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# Recent problems solved by 'vasu2qute'

 Triangles/15868: the hypotenuse of a right triangle measures 13 feet and one measures 5 feet. find the lenght of the other leg?1 solutions Answer 7822 by vasu2qute(17)   on 2005-10-18 06:40:58 (Show Source): You can put this solution on YOUR website!Hypotenuse = 13ft Length of one leg = 5ft Let length of other leg be x ft According to Pythogora's Theorem Side^2 + Side^2 = Hypotenuse^2 5^2 + x^2 = 13^2 25 +x^2 = 169 x^2 =169 - 25 = 144 x= 12 ft There fore the length of the other leg = 12 ft
 Linear_Equations_And_Systems_Word_Problems/15676: Tickets for a play at the community theater cost \$12 for an adult and \$4 for a child. If 130 tickets were sold and the total receipts were \$840, how many of each type of ticket were sold?1 solutions Answer 7769 by vasu2qute(17)   on 2005-10-17 12:04:18 (Show Source): You can put this solution on YOUR website!Let no: of adults be x Cost of tickets for x adults = 12x Let no: of children be y Cost of tickets for y children = 4y Total no: of tickets sold = x + y = 130 ----(1) Total amount received =12x + 4y = 840 ----(2) Equation (2) can be reduced to 3x + y = 210 ----(3) (this is obtained by dividing the equation with 4) Subracting (1) from (3) we get 2x = 80 x = 40 No: of adults = 85 x + y = 130 40 + y = 130 y = 130 - 40 = 90 No: of children = 90
 Polynomials-and-rational-expressions/15615: A rectangle is twice as long as it is wide. If both its dimensions are increased by 4 meters, its area is increased by 88meters squared. Find the dimesions of the original rectangle. I have tried this, but know it's not right. (2x+4)(x+4)-(2x)(x)=x+88 2xsquared+8x+4x+16-2xsquared=x+88 12x+16=x+88 12x=x+72 11x=72 Where have I gone wrong?? I sent two questions, but this the one I need help on.1 solutions Answer 7758 by vasu2qute(17)   on 2005-10-17 08:02:38 (Show Source): You can put this solution on YOUR website!Solution: Let the width of the original rectangle be x Then length = 2x Area=length x breadth =2x X x=2x^2 After the increase : width = x + 4 Length = 2x + 4 Area =(x + 4) X (2x + 4) = 2x^2 + 12x + 16 This area is 88 SqMetres more than the previous area ie. 2x^2 + 12x + 16 = 2x^2 +88 ===> 12x + 16 = 88 ===> 12x = 88 – 16 ===> 12x = 72 ===> x = 72/12 ===> x = 6 therefore width= 6m and length = 2x = 2 X 6 = 12m
 Quadratic_Equations/15449: I want to know how to factor from the standard form of a quadratic equation. I'm in the beginning of college algebra, and can't remember how to do it. The problem is: 10x^2 - 3x - 4 = 0 how do i figure out x without doing the whole quadratic equation? I know the answer to factoring is (2x + 1) (5x - 4). how do you get that??1 solutions Answer 7700 by vasu2qute(17)   on 2005-10-16 11:14:39 (Show Source): You can put this solution on YOUR website!Given 10x^2 - 3x - 4 = 0 10x^2 -8x + 5x - 4 = 0 2x(5x - 4) + 1(5x - 4) = 0 (5x-4)(2x+1) = 0 (I have written -3x as (-8x+5x) then took 2x common from the first two terms and 1 common for the next two terms . In the next step I took 5x-4 as common)
 Angles/9026: I don't understand angles at all. how do you know when it's a linear or adjacent pair?1 solutions Answer 7697 by vasu2qute(17)   on 2005-10-16 11:08:10 (Show Source): You can put this solution on YOUR website! A \ \ \ \ \ C ______________\______________ D O In the above illustration angle AOC and angle AOD form a linear pair. The pair is said to be linear because the sum of the angles is 180 degrees. You can tell that their sum is 180degrees as the points C , O and D are collinear ie they lie in the same straight line. So angle COD = 180 degrees. Therefore angle AOC + angle AOD = 180 degrees. You can say that angle AOC and angle AOD are adjacent angles . all linear pairs can be called adjacent angles but all adjacent angles need not be linear pairs. It is not necessary that the sum of two adjacent angles to be equal to 180 degrees.
 Linear-systems/15519: Please solve the following system of equations: x + y = -1 1/x + 1/y = 1/2 I've tried cross multiplying and all sorts to eliminate one of the unknowns, but have just made things worse. Please help.1 solutions Answer 7690 by vasu2qute(17)   on 2005-10-16 10:49:56 (Show Source): You can put this solution on YOUR website!Given: x + y =-1 ----(1) 1/x+1/y=1/2 -----(2) 1/x+1/y=1/2 ===> (x+y)/xy =1/2 x+y = xy/2 (x+y=-1 according to Equation 1) -1 = xy/2 (Substituting x+y with -1 ) xy= -2 We know that (x-y)^2 = (x+y)^2-4xy = (-1)^2 -4(-2) = 1 -(-8)=1+8=9 (x-y)^2 = 9 therefore x - y = 3 ------(3) x + y = -1 ------(1) adding (3)&(1) we get 2x = 2 x = 1 x + y = -1 1 + y = -1 y = -1 -1 = -2 therefore x=1 , y= -2
 Equations/12767: Help! I need the answer to this problem: A soccer field is 75 yards shorter than 3 times its width. Its perimeter is 370 yards. Find its dimensions.1 solutions Answer 6474 by vasu2qute(17)   on 2005-09-27 08:12:17 (Show Source): You can put this solution on YOUR website!let the width be x yards length=3x-75 perimeter=2(length+width)=2(x+3x-75)= 2(4x-75) = 370 4x-75 =370/2 4x-75 =185 4x=185+75 4x=260 x=260/4=65 therefore width=65yards , length= 3x-75=3x65-75=195-75=120yards
 Exponents/12777: what is the answer to(3y^2)(2y^3)1 solutions Answer 6473 by vasu2qute(17)   on 2005-09-27 07:55:42 (Show Source): You can put this solution on YOUR website!solution: (3y^2)(2y^3)=3x2x(y^(2+3))=6y^5 or 3xyxyx2xyxyxy=3x2xyxyxyxyxy=6y^5
 Geometry_Word_Problems/12457: it is possible for two lines to intersect in such a way that three of the angles formed have measures of 20, 70, 20. true or false1 solutions Answer 6351 by vasu2qute(17)   on 2005-09-24 23:50:01 (Show Source): You can put this solution on YOUR website!solution: No when two lines intersect ,then two pairs of vertically opposite angles are formed so 20 and 20 is one pair of vertically opposite angles if the third angle is 70 then the fourth angle should be 70 the sum of the angles=20+20+70+70=180 but the total of angles should be 360 so it is impossible for two lines to intersect in such a way that three of the angles are 20,70,20
 Exponents/12480: How do we simplify 8 to thee 1/3 power? This is the problem I am currently working on so if you could give me a different example that is explained and answered I would be pleased! thankyou1 solutions Answer 6350 by vasu2qute(17)   on 2005-09-24 23:40:36 (Show Source): You can put this solution on YOUR website!Solution: 8^(1/3) = (2^3)^(1/3)= 2^(3x1/3)=2^1=2
 Linear_Equations_And_Systems_Word_Problems/12481: a group of 65 people attend a ball game. there were four times as many children as adults in the group. write a system of equations that you could use to set up this problem, where a is the number of adults and c is the number of children in the group. solve the system of equations for c.1 solutions Answer 6349 by vasu2qute(17)   on 2005-09-24 23:36:16 (Show Source): You can put this solution on YOUR website!solution: No: of adults = a No: of children =c children = 4 times adults c = 4xa=4a total=65 a+c=65 a+4a=65 5a=65 a=65/5=13 c=4a=4x13=52
 Quadratic_Equations/11691: Simplify: (-3a^2b^-2)^2 / (5a^3)^2 Thanks guys for your help, this is a huge help1 solutions Answer 5998 by vasu2qute(17)   on 2005-09-19 10:13:00 (Show Source): You can put this solution on YOUR website!Solution : (-3a^2b^-2)^2 / (5a^3)^2= (-3^2 x a^4 x b^-4)/(5^2 x a^6) = (-3 x -3 x a^4 x b^-4))/(5 x 5 x a^6) = 9a^4b^-4/25a^6 = (9a^-2b^-4)/25
 Travel_Word_Problems/11543: when you give me the answer could you explain it please so that i understand. It takes 1 hour longer to fly to St. Paul at 200mi/h than it does to return at 250 mi/h. How far away is St. Paul?1 solutions Answer 5970 by vasu2qute(17)   on 2005-09-18 12:05:36 (Show Source): You can put this solution on YOUR website!let us assume that it takes xhrs to return at 250mi/hr then time taken to fly to St.Paul = (x+1)hrs at 200m/hr distance=time x speed onward distance= 250x return distance=200(x+1) onward distance=return distance 250x=200(x+1) 250x=200x+200 250-200x=200 50x=200 x=200/50 x=4hrs distance=250x=250x4=1000miles
 Angles/11517: what is an angle more than 180 degrees and less than 360 degrees1 solutions Answer 5969 by vasu2qute(17)   on 2005-09-18 11:57:36 (Show Source): You can put this solution on YOUR website!It's called a reflex angle
 Exponents/11501: Can someone please help me with this problem I have been working on it all day. Multiply (x-2)(3x-6)(x+3)1 solutions Answer 5968 by vasu2qute(17)   on 2005-09-18 11:50:50 (Show Source): You can put this solution on YOUR website!(x-2)(3x-6)(x+3)= (x-2)[3(x-2)](x+3)=3[(x-2)^2](x+3)= 3(x^2-4x+4)(x+3)= =3(x^3-3x^2-8x+12)
 Numeric_Fractions/11539: Could you please help me solve the following: 4(-3/5) - 3(1/4) divided by [2(-3/5] I came up with the answer of -213/120, but the textbook gave a different answer (sorry, can't find the divided by symbol on the keyboard)1 solutions Answer 5967 by vasu2qute(17)   on 2005-09-18 11:36:46 (Show Source): You can put this solution on YOUR website!let us solve the numerator first: Numerator =4(-3/5)-3(1/4)= -12/5 -3/4 =(-12x4-3x5)/20 = (-48-15)/20= -63/20 Denominator =[2(-3/5)]= -6/5 Numerator/denominator =(-63/20)/(-6/5)=(-63/20)x(-5/6)=315/120=21/8