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# Recent problems solved by 'ewatrrr'

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 Polynomials-and-rational-expressions/469553: (y^3-3y^2)/(y^2+2y-15)=(13y-40)/(y+5)1 solutions Answer 322173 by ewatrrr(10682)   on 2011-07-12 15:11:23 (Show Source): You can put this solution on YOUR website! ``` Hi, y^2 = 13y - 40 y^2 - 3y + 40 = 0 factoring (y-8)(y-5) = 0 (y-8)= 0 y = 8 (y-5)= 0 y = 5 ```
 Numbers_Word_Problems/469597: Ron and Kathy are ticket-sellers at their class play. Ron is selling students tickets for \$2.00 each, and Kathy selling adult \$5.50 each. If there toatal income for was \$83.00, how many tickets did Ron sell?1 solutions Answer 322167 by ewatrrr(10682)   on 2011-07-12 14:23:34 (Show Source): You can put this solution on YOUR website! ``` Hi, Need more information: either total number tickets sold or the proportion each sold, for ex 24 ticket sold Let x and (24-x) represent the number of \$5.50 and \$2 tickets sold Question states*** 5.50x + 2(24-x) = 83 Solving for x 3.50x = 35 x = 10, number of \$5.50 tickets sold and... There were 14 \$2 tickets sold by Ron (24-10) CHECKING our Answer*** \$5.50*10 + \$2*14 = \$55 + \$28 = \$83 ```
 Equations/469598: Simplify the equation using synthetic Division (10x^3-61x^2+115x-66)/(x-3) 1 solutions Answer 322165 by ewatrrr(10682)   on 2011-07-12 14:20:35 (Show Source): You can put this solution on YOUR website! ``` Hi, = (x-3)(10x^2 - 31x + 22) Found by using synthetic Division: 3 10 -61 115 -66 30 -93 66 10 -31 22 0 (x-3)(10x^2 - 31x + 22) factoring (x-3)(10x -11)(x - 2) ```
 Expressions-with-variables/469589: I AM HAVING TROUBLE SOLVING THE FOLLOWING EQUATION: SLOVE FOR a t = ab over a+b1 solutions Answer 322163 by ewatrrr(10682)   on 2011-07-12 14:07:38 (Show Source): You can put this solution on YOUR website! ``` Hi, solving for a: Plan a strategy to place variable a on one side of the EQ t(a+b) -ab = 0 at +bt - ab = 0 a(t-b) = bt ```
 Mixture_Word_Problems/469446: 1) how many gallons each of 25% alcohol and 35% alcohol should be mixed to get 20 gallons of 32% alcohol?1 solutions Answer 322135 by ewatrrr(10682)   on 2011-07-12 10:25:17 (Show Source): You can put this solution on YOUR website! ``` Hi, mixed to get 20 gallons Let x and (20-x) represent the amount of the 35% and 25% solutions respectively Question states*** mixing to get 20 gal of 32% alcohol .35x + .25(20-x) = .32*20G Solving for x .10x = .07*20G = x = 14G, the amount of the 35% Solution. 6G of the 25% solution CHECKING our Answer*** .35*14 + .25*6 = 4.9 + 1.5 = .32*20 = .64 ```
 Mixture_Word_Problems/469447: 2) How many Liters each of 15% acid and 33% acid should be mixed to get 120 Liters of 21% acid?1 solutions Answer 322134 by ewatrrr(10682)   on 2011-07-12 10:19:41 (Show Source): You can put this solution on YOUR website! ``` Hi, mixed to get 120 Liters Let x and (120-x) represent the amount of the 33% and 15% solutions respectively Question states*** mixing to get 120 Liters of 21% acid? .33x + .15(120-x) = .21*120L Solving for x .18x = .06*120L = 7.2L x = 40L, the amount of the 33% Solution. 80L of the 15% solution CHECKING our Answer*** .33*40 + .15*80 = 13.2 + 12 = 25.2 = .21*120 ```
 percentage/469471: A pizza place sold 57 pizzas on Friday night for a total sales of \$722. If a medium pizza costs \$12 and a large costs \$14, how many of each size were sold?1 solutions Answer 322132 by ewatrrr(10682)   on 2011-07-12 10:09:01 (Show Source): You can put this solution on YOUR website! ``` Hi, sold 57 pizzas Let x and (57-x) represent the number of \$14 and \$12 sold respectively Question states*** \$14x + \$12(57-x) = \$722 Solving for x 2x = 38 x = 19,number of \$14 sold. 38 \$12 pizzas sold (57-19) CHECKING our Answer*** \$14*19 + \$12*38 = \$722 ```
 Travel_Word_Problems/469510: Two cars start from the same point and travel on a straight course for 2 hours in opposite directions. They are 208 miles apart from eachother. If one car traveled, on average 8mph faster than the other car, what was the average speed of each car for the 2-hour trip? (steps please)1 solutions Answer 322131 by ewatrrr(10682)   on 2011-07-12 10:02:28 (Show Source): You can put this solution on YOUR website! ``` Hi, one car traveled, on average 8mph faster than the other car Let x and (x + 8mph) represent the respective speeds of these cars Question states*** Note: D = r*t OR t = D/r 2x + 2(x+8) = 208 Solving for x 4x = 192 x = 48mph, the faster car is traveling at 56mph (44mph + 8mp) CHECKING our Answer*** 96mi + 112m = 208mi ```
 Angles/469512: Two angles are supplementary; that is, the sum of their measures is 180°. The measure of one angle is 30° more than twice the other. What is the measure of each angle?1 solutions Answer 322128 by ewatrrr(10682)   on 2011-07-12 09:54:41 (Show Source): You can put this solution on YOUR website! ``` Hi, The measure of one angle is 30° more than twice the other Let x and (2x +30°) represent the measures of these angles Question states*** "Angles are supplementary x + (2x +30°) = 180° Solving for x 3x = 150° x = 50°, It's supplementary angle is 130° (2*50°+30 CHECKING our Answer*** 50° + 130° = 180° ```
 Functions/469486: Tickets sold = \$2052. Advance tickets \$4.00 and \$6.00 There were 3 times as many \$4.00 sold than \$6.00 How many of each were sold 1 solutions Answer 322127 by ewatrrr(10682)   on 2011-07-12 09:49:42 (Show Source): You can put this solution on YOUR website! ``` Hi, There were 3 times as many \$4.00 sold than \$6.00 Let x and 3x represent the number of \$6 and \$4 tickets respectively Question states*** \$6x + \$4(3x) = \$2052 Solving for x 18x = 2052 x = 114, number of \$6 tickets. 342 \$4 tickets sold (3*114) CHECKING our Answer*** \$6*114 + \$4*342 = \$2052 ```
 Probability-and-statistics/469509: . If there are 16 total bottles of diet soda, 8 total bottles of regular soda, and 4 total bottles of water, what is the probability of each of the following: (i) Choosing a bottle of diet soda when a bottle is chosen at random (ii) Choosing a bottle of regular soda when a bottle is chosen at random (iii) Choosing a bottle of water when a bottle is chosen at random **Answers I came up w/ are below not sure if they are correct** i) 2/3 ii) 1/3 iii) 1/6 1 solutions Answer 322126 by ewatrrr(10682)   on 2011-07-12 09:44:38 (Show Source): You can put this solution on YOUR website! ``` Hi, 28 bottles in ALL,of which: 16 are diet soda, 8 are regular soda, and 4 are water. Chosing 1 bottle.. P(diet soda) = 16/28 P(reg soda) = 8/28 P(water) = 4/28 reduce the fractions and You are done. ```
 Mixture_Word_Problems/469483: HOW MUCH FERTILIZER CONTAINING 8% NITROGEN SHOULD BE MIX WITH A FERTILIZER CONTAINING 12% NITROGEN TO GET 8 L OF A FERTILIZER CONTAINING 11% NITROGEN1 solutions Answer 322118 by ewatrrr(10682)   on 2011-07-12 09:38:29 (Show Source): You can put this solution on YOUR website! ``` Hi, Mixing TO GET 8 L OF A FERTILIZER Let x and (8L-x) represent the amount of the 12% and the 8% respectively Question states*** Mixing to form 8 L OF A FERTILIZER CONTAINING 11% NITROGEN .12x + .08(8-x) = .11*8L .04x = .88 - .64 Will let You finish it Up ```
 Angles/469220: 1 and 2 are supplementary. If m 1 = 60° and m 2 = (2x + 20). What is the value of x? i dont understand what they are asking? 1 solutions Answer 321926 by ewatrrr(10682)   on 2011-07-11 15:09:02 (Show Source): You can put this solution on YOUR website! ``` Hi, 1 and 2 are "supplementary". If m 1 = 60° and m 2 = (2x + 20) What is the value of x? 60° + (2x+20) = 180° 2x = 100 x = 50° ```
 Quadratic_Equations/469211: write in simplest form. x^2 - 6x + 8 _________________ x^2 - 16 or x^2 - 6x + 8 divided by x^2 -161 solutions Answer 321923 by ewatrrr(10682)   on 2011-07-11 14:56:30 (Show Source): You can put this solution on YOUR website! ``` Hi, ```
 Length-and-distance/469212: Point A is at (4,6) and point B is at (-4,0) in the xy coordinate plane. What is the length of the line segment AB?1 solutions Answer 321921 by ewatrrr(10682)   on 2011-07-11 14:51:55 (Show Source): You can put this solution on YOUR website! ``` Hi, A is at (4,6) B is at (-4,0) D = D = ```
 Matrices-and-determiminant/469233: How do I solve: x+y+z=4 x+y-z=6 2x-3y+z=-1 Thank you for your time.1 solutions Answer 321920 by ewatrrr(10682)   on 2011-07-11 14:43:25 (Show Source): You can put this solution on YOUR website! ``` Hi, Different ways to solve this system. EQs lend to elimination, substitution methods x+y+z=4 x+y-z=6 x +y+z=4 -x -y+z =-6 |multiplying 2nd Eq thru by -1 to eliminate both x and y 2z = -2 z = -1 2x-3y+(-1)=-1 |substituting z = -1 x+y+(-1)=4 therefore: 2x-3y = 0 x+y = 5 2x-3y = 0 -2x-2y = -10 Multiplying 2 EQ thru by -2 to eliminate x -5y = -10 y = 2 and x = 3 (x + y = 5) ```
 Radicals/468380: divide: x^2-10x+21 over x^2-49 divided by x-3 over 51 solutions Answer 321381 by ewatrrr(10682)   on 2011-07-08 15:30:12 (Show Source): You can put this solution on YOUR website! ``` Hi = ```
 Travel_Word_Problems/468384: find the LCM (7+6w),(49-36w^2), and (7-6w)1 solutions Answer 321379 by ewatrrr(10682)   on 2011-07-08 15:24:40 (Show Source): You can put this solution on YOUR website! ``` Hi find the LCM (7+6w),(49-36w^2), and (7-6w) Note: (49 - 36w^2) = (7-6w)(7+6w) (49 - 36w^2) is the LCM ```
 Linear-systems/468361: I am trying to figure out how to solve this problem using the substitution method. I know that it equals 1000, but I can't figure out how to show the proper work. Any help of guidance would be appreciated. Thank you. 60+.20(x-550)=120+.15(x-800)1 solutions Answer 321378 by ewatrrr(10682)   on 2011-07-08 15:22:59 (Show Source): You can put this solution on YOUR website! ``` Hi solving by: 60 + .20(x-550)=120 +.15(x-800) 1) removing the parenthesis 60+.20x-110 =120+.15x-120 2)combining Like terms .20x - 50 = .15x 3) Isolating the variable on one side of the EQ .05x = 50 x = 50/.05 x = 1000 ```
 Quadratic_Equations/468323: Determine the graph of the quadratic equation y = x2 + 4x – 1.1 solutions Answer 321369 by ewatrrr(10682)   on 2011-07-08 14:47:28 (Show Source): You can put this solution on YOUR website! ``` Hi, Using the vertex form of a parabola, where(h,k) is the vertex y = x^2 + 4x – 1 f(x)= (x+2)^2 -4 - 1 f(x)= (x+2)^2 -5 V(-2,-5) minimum a =1 a>0 Parabola opens upward Line of symmetry x = -2 ```
 Quadratic_Equations/468337: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function and graph the function. Help!, these are the only two I do not understand. f(x)= -x^2+6x+6 f(x)= 2-x^21 solutions Answer 321367 by ewatrrr(10682)   on 2011-07-08 14:42:33 (Show Source): You can put this solution on YOUR website! ``` Hi, Using the vertex form of a parabola, where(h,k) is the vertex f(x)= -x^2+6x+6 f(x)= -[(x-3)^2 -9]+6 f(x)= -(x-3)^2 +15 V(3,15) maximum a = -1 a<0 Parabola opens downward Line of symmetry x = 3 f(x)= 2-x^2 f(x)= -(x-0)^2 + 2 V(0,2) maximum a = -1 a<0 Parabola opens downward Line of symmetry x = 0 (y-axis) ```
 Exponential-and-logarithmic-functions/468363: Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = x3 + 5x2 + 6x + 2 1 solutions Answer 321365 by ewatrrr(10682)   on 2011-07-08 14:31:43 (Show Source): You can put this solution on YOUR website! ``` Hi, f(x) = x3 + 5x2 + 6x + 2 | x = -1 a root as -1 + 5 - 6 + 2 = 0 Using synthetic division (x3 + 5x2 + 6x + 2)/(x+1) = x^2 + 4x + 2 -1 1 5 6 2 -1 -4 -2 1 4 2 0 (x+1)(x^2 + 4x + 2) zeros are: -1, -2+sqrt(2),-2-sqrt(2) ```
 Exponential-and-logarithmic-functions/468360: Solve the problem. Solve the equation 2x3 - 23x2 + 71x - 30 = 0 given that 5 is a zero of f(x)= 2x^3- 23x^2 = 71x- 30 . 1 solutions Answer 321363 by ewatrrr(10682)   on 2011-07-08 14:24:08 (Show Source): You can put this solution on YOUR website! ``` Hi, (2x3 - 23x2 + 71x - 30)/(x-5) = 2x^2 -13x + 6 Using synthetic division to determine the 2x^2 -13x + 6 5 2 -23 71 -30 10 -65 30 2 -13 6 0 (x-5)(2x^2 - 13x + 6) = 0 factoring (x-5)(2x -1)(x-6) = 0 (x-5)= 0 x= 5 (2x -1)= 0 x= 1/2 (x-6) = 0 x= 6 ```
 Exponential-and-logarithmic-functions/468355: how do I Divide using long division. 2x^3-29x+12/ x+4 1 solutions Answer 321357 by ewatrrr(10682)   on 2011-07-08 14:14:18 (Show Source): You can put this solution on YOUR website! ``` Hi Long Division is performed in a similar fashion as with numbers (2x^3-29x+12)/ (x+4) = 2x^2 -8x + 3 2x^2 + (-8x) + 3 __________________________ x + 4 | 2x^3 -29x +12 - (2x^3 + 8x^2) --------------- -8x^2 - 29x - (-8x^2 - 32x)) -------------- 3x + 12 - (3x + 12) -------- 0 ```
 Equations/468318: Find 15C41 solutions Answer 321353 by ewatrrr(10682)   on 2011-07-08 14:06:21 (Show Source): You can put this solution on YOUR website! ``` Hi 15C4 = 15!/(4!11!) = 15*14*13*12/(4*3*2*1) = 15*7*13 = 1365 Can be done quickly on a scientific calculator as well. ```
 Radicals/468336: rewrite with rational exponents (5V2x^6y)^3 the v is suppose to be a square root symbol and ^is raising to that certain power. The 5 is in that indentation of the square root, not directly to the side of it1 solutions Answer 321349 by ewatrrr(10682)   on 2011-07-08 13:59:24 (Show Source): You can put this solution on YOUR website! ``` Hi ```
 Exponential-and-logarithmic-functions/468306: Suppose you invest \$130 at 4% compounded continuously. a. Write an exponential function to model the amount in your investment account. b. Explain what each value in the function model represents. c. In how many years will the total reach \$600? Show your work.1 solutions Answer 321320 by ewatrrr(10682)   on 2011-07-08 11:23:40 (Show Source): You can put this solution on YOUR website! ``` Hi, invest \$130 at 4% compounded continuously A = Pe^(rt) where P is the amount Invested, r the rate, t the number of years \$600 = \$130 e^.04t ln(600/130) = .04t 1.5294/.04 = t 38.2349yrs = t ```
 Probability-and-statistics/468265: A bag contains four marbles: one red, one black, one white, and one orange. Two marbles are to be selected at random from the bag, with replacement. List the sample space. Find the probability that the black marble is chosen twice.1 solutions Answer 321318 by ewatrrr(10682)   on 2011-07-08 11:03:03 (Show Source): You can put this solution on YOUR website! ``` Hi, A bag contains four marbles: one red, one black, one white, and one orange. Two marbles are to be selected at random from the bag, with replacement. Sample Space: RR,BB,WW,OO, RB,BR,RW,WR,RO,OR,BW,WB,B0,OB, WO,OW P(2B) = 1/4*1/4 = 1/16 ```
 Exponential-and-logarithmic-functions/468302: Solve the equation log 3x+5=31 solutions Answer 321315 by ewatrrr(10682)   on 2011-07-08 10:52:51 (Show Source): You can put this solution on YOUR website! ``` Hi, log 3x+5=3 then 10^3 = 3x+5 3x+5 = 1000 3x = 995 x = 331 2/3 = 331.6667 ```
 Number-Line/468303: plot the point on the number line 2 2/31 solutions Answer 321314 by ewatrrr(10682)   on 2011-07-08 10:48:17 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: 2 2/3 = 8/3 ```
 Pythagorean-theorem/468297: One number is 6 more than twice another. Their product is 6 more than twice their sum. Find the numbers x and y1 solutions Answer 321313 by ewatrrr(10682)   on 2011-07-08 10:46:15 (Show Source): You can put this solution on YOUR website! ``` Hi, One number is 6 more than twice another Let x and ( 2x+6) represent the numbers Question states*** x(2x+6) = 2[x + (2x+6)] + 6 Solving for x 2x^2 + 6x = 6x + 18 2x^2 = 18 x^2 = 9 x = ± 3 Numbers are 3 and 12 OR -3 and 0 CHECKING our Answer*** 3*12 = 2*15 + 6 = 36 -3*0 = 0 = 2*(-3) + 6 ```