Ch. 11 (Part 2) Review ANSWERS 11-7 Long Division of ...

Ch. 11 (Part 2) Review ANSWERS11-7 Long Division of PolynomialsWrite the expression in mixed-number form if the remainder is not 0 or as a singlepolynomial if the remainder is 0.x " 2x " 5)x 2 " 7x +104x + 8 + 232x " 32x " 3 8x 2 + 4 x "1)1.____ "x 2 + 5x________" 2x +10________"2x "10____________02._____"8x 2 +12x__________16x "1__________ "16x + 24________________ 23!x 2 + 8x + 20 + 28x " 2x " 2 x 3 + 6x 2 + 4x "12)"x 3 + 2x 2!x 2 + 4x +16x " 4)x 3 + 0x 2 + 0x " 64____"x 3 + 4x 2_________ 4x 2 + 0x3.0 + 8x 2 + 4 x__"8x 2 +16x________20x "12________"20x + 40___________________284._________"4 x 2 +16x_______________16x " 64_______________"16x + 64____________________0!!11-8 Fractional Equations and Extraneous SolutionsSolve for x.1.x + 53 = x 53x = 5x + 25"2x = 25x = "12.52x "1= 2 4x x2x 2 " x = 8x2. 2x 2 " 9x = 0( ) = 0x 2x " 9x = 0,4.5!!

"35x 1 x + 3 7 = 2 %$ '# 5&3. 35 +15x =14 xx = (354.# x( x " 6)%x " 6 " 6$ x " 6 = 4 &('x " 6 = 4x " 24"3x = "16x = 6(but _6_is_ extraneous)Answer = no_ solution!!5." 8( x + 4)$# x + 4 +8 + x = 3x +12(4 = 2xx = (2xx + 4 = 3 %'&!6.( x + 3) ( x " 2)# 2%x + 3 " 4$ x " 2 = 5 &('( )2x " 4 " 4x "12 = 5 x 2 + x " 6"2x "16 = 5x 2 + 5x " 300 = 5x 2 + 7x "14x = "7 ±49 " ( 4 •5•"14 )10"7 ± 329=10"7 ±18.14= = "2.51,1.111011-9 Problems Involving Ratio & Proportion!1. The ratio of 2 integers is 8:15. The larger integers is 120. Find the smaller integer.815 = x " 15x = 960 " x = 641202. The ratio of 2 integers is 3:10. The sum of the integers is 156. Find the two integers.!!3x +10x =156 " 13x =156 " x =123•12 = 36,10•12 =1203. Smallville had a great football team last year. They outperformed their opponents inalmost every category of play. One of their more impressive statistics was that, onaverage, they outscored their opponents by 3:1 in every game they played. If they scoredan average of 18 points per game, what was the average number of points scored by theiropponents per game?31 = 18 x" 3x =18 " x = 6 _ point s!

4. It was recently estimated by the Extraterrestrial Alien Monitoring Agency, thatunregistered extraterrestrials outnumber registered ones by about seven-to-five. If thereare a total of 2,280 extraterrestrials, about how many of them are registered?7x + 5x = 2280 " 12x = 2280 " x =1905•190 = 950 _ registered!5. The length and width of a rectangle are in the ratio of 4:9. The perimeter is 390 m.Find the length and width.4x + 4x + 9x + 9x = 390 " 26x = 390 " x =154 •15 = 60cm,9 •15 =135cm!11-10 Problems Involving Probability & Other Rational ExpressionsCurrent (taken from Foerster’s Algebra I: Expression, Equations, & Applications)A helicopter moves through the air at 100 km/h. It flies 200 km with a tail wind of xkm/h. On ther return trip it flies the 200 km with a head wind of y km/h.1. Write an expression for the total time taken for the round trip.200100 + x + 200100 " y!2. If the tail wind is 20 km/h and the head wind is 30 km/h, how long will the round triptake?200100 + 20 + 200100 " 30 = 200120 + 200 =1.67 + 2.86 = 4.53hours70!

3. If the tail wind and the head wind both equal x for both parts of the trip and the roundtrip takes 5 hours, how fast is the wind blowing?200100 + x + 200100 " x = 5( 100 + x) ( 100 " x)# 200%100 + x + 200$ 100 " x = 5 &('( )20000 + 200x + 20000 " 200x = 5 10000 " x 240000 = 50000 " 5x 2"10000 = "5x 22000 = x 244.72mph,"44.72!4. Gawain Upp runs up the down escalator! After he has gone 13 meters he realizes hismistake, turns around, and runs back down, still going the same speed. The escalatormoves at 0.7 meters per second, and the round trip takes a total of 10 seconds. How fastdoes Gawain run?13x + 0.7 + 13x " 0.7 =10( x + 0.7) ( x " 0.7)# 13x + 0.7 + 13%$ x " 0.7 =10 &('13x + 9.1+13x " 9.1 =10 x 2 " 0.4926x =10x 2 " 4.90 =10x 2 " 26x " 4.9x = 26 ±( )676 " ( 4 •10 •"4.9 )20=26 ± 87220=26 ± 29.5320= 2.78mps!

Work problems (taken from Foerster’s Algebra I: Expression, Equations, &Applications)1. John and Fred must mow the lawn before they can go swimming. By themselves,John would take 30 minutes and Fred would take 45 minutes. How long would it take tomow the lawn with both working together?!!John :1 = 30r " r = 1 30Fred :1 = 45r " r = 1 45"x 1 30 + 1 %$ ' =1# 45&x30 + x45 =1"90$x30 + x# 45 =1 %'&3x + 2x = 905x = 90x =18 _minutes2. Marsha must mow the lawn before she can go swimming. She realizes that it wouldtake her 50 minutes to!do it by herself. So she gets Fran to help her. The job iscompleted in 30 minutes. How long would it have taken Fran to do the job alone?!Marsha :1= 50r " r = 1 50Fran :1 = xr " r = 1 x"30 1 50 + 1 %$ ' =1# x &3050 + 30x =1"50x$3050 + 30# x =1 %'&30x +1500 = 50x1500 = 20xx = 75 _minutes!3. A bathtub can be filled in 12 minutes with the drain closed. When the drain is opened,it empties in 20 minutes (it is clogged). How long would it take the bathtub to fill withthe drain open? !#x 112 " 1 &% ( =1Closed :1 =12r " r = 1 $ 20'12x12 " xOpen :1 = 20r " r = 1 20 =120#60%x12 " x$ 20 =1 &('5x " 3x = 602x = 60x = 30minutes!

4. The drain can empty the water from a full sink in 3 minutes. If the water is runningwhile the drain is open, it takes 8 minutes to empty a full sink. How long would it take tofill an empty sink with the drain closed?!Empty :1= 3r " r = 1 3Fill :1= xr " r = 1 x#8 1 3 " 1 &% ( =1$ x '83 " 8 x =1#3x%8 3 " 8 $ x =1 &('8x " 24 = 3x"24 = "5x4.8minutes = x!