Math 009 6383 Final Exam, Fall 2016 ID: 12 M W2N0U1u6m vKUurtpaW ESjoZfrtswRaXroeO PLaLxC^.O N FAxlNlX `rFicgEhEt^so _rxeHs[etrOv_eEdx. Follow order of operations to simplify the following expression: 1) (-5) - 3 + (-4) 2 -8 Evaluate the expression using the values given for the variables. 2 2) p+m+ p ; use m = -8, and p = -1 4 Simplify the expression. 3) 4(2 - 7r) - 6(3r - 7) Simplify the expression and write your answer as a fraction in lowest terms. 4) 2 - ( ) 1 4 + 5 3 Use a proportion to set up and solve the following problem. Round your answer to the nearest tenth if necessary. 5) A 4.7 ft tall woman standing next to an adult giraffe casts a 20.7 ft shadow. If the adult giraffe casts a shadow that is 70.4 ft long, then how tall is it? Worksheet by Kuta Software LLC -1- _ d2j0b1F6C EKdurt[aO QSuopfOt^wdafrBeR gLcLnC[.v a [AzlXlK HrOirgthytusL Irce[sdexrtvGezdq.D k zM`aLd[eU \\wNidtghm yIznlfRilnriutKeY QPYrseY-uARlmgPe`blr\\aj. Set up and solve an equation to answer the question below. Round your answer to the nearest tenth of a percent if necessary. 6) 43 is what percent of 128? Find the percentage change. Round to the nearest tenth of a percent if necessary and state whether the change is an increase or a decrease. 7) From 68 minutes to 33 minutes Find the final price of the item below, given that the tax will be applied to the discounted price. 8) Original price of a sweater: $49.95 Discount: 58% Tax: 6% Use simple interest to find the ending balance, given the following values for principal, rate, and time. 9) $40,800 at 11.2% for 2 years Solve the equation given in #10. 10) 4x + 2 = -34 Sove the equation given in #11. 11) 8(6 - 6x) - 8(-2x + 6) = 64 Solve the equation given in #12. 12) 3 1 25 x+ x=2 6 6 Solve the equation given in #13. 13) 1 + 1.1a = 5.44 + 2.3a Worksheet by Kuta Software LLC -2- ] u2f0M1O6S fKRuqttaf CSXoyfStpw^aErWej hLMLiCL.X b dAelUlh Xrgi\\gOhvt`sG srmewscedrNvgeOdv.O l YMcaEdEek aweiDtehm VIEnofUiXnfiktUeD rPQrpeQ-gAyljgFeLbTrqaB. Solve the inequality in #14, write its solution set in interval notation, and graph the solution set on a number line. 14) 9 p + 1 < 154 Solve the inequality in #15, write its solution set in interval notation, and graph the solution set on a number line. 15) 1 - (1 - 4x) 3(2x - 2) + x Find the slope of the line. Assume that the scale on each axis is 1 unit per tick mark. 16) y x Find the x- and y-intercepts of the line represented by the equation below. Plot both intercepts on a coordinate system and draw the line through them. 17) x - 4 y = 4 Write the slope-intercept form of the equation of the line through the given points. 18) through: (4, -5) and (-4, -3) Find at least three ordered pairs that satisfy the equation and sketch the graph of the line through them. 19) x + 3 y - 9 = 0 Worksheet by Kuta Software LLC -3- j H2d0C1O6H IKyuHtfam iS_oufvtLwoatriet xLdL_CT.^ P WADlKl] ZrvivgyhGtask vrIe_sTeLrmv^eedF.R R nMKaodHet SwwiVtJhc hIDnRfnitnhi\\tEeG sPIrOeN-\\ANlhgreabNryat. Solve the system of equations by the method of substitution. 20) y = 5x -8x + 2 y = -10 Write the point-slope form of the equation of the line described. 2 21) through: (5, -1), parallel to y = - x - 2 5 Write the slope-intercept form of the equation of the line described. 5 22) through: (5, -3), perpendicular to y = x + 3 4 Solve the system by graphing both lines on one coordinate system. 23) x - y = 3 4x + y = 2 Solve the system of equations by the method of elimination. 24) 4x - 2 y = -24 -12x - 3 y = -18 25) John and Kim are selling cookie dough for a school fundraiser. Customers can buy packages of sugar cookie dough and packages of oatmeal cookie dough. John sold 10 packages of sugar cookie dough and 11 packages of oatmeal cookie dough for a total of $360. Kim sold 5 packages of sugar cookie dough and 1 package of oatmeal cookie dough for a total of $90. Find the cost each of one package of sugar cookie dough and one package of oatmeal cookie dough. Worksheet by Kuta Software LLC -4- g C2]0L1Y6x bKZuUtIaf oSnodfVtrwXaLrKei zL[L^Cd.\\ Q CAOl`l^ TrjidgphVtXsS prseDsbejrlvwetdV.f b iMjaddtex xwJiBt_hg BIInEfsiBnPiutGeE EPQrQek-QAklBgteUbvrOaB. SOLUTIONS 1) ( (58)3 + (4) ) 2 + (4 ) ) ( 8 8 8 +16 8 2 1+ 16 17 2) p+ m+ p2 ,m=8,p=1 4 (1 ) + (8 ) + (1 )2 4 181 4 8 4 2 3) 4 (27 r )6 ( 3 r - 7 ) 828r 18 r +42 (28 r18 r )+42+8 46 r +50 4) 1 4 2 + 5 3 ( ) 1 4 2 5 3 7 15 5) Using Linear Scale Factor Height of giraffe Shadow of giraffe = Height of woman shadow of woman Height of giraffe 70.4 = 4.7 20.7 Height of giraffe= 70.4 4.7 20.7 15.98 16.0 ft 6) 43 is what percent of 128? if 128=100% 43=? 43100 128 4300 128 33.6 7) From 68 minutes to 33 minutes Change=6833=35 change= change 100 original 35 100 68 51.5 8) Original price of a sweater: $49.95 Discount: 58% Tax: 6% 10058 Discounted price= 49.95 100 $ 20.98 Final price= 94 20.98 100 $ 19.72 9) $40,800 at 11.2% for 2 years Interest=Principalratetime 40,8001.2 2 100 $ 979.20 Ending balance=Principal +interest 40800+ 979.20 $ 41779.20 4 x +2=34 10) 4 x =342 4 x =36 x=9 8(66 x )8(2 x+6)=64 11) Expanding the brackets 4848 x +16 x48=64 (4848)+(48 x+16 x )=64 32 x=64 X= 64 32 X =2 3 1 25 x+ x= 2 6 6 12) 5 25 x= 3 6 5 x= 25 3 6 5 x= 75 6 X= 75 65 X =2.5 1+1.1 a=5.44+ 2.3 a 13) 1.1 a2.3 a=5.441 1.2 a=4.44 a= 4.44 1.2 3.7 9 p+1<154 14) 9 p<1541 9 p<153 P< 153 9 P<17 1(14 x)3 (2 x2)+ x 15) 11+ 4 x6 x6+ 7 3 6 x2 16) lower point (-4,-4) and upper point(1,3) slope =(change y axis) (change 34 14 5 x4 17) equation of the line +4 1 x1at intercept , replacing (0) =4 (4,0) formula 04 (0,-1) 18) through: (4, -5) (-4, -3) 53 44 5+3 4+ 2 8>