to 4 is dividedby the number plus 11, the result is four the )Mark can finish a landscaping job in 2 hours,while it takes Rachel 3 hours to finish the samejob. If Mark and Rachel will work together onthe job, and the cost of labor is $60 per hour,what should the labor estimate be? (Round tothe nearest cent, if necessary.)93)A car travels 400 miles on level terrain in thesame amount of time it travels 160 miles onmountainous terrain.

7 If the rate of the car is 30miles per hour less in the mountains than onlevel ground, find its rate in the ) x + 163x - 13095) 10a + 1010a - 1096) 1 - 3xx - 9xSection the root. Assume that all variables representnonnegative real )4910098)- 10099)3-8x6100)481x8y16 Section radical notation to write the expression. Simplify )161/2 Write with positive exponents. Simplify if )25-3/2 Use the properties of exponents to simplify theexpression. Write with positive )(b5)2/5104)z-2/7 z3/7 Section the radical expression. Assume that all variablesrepresent positive real )80x2y49106)75k7q8107)340108)364x4y55 Section or subtract. Assume all variables represent positivereal )-2 48 + 10 192 - 6 108110)43a + 364aMultiply, and then simplify if )6 5( 11 + 5)112)( 7 + 13)( 7 - 13)Section the denominator and )2 73 Write the conjugate of the )-8 5 - 11 yRationalize the denominator and )5 - 65 + 6 Section )4x + 6 - 7 = 0117)5x - 11 = 5 - x118)Scott set up a volleyball net in his of the poles, which forms a right anglewith the ground, is 7 feet high.

8 To secure thepole, he attached a rope from the top of thepole to a stake 3 feet from the bottom of thepole. To the nearest tenth of a foot, find thelength of the in terms of )-16 Perform the indicated operation. Write the result in theform a + )(3 + 7i) - (-8 + i)121)(7 + 2i)2122)8 - 3i4 + 2iSection the quadratic formula to solve the = -b b2 - 4ac2a123)x2 + 14x + 34 = 0124)x2 - 6x + 25 = )A ball is thrown downward with an initialvelocity of 28 meters per second from a cliffthat is 40 meters high. The height of the ball isgiven by the quadratic equationh = - 28t + 40 where h is in meters and tis the time in seconds since the ball wasthrown. Find the time it takes the ball to hit theground. Round your answer to the nearesttenth of a