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# Recent problems solved by 'ewatrrr'

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 Equations/427417: Solve by the elimination method 5r - 8s = -3 8r + 5s = 102 I came up with (9,6) r being 9 and s being 6. Is that correct? 1 solutions Answer 297242 by ewatrrr(10682)   on 2011-03-26 15:44:58 (Show Source): You can put this solution on YOUR website! ``` Hi, Yes! You are exactly corect Solving by the elimination method 5r - 8s = -3 8r + 5s = 102 25/8r - 5s = -3*5/8 |multiplying 1st EQ by 5/8 8r + 5s = 102 89/8 r = -15/8 + 102 89r = -15 + 816 89r = 801 r = 9 and s = (5r+3)8 = 48/8=6 ```
 percentage/427411: In the following percentage increase problem, I was ok until this step. How would I get rid of x on the right side in order to solve the problem, please: 0.15x = 31.97-x1 solutions Answer 297239 by ewatrrr(10682)   on 2011-03-26 15:26:02 (Show Source): You can put this solution on YOUR website! ``` Hi 0.15x = 31.97-x |adding x to both sides to combine Like terms 0.15x + x = 31.97 1.15x = 31.97 x = 27.8 As You know, we really don't 'get rid' of the x... We combine Like terms! ```
 Geometry_Word_Problems/427413: The number of weekly domestic violence arrest in urban St. KLouis increased from 120 in 2003 to 135 in 2006. Predict the nunmber of weekly domestiv violence arrest in 20091 solutions Answer 297237 by ewatrrr(10682)   on 2011-03-26 15:21:43 (Show Source): You can put this solution on YOUR website! ``` Hi (3,135) (0,120 m = 15/3 OR increase of 15 every 3 years. Predicting 150 of weekly domestic violence arrest in 2009 ```
 Polynomials-and-rational-expressions/427352: I can't figure out how to do this: using long division solve and then check-please show how to check the answer 1 solutions Answer 297235 by ewatrrr(10682)   on 2011-03-26 15:18:28 (Show Source): You can put this solution on YOUR website! ``` Hi As to checking the answer: Note: 1) (x-1) is a factor as when x=1, then f(1)= 1+2+3-6= 0 (x^3+2x^2+3x-6)/(x-1)= x^2 + 3x + 6 2) checking the result of the division could be done by showing: (x-1)(x^2 + 3x + 6) = x^3+2x^2+3x-6 x^2 + (3x) + 6 __________________________ x - 1 | x^3 +2x^2 +3x -6 - (x^3 -x^2) --------------- 3x^2 + 3x - (3x^2 -3x)) -------------- 6x - 6 - (6x - 6) -------- 0 ```
 Inequalities/427405: Use the intercepts to graph the equation x + 5y = 10 I got (0, 2) and (10, 0) Is that correct?1 solutions Answer 297232 by ewatrrr(10682)   on 2011-03-26 15:05:40 (Show Source): You can put this solution on YOUR website! ``` Hi the x and y intercepts x + 5y = 10 Yes! (10,0) and (0,2) is correct: ```
 Evaluation_Word_Problems/427338: find all the REAL zeros of the function x^4-4x^3+4x-11 solutions Answer 297231 by ewatrrr(10682)   on 2011-03-26 15:01:26 (Show Source): You can put this solution on YOUR website! ``` Hi x^4-4x^3+4x-1 = 0 |If x=1 then 1-4+4-1 = 0 (x-1) a factor dividing the above by (x-1) x^3 - 3x^2 - 3x + 1 |If x= -1 then -1-3+3+1 = 0 (x+1) a factor dividing the above by (x+1) x^2 - 4x + 1 all the REAL zeros of the function: {-3.7321,-1, -.2679, 1 } ```
 Radicals/427363: Solve equation. Check results. √(x-2) = x-41 solutions Answer 297228 by ewatrrr(10682)   on 2011-03-26 14:47:20 (Show Source): You can put this solution on YOUR website! ``` Hi |Squaring both sides of the Equation x-2 = x^2 - 8x + 16 x^2 -9x + 18 = 0 factoring (x-3)(x-6) = 0 Note:SUM of the outside terms(-6x) and the inside terms(-3x) = -9x (x-3)= 0 x = 3 |Tossing out: sqrt(1) ≠ -1 (x-6) = 0 x = 6 It is always recommended to 'check out' the solutions found in the original EQ ```
 Square-cubic-other-roots/427369: is 32 a perfect square?1 solutions Answer 297225 by ewatrrr(10682)   on 2011-03-26 14:41:08 (Show Source): You can put this solution on YOUR website! ``` Hi is 32 a perfect square? NO A number p is called a perfect square if and only if there exists a whole number n for which p = n^2 As to 32, there is no whole number such that 32 = n^2 ```
 Polygons/427386: find the value of x of thes triangles big tiangle 20 in and 12 in small triangle 6in and x what is the value of x ?1 solutions Answer 297224 by ewatrrr(10682)   on 2011-03-26 14:35:32 (Show Source): You can put this solution on YOUR website! ``` Hi If these are corresponding sides of similar triangles: |Cross Multiplying 20x = 72 x = 72/20 = 18/5 = 3 3/5 ```
 Travel_Word_Problems/427401: a car travels 300 km in 6 hours what is the average speed of the car in km/hr?? 1 solutions Answer 297221 by ewatrrr(10682)   on 2011-03-26 14:27:49 (Show Source): You can put this solution on YOUR website! ``` Hi 300km/6hr = 50kmph ```
 Polynomials-and-rational-expressions/427400: 0.54 tons/yd^3 = ?lb/ft^31 solutions Answer 297220 by ewatrrr(10682)   on 2011-03-26 14:26:46 (Show Source): You can put this solution on YOUR website! ``` Hi Note 1 ton = 2000lb and 1 yd^2 = 27 ft^2 0.54 tons/yd^3 = .54*2000lb/27ft^3 = 40lb/ft^3 ```
 Rational-functions/427397: what do I do when multiplying rational functions. My teacher said add them across then subtract or somethin like that. But I looked up the answer and i cannot figure out where the 4 came from. (6x^3 y)* (3x^2 y) _______ ________ ....the correct answer is 9x over 4. Help?! (xy^2) * (8x^3)1 solutions Answer 297218 by ewatrrr(10682)   on 2011-03-26 14:22:22 (Show Source): You can put this solution on YOUR website! ``` Hi Note: x^2*x^3 = x^(2+3) OR x^(1+4) ```
 Linear-equations/427399: Find the slope if it exists, of the line containing the pair of points: (4, 2) and (5, -2) I got 4 is that correct?1 solutions Answer 297217 by ewatrrr(10682)   on 2011-03-26 14:14:44 (Show Source): You can put this solution on YOUR website! ``` Hi Using the point-slope formula, (4, 2) and (5, -2) m = 4/-1 = -4 Always important to watch the signs. Line y = -4x for example slants to the left Line y = 4x slants to the right ```
 Pythagorean-theorem/427398: How do you find the perimeter of triangle ABC on the Pythagorean theorem?1 solutions Answer 297216 by ewatrrr(10682)   on 2011-03-26 14:10:37 (Show Source): You can put this solution on YOUR website! ``` Hi How do you find the perimeter of triangle ABC on the Pythagorean theorem? The pythagorean Theorem States: a^2 + b^2 = c^2 that allows one to find a third side given the other two sides ... which allows for finding the P = a + b + c for example: if a = 3 and b = 4, the c = and therefore, P = 3 + 4 + 5 = 12 units ```
 Rectangles/427361: ABCD is a rectangle. what is the length of the diagonals if AC= 3y/5 and BD= 3(y-4)1 solutions Answer 297214 by ewatrrr(10682)   on 2011-03-26 14:00:11 (Show Source): You can put this solution on YOUR website! ``` Hi Note: Diagonals of a Rectangle are equal to each other: 3y/5 = 3(y-4) 3y = 15(y-4) 3y = 15y - 60 60 = 12y y = 5 Diagonals are both 3 units ```
 Triangles/427379: What is the area of a right triangle with legs of length 9 cm and 12 cm and a hypotenuse of length 15 cm? 1 solutions Answer 297209 by ewatrrr(10682)   on 2011-03-26 13:35:53 (Show Source): You can put this solution on YOUR website! ``` Hi area(triangle) = (1/2)b*h = (1/2)9cm*12cm = 54 cm^2 ```
 logarithm/427380: If log(subscript 2) 8 = 3 and log ( subscript 2) 16 = 4, then find log(subscript 6) 216. Please explain what log is before doing the problem please. 1 solutions Answer 297205 by ewatrrr(10682)   on 2011-03-26 13:16:08 (Show Source): You can put this solution on YOUR website! ``` Hi ```
 Graphs/427135: Graph the conic: (x-4)^2 + (y+1)^2 = 41 solutions Answer 297037 by ewatrrr(10682)   on 2011-03-25 16:18:19 (Show Source): You can put this solution on YOUR website! ``` Hi (x-4)^2 + (y+1)^2 = 4 Standard Form of an Equation of a Circle is where Pt(h,k) is the center and r is the radius ```
 Graphs/427124: Graph the conic: (x-2)^2 over 36 + (y+4)^2 over 25 = 11 solutions Answer 297032 by ewatrrr(10682)   on 2011-03-25 15:56:21 (Show Source): You can put this solution on YOUR website! ``` Hi Standard Form of an Equation of an Ellipse is where Pt(h,k) is the center and a and b are the respective vertices... distances from center. ```
 Quadratic-relations-and-conic-sections/427115: How do you find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse whose equation is given 4x^2 + 8y^2 = 32 1 solutions Answer 297031 by ewatrrr(10682)   on 2011-03-25 15:51:59 (Show Source): You can put this solution on YOUR website! ``` Hi Ellipse: 4x^2 + 8y^2 = 32 Standard Form of an Equation of an Ellipse is where Pt(h,k) is the center and a and b are the respective vertices.. Distances from center. Center is (0,0) Vertices: (sqrt(8),0) and (-sqrt(8),0) AND (0,2) and (0-2) foci: (2,0) and (-2,0) c = length of major axis is : 2sqrt(8) length of minor axis is : 2*2 = 4 ```
 Geometry_Word_Problems/427109: Please help me solve this algebra/geometry question I haven't been able to come up with anything and frankly I am completely confused as to what is going on in this problem. In a parallelogram, a base and a corresponding height are in the ratio 5 : 2. The area is 250 cm2. Find the lengths of the base and the corresponding height. (Hint: Use 2x for the base and 5x for the height of the parallelogram.)1 solutions Answer 297030 by ewatrrr(10682)   on 2011-03-25 15:32:05 (Show Source): You can put this solution on YOUR website! ``` Hi Area(parallelogram) = b*h = 2x*5x = 250cm^2 10x^2 = 250 cm^2 x^2 = 25 x = 5cm (tossing out negative solution for a measure) Base is 10cm and Height is 25cm CHECKING our Answer*** 10cm*25cm = 250 cm^2 ```
 Polynomials-and-rational-expressions/427105: how do you express 96 as the product of only prime numbers?1 solutions Answer 297028 by ewatrrr(10682)   on 2011-03-25 15:25:52 (Show Source): You can put this solution on YOUR website! ``` Hi Note Prime Numbers between 1 and 100 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 how do you express 96 as the product of only prime numbers? 2*2*2*3*2*2 = ```
 Radicals/427096: The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=4x^2-24x+81. Find the number of autromobiles that must be produced to minimize cost. Answer key states 3,000.1 solutions Answer 297026 by ewatrrr(10682)   on 2011-03-25 15:18:57 (Show Source): You can put this solution on YOUR website! ``` Hi The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=4x^2-24x+81. Find the number of autromobiles that must be produced to minimize cost. 4x^2-24x+81 |parabola opening upward. completing the square to find the vertex c(x)= 4[(x-3)^2 -9] + 81 c(x)= 4(x-3)^2 - 36 + 81 c(x)= 4(x-3)^2 + 45 Vertex(3,45) x= 3 OR 3000 automobiles ```
 Radicals/427100: April shoots an arrow upward into the air at a speed of 64 ft per second from a platform that is 34 feet high. The height of the arrow is given by the function h(t)=-16t^2+64t+34, where t is the time in seconds. What is the maximum height of the arrow?1 solutions Answer 297023 by ewatrrr(10682)   on 2011-03-25 15:03:46 (Show Source): You can put this solution on YOUR website! ``` Hi The height of the arrow is given by the function h(t)=-16t^2+64t+34, where t is the time in seconds. What is the maximum height of the arrow? -16t^2+64t+34 |parbola opening downward, completing the square to find vertex h(t)=-16t^2+64t+34, h(t)=-16(t-2)^2 + 64 +34 h(t)=-16(t-2)^2 + 98 |Vertex(2,98) 98ft is the maximum height of the arrow ```
 Graphs/427101: If the first and third of three consecutive odd integers are added, the result is 69 less than five times the second integer. Find all three integers. 1 solutions Answer 297021 by ewatrrr(10682)   on 2011-03-25 14:55:04 (Show Source): You can put this solution on YOUR website! ``` Hi Let x, (x+2) and (x+4) represent the consecutive odd Integers respectively Question states*** x + (x+4) = 5(x+2) - 69 Solving for x 2x + 4 = 5x - 59 63 = 3x 21 = x The consecutive odd Integers are 21,23,25 CHECKING our Answer*** 46 = 5*23 - 69 = 115-69 = 46 ```
 Polynomials-and-rational-expressions/427099: how would you factor? also check the factors? need to understand a^2+7a+12=01 solutions Answer 297019 by ewatrrr(10682)   on 2011-03-25 14:49:18 (Show Source): You can put this solution on YOUR website! ``` Hi factoring a^2+7a+12=0 (a+4)(a+3)= 0 Note:SUM of the inner product(4a) and the outer product(3a) = 7a (a+4)=0 a = -4 (a+3)= 0 a = -3 CHECKING our Answer*** SUBSTITUTING our Answers back into the original Equation a^2+7a+12=0 16 -28 + 12 = 0 |checking a = -4 9 -21 + 12 = 0 |checking a = -3 ```
 Miscellaneous_Word_Problems/427069: If the cost of a new car is 25,000 dollars plus 8% sales tac and a down payment of 15% including the tx is required, how much money will a consumer need to drive out in a new car:1 solutions Answer 297008 by ewatrrr(10682)   on 2011-03-25 13:40:45 (Show Source): You can put this solution on YOUR website! ``` Hi Sales tax = .08*25,000 = \$2000 DP = .15*25,000 = \$3750 with tax \$5750 OR .23*25,000 = \$5750 ```
 Equations/427061: Solve the following system of equations using substitution. 2x+4y=12 4x+16y=8 I substituted 2x+4y for x in the second equation and I ended up with 8x+32y=8. I've tried so many of these problems and I just can't understand them.1 solutions Answer 297007 by ewatrrr(10682)   on 2011-03-25 13:35:51 (Show Source): You can put this solution on YOUR website! ``` Hi Note: the idea solving using substitution is for that to result in an equation with ONE unknown. 2x+4y=12 OR x = 6-2y |solving for x 4x+16y=8 |Substituting that into the 2nd EQ 4(6-2y)+16y = 8 |now we have an EQ with ONE unknown solving for y 24 - 8y + 16y = 8 8y = -16 y = -2 and x = 10 (6- 2*-2) CHECKING our Answer*** 4x+16y=8 40 -32=8 ```
 Rational-functions/427063: solve the system of equations using the addition method. equ 1: 2x-1/5y=-5 equ 2: 3x-5/2y=-37/2 I have tried tried multiplying -5 to (equ 1) to take out the fraction and and -2 to (equ 2) and I'm not sure if that's correct so far. Answer: equ 1: 10x+y=25 equ 2: 6xt10y=74 1 solutions Answer 297006 by ewatrrr(10682)   on 2011-03-25 13:26:10 (Show Source): You can put this solution on YOUR website! ``` Hi, would like to accomplish eliminating the y-terms in one step: solve the system of equations using the addition method. 2x-(1/5)y=-5 3x-(5/2)y=-37/2 -25x +(5/2)y = 125/2 |Mulitplying 1st EQ by -25/2 Note: = -25x 3x -(5/2)y = -37/2 -22x = 88/2 = 44 x = -2 and y = (2x+5)5 = 5 Ordered pair (-2,5) the solution for this system CHECKING our Answer*** 3x -(5/2)y= -37/2 -6 - 25/2 = -12/2 - 25/2 = -37/2 ```
 Polynomials-and-rational-expressions/427065: I am to sove and put answer in scientific notation (8.28x10^6)+(6.17x10^5)= but could you explain how to do it so that I know1 solutions Answer 297005 by ewatrrr(10682)   on 2011-03-25 13:05:16 (Show Source): You can put this solution on YOUR website! ``` Hi Note: To combine(add) must be 'Like' terms: In this case to the same 'power of ten' (which can be done by moving the decimal point) (8.28x10^6)+(6.17x10^5)= (82.8x10^5)+(6.17x10^5)= 88.97x10^5 = 8.897x10^6 OR (8.28x10^6)+(6.17x10^5)= (8.28x10^6)+(.617x10^6)= 8.897x10^6 ```
 Miscellaneous_Word_Problems/427023: 6 teams are involved in a round robin tournament. In a tournament, each team plays every other team once and only once. It does not matter who wins how many games in all are played..1 solutions Answer 297003 by ewatrrr(10682)   on 2011-03-25 12:54:04 (Show Source): You can put this solution on YOUR website! ``` Hi 6 teams are involved in a round robin tournament each team plays every other team once and only once how many games in all are played? 15 Example: 5 Rounds : 3 games each round. 1 2 3 4 5 6 1 II III IV V I 2 IV V I III 3 I II V 4 III II 5 IV 6 ```