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# Recent problems solved by 'mananth'

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 Complex_Numbers/563537: I have a few I am totally stuck on. #1)2/x+3 - 2x+3/x-1 = 6x-5/x^2+2x-3 Okay so I know that the LCD here is going to be (x+3) and (x+1) but I can not figure out how to distribute it. #2.)x^2-10/x^2-x-20 = 1 + 7/x-5 Here I have I think the LCD is (x-5) (x+4) but again am not being able to figure out how to distribute it properly. #3)5y^(negative)2 +1=6y^(negative)1 No clue the negative exponents are really throwing me here....Thanks so much for your help1 solutions Answer 364929 by mananth(12270)   on 2012-01-27 06:10:19 (Show Source): You can put this solution on YOUR website! LCD = (x+3) (x-1) Multiply the equation by LCD = (x+6)(2x+1)=0 x=-6 OR -0.5 m.ananth@hotmail.ca
 Travel_Word_Problems/563481: An airplane can cover a distance of 15,846 miles in 19 hours with a tailwind (with the wind) and a distance of 10,724 miles in 14 hours with a head wind (against the wind). Find the speed of the wind in miles per hour.1 solutions Answer 364896 by mananth(12270)   on 2012-01-26 23:01:13 (Show Source): You can put this solution on YOUR website!with wind speed = 834 mph against wind speed= 766 Speed in still air = (834+766)/2 = 800 mph so wind speed = 34 mph
 Numbers_Word_Problems/563489: find four consecutive integers such that the sum of the first three is 54 more than the fourth.1 solutions Answer 364887 by mananth(12270)   on 2012-01-26 22:29:11 (Show Source): You can put this solution on YOUR website!Let the consequtive numbers be x,x+1,x+2,x+3 x+x+1+x+2=x+3+54 3x+3=x+57 3x-x=57-3 2x=54 /2 x=27 27,28,29,30
 Word_Problems_With_Coins/563483: You only have nickels and dimes. You have 5 times more dimes then nickels. You also have \$1.35 more in dimes then you do nickles. How many dimes and nickels do you have? Is this logical? It was a pop question in algebra. I have worked every solution I know. Please and thank you, James1 solutions Answer 364886 by mananth(12270)   on 2012-01-26 22:27:09 (Show Source): You can put this solution on YOUR website!nickels =x dimes = 5x 10*5x-5*x=135 45x=135 /45 x=3 the number of nickels dimes = 5*x= 5*3 = 15 CHECK 15*10-3*5= 135 =\$1.35
 Linear_Equations_And_Systems_Word_Problems/563486: I am trying to help my daughter with homework and apparently it has been too long since I last did algebra. Can you please help me understand so that I can help her? This is the problem: 21 animals total , all sheep and chickens. 56 legs total, how many of the 21 animals are sheep and how many are chickens? Thank you.1 solutions Answer 364884 by mananth(12270)   on 2012-01-26 22:22:39 (Show Source): You can put this solution on YOUR website!Let the number of sheep be x Let the number of chikens be x x+y = 21.......................(1) we all know sheep has 4 legs and chicken has two the number of legs are56 4x+2y=56.......................(2) Multiply equation (1) by -2 we get -2x-2y=-42 add this equation to (2) -2x-2y=-42 4x+2y=56 2x= 14 /2 x=7 , number of sheep so the number of chickens will 21-7 = 14 CHECK 14*2+7*4=56 cheers m.ananth@hotmail.ca
 Permutations/563408: Show that (1,2), (4,6) and (10,14) are collinear By using the distance formula. And slope!1 solutions Answer 364866 by mananth(12270)   on 2012-01-26 20:42:56 (Show Source): You can put this solution on YOUR website!Distance between two points (1,2)(4,6) x1 y1 x2 y2 d= 1 2 4 6 d= d= d= d=5 Distance between two points (10,14)(4,6) x1 y1 x2 y2 d= 10 14 4 6 d= d= d= d= 10.00 Distance between two points (10,14) (1,2) x1 y1 x2 y2 d= 10 14 1 2 d= d= d= d= 15.00 5+10 = 15 A=(4,6), B=(10,14) C=(1,2) d(BC) = 15 d(AB)=10 d(AC)=5 d(AB) +d(AC)= d(BC) 10+5=15 This is possible only if the points are colinear, else the sum of any two distances will not be equal to the third distance. so the points are colinear. BY slopes (1,2)(4,6) x1 y1 x2 y2 1 2 4 6 slope m =(y2-y1)/(x2-x1) (6-2)/( 4-1) ( 4 / 3 ) m= 4/ 3 (4,6)(10,14) x1 y1 x2 y2 4 6 10 14 slope m = (y2-y1)/(x2-x1) (14-6)/(10-4) (8/6) m= 4/ 3 the slopes are same
 Linear-systems/563390: how do you show the equation of a line that passes through point (0, b)and (1,b + m)is y=mx+b and how do you explain that point (-1, b -m) also is on the line? (linear equations in slope intercept from) 1 solutions Answer 364862 by mananth(12270)   on 2012-01-26 20:27:25 (Show Source): You can put this solution on YOUR website!(0,b) (1,b+m)are the points (b+m-b)/1 = m is the slope The equation of line (y-y1)= m(x-x1) plug (0,b) & m in the equation (y-b)=m(x-0) y-b=mx y=mx+b --- substitute -1, b-m in the equation y= mx+b b-m = m*-1+b b-m = b-m so the point is on the line
 Pythagorean-theorem/562913: I have a question. what do you do if you need to prove a triangle is a right triangle, but you only have variable coordinates for that triangle. Here's what I have so far: Triangle ABC: A(x,0); B(x,y); C(2x,0) Finding AB: Finding BC: Finding AC: Final Steps: a^2+b^2=c^2 I'm confused on what to do next. I know that if a^2+b^2=c^2 then it is a right triangle. But, I can't solve it any furthur. I also can't use sin, cos, or tan. Thannk you in advance. 1 solutions Answer 364740 by mananth(12270)   on 2012-01-26 06:15:31 (Show Source): You can put this solution on YOUR website!Triangle ABC: A(x,0); B(x,y); C(2x,0) Finding AB: =y Finding BC: Finding AC: =x Final Steps: a^2+b^2=c^2 m.ananth@hotmail.ca
 Proportions/562937: My teacher gave the answer -12. What is the steps to solve? x/8 - 8 = -121 solutions Answer 364739 by mananth(12270)   on 2012-01-26 05:52:03 (Show Source): You can put this solution on YOUR website! add 8 multiply by 8 x=-32 Please check with your teacher
 Quadratic_Equations/562960: Give exact and approximate solutions to three decimal places. y^2-2y+1=81 a. The solutions are y= -8,10 b. There are no approximate solutions since the solutions are integers. Since the solutions I got are integers, I'm confused as to whether my answer is right. Thank You 1 solutions Answer 364738 by mananth(12270)   on 2012-01-26 05:43:53 (Show Source): You can put this solution on YOUR website!your solution is right
 Human-and-algebraic-language/562961: THe area of the floor in Samantha's rectangular room is 120 square feet. The length of the room is eight feet less than twice the width. What are the dimensions of the floor?1 solutions Answer 364737 by mananth(12270)   on 2012-01-26 05:42:39 (Show Source): You can put this solution on YOUR website!let width be x length = 2x-8 Artea = L*W Area = x(2x-8)=120 2x^2-8x=120 /2 x^2-4x=60 x^2-4x-60=0 x^2-10x+6x-60=0 x(x-10)+6(x-10)=0 (x-10)(x+6)=0 x= 10 OR -6 ignore the negative value width = 10 feet length = 2x-8 2*10-8 20-8 =12 length = 12 feet
 Geometry_proofs/562942: How do I proof a parallelogram? I am very confused in proofs. Is there a list I can see on the vocabularies to proof? The question is, Given (square)ABCD prove: AC and BD bisect each other at E. 1 solutions Answer 364736 by mananth(12270)   on 2012-01-26 05:38:57 (Show Source): You can put this solution on YOUR website!In the square ABCD AC & BD are the diagonals They intersect at E Consider triangles ADE & BEC Angle ADE is congruent to angle angle EBC ( they are alternate angles. Side AD & side BC are parallel and the transversal is BD ) Angle ABE is congruent to angle CDE ( they are alternate angles. Side AB & side CD are parallel and the transversal is BD ) Side AD is conguent to side BC ( sides of a square) so the trainagle are congruent ( by Side , Angle,Angle test) therefore AE = EC & BE = ED Hence they bisect each other m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/562943: PLEASE HELP WITH THIS WORD PROBLEM...THE PRODUCT OF THE PAGE NUMBERS ON TWO FACING PAGES OF A BOOK IS 600.FIND THE PAGE NUMBERS.1 solutions Answer 364735 by mananth(12270)   on 2012-01-26 05:29:04 (Show Source): You can put this solution on YOUR website!the pages of facing pages are always consequitive if one is x the other will be x+1 x(x+1)=600 x^2+x=600 x^2+x-600=0 x^2+25x-24x-600=0 x(x+25)-24(x+25)=0 (x+25)(x-24)=0 taking the positive values x= 24 the pages are 24 & 25
 Geometry_Word_Problems/562950: Each side of a flower garden, 30 meters long and 20 meters wide, is increased by the same amount so that the new area will be twice as big as the original area. By how many meters was each side extended? 1 solutions Answer 364734 by mananth(12270)   on 2012-01-26 05:24:32 (Show Source): You can put this solution on YOUR website! dimensions = 30 by 20 area = 600 sq.m let it be increased by x increased dimensions = x+30, x+20 (x+30)(x+20)= 2*600 x^2+30x+20x+600=1200 x^2+50x+600=1200 x^2+50x-600=0 X^2+60x-10x+600=0 x(x+60)-10(x+60)=0 (x+60)(x-10)=0 x= 10 OR -60 take the positive x= 10
 Numbers_Word_Problems/562958: Twenty-four is equal to twice a number increased by 8. Find the numbers. Here is my question. The one i type above this statement and i want to know what is the represent,relate,equate,and proof. Pls.1 solutions Answer 364733 by mananth(12270)   on 2012-01-26 05:20:07 (Show Source): You can put this solution on YOUR website!let number be x twice the number = 2x increased by 8 = 2x+8 2x+8 =24 -8 2x+8-8=24-8 2x=16 /2 x=8
 Equations/562953: 3x+2y=0 9x-24=2y1 solutions Answer 364732 by mananth(12270)   on 2012-01-26 05:18:21 (Show Source): You can put this solution on YOUR website!3 x + 2 y = 0 .............1 9 x -2 y = 24 .............2 Eliminate y multiply (1)by 1 Multiply (2) by 1 3 x 2 y = 0 9 x -2 y = 24 Add the two equations 12 x = 24 / 12 x = 2 plug value of x in (1) 3 x + 2 y = 0 6 + 2 y = 0 2 y = 0 2 y = -6 y = -3
 Quadratic_Equations/562955: Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form,ax^2+bx+c=0. The solutions are -5,1 Thank You1 solutions Answer 364731 by mananth(12270)   on 2012-01-26 05:13:47 (Show Source): You can put this solution on YOUR website!(x+5)(x-1) x(x-1)+5(x-1) x^2-x+5x-5 x^2+4x-5 =0
 Rectangles/562778: Need to find the dimension of a rectangle with a perimeter of 640yds. All I have is one side is w and the other is 3w-12. 3w has me confused. Thanks. 1 solutions Answer 364687 by mananth(12270)   on 2012-01-25 20:44:50 (Show Source): You can put this solution on YOUR website!Perimeter = 2*(L+W) 640= 2*(W+3W-12)) 640=2(4W-12) 640=8W-24 8W=664 /8 W=83 yards one side other side = 3w-12 3*83-12 249-12 237 yards 219+77=326
 Expressions-with-variables/562776: Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. 10x + 11y = -26.5 20x + 5y = -27.5 1 solutions Answer 364679 by mananth(12270)   on 2012-01-25 20:35:20 (Show Source): You can put this solution on YOUR website!10 x + 11 y = -26.5 .............1 20 x + 5 y = -27.5 .............2 Eliminate y multiply (1)by -5 Multiply (2) by 11 -50 x -55 y = 132.5 220 x 55 y = -302.5 Add the two equations 170 x = -170 / 170 x = -1 plug value of x in (1) 10 x + 11 y = -26.5 -10 + 11 y = -26.5 11 y = -26.5 + 10 11 y = -16.5 y = -1.50
 Volume/562774: what is the volume of a box that is 14 cm long, 10 cm wide, and 3 cm high?1 solutions Answer 364676 by mananth(12270)   on 2012-01-25 20:31:15 (Show Source): You can put this solution on YOUR website!Volume = L*W*H multiply all the three you will get the volume in cu. cm
 Travel_Word_Problems/562764: The giants left san francisco heading northeast at 210 km/hr. at the same time the patriots left boston and headed southwest traveling at 180km/hr. after 8 hours both teams landed at the airport in indianapolis at the same time, how far apart are boston and san francisco?1 solutions Answer 364673 by mananth(12270)   on 2012-01-25 20:30:12 (Show Source): You can put this solution on YOUR website!They are travelling in a straight line towards each other combine their speeds 210+180=390 km/h t=8 distance =d d=r*t d=390*8 d=3120 km
 Numbers_Word_Problems/562765: The difference between two counting numbers is odd. What does that say about the sum of the numbers?1 solutions Answer 364670 by mananth(12270)   on 2012-01-25 20:27:03 (Show Source): You can put this solution on YOUR website!They are always even
 Numbers_Word_Problems/562753: What is 6 less than twice the number?1 solutions Answer 364669 by mananth(12270)   on 2012-01-25 20:26:18 (Show Source): You can put this solution on YOUR website!let number be x twice the number = 2x 6 less 2x-6
 Expressions-with-variables/562761: To buy both a new car and a new house, Tina sought two loans totalling \$321,929. The simple interest rate on the first loan was 1.0%, while the simple interest rate on the second loan was 8.8%. At the end of the first year, Tina paid a combined interest payment of \$25,677.83. What were the amounts of the two loans? I think i know the expression and answer but not sure how to work it out .01x + .088(321929-x) = 25677.83 x=33,999 (321929-x)=287,930 Answer: first loan (x)=\$33,999 .....second loan (321929-x)=287,930 1 solutions Answer 364667 by mananth(12270)   on 2012-01-25 20:24:17 (Show Source): You can put this solution on YOUR website!Yes you are correct
 Linear-equations/562759: Find the equation of the line containing the point (4,-2) and having the slope m=6. 1 solutions Answer 364665 by mananth(12270)   on 2012-01-25 20:20:47 (Show Source): You can put this solution on YOUR website!m= 6 Plug value of the slope and point ( 4 , -2 ) in Y = m x + b -2.00 = 24 + b b= -2 - 24 b= -26 So the equation will be Y = 6 x -26 m.ananth@hotmail.ca
 Expressions-with-variables/562757: solve by substitution and show work 10x + 11y = -26.5, 20x + 5y = -27.5 1 solutions Answer 364664 by mananth(12270)   on 2012-01-25 20:19:41 (Show Source): You can put this solution on YOUR website!10x+11y =-26.5 .............1 5y=-27.5-20x ---------2 / 5 = y=-5.5-4x Substitute y in (1) 10x+11( -5.5-4x)=-26.5 10 x -60.5 + -44 x = -26.5 10 x -44 x = -26.5 60.5 -34 x = 34 / -34 x= -1 Plug the value of x in (1) 10 x + 11 y = -26.5 10 * -1 + 11 y = -26.5 -10 + 11 y = -26.5 11 y = -16.5 / 11 y= -1.5 m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/562754: Write an expression for the area of a rectangle with length 5x2+3x and width 3x2. Hint: A=LW.1 solutions Answer 364663 by mananth(12270)   on 2012-01-25 20:15:59 (Show Source): You can put this solution on YOUR website!(5x^2+3x)*3x^2 15x^4+9x^3
 expressions/562739: I am doing a worksheet in math , and one of the question's is asking me to evaluate ( 1/8 ) to the exponent negative 1/3 ?1 solutions Answer 364662 by mananth(12270)   on 2012-01-25 20:14:56 (Show Source): You can put this solution on YOUR website! that means cuberoot of (1/8) =
 Travel_Word_Problems/562732: PLEASE help me with this; I've been doing homework for hours and I don't know how to do this problem. "After t seconds, the height (t) of a bottle rocket launched from the ground into the air is given by the function h(t) = -16tē + 80t. Find how long it takes the rocket to teach a height of 96 feet." THANK YOU!1 solutions Answer 364659 by mananth(12270)   on 2012-01-25 20:08:22 (Show Source): You can put this solution on YOUR website!h(t) = -16tē + 80t. h(t)=96 feet find t 96 = -16t^2+80t 16t^2-80t+96=0 16t^2-32t-48t+96=0 16t(t-2)-48(t-2)=0 16t-48)(t-2)=0 16(t-3)(t-2)=0 t=3 & 2 It will take 2 seconds
 test/562733: How do I write 6x+9y=27 in slope Intercept form ?1 solutions Answer 364656 by mananth(12270)   on 2012-01-25 19:55:28 (Show Source): You can put this solution on YOUR website!6x+9y=27 9y=-6x+27 /9 y=(-6/9)x+3 y=(-2/3)x+3
 test/562727: How do I write the equation in slope -intercept form1 solutions Answer 364655 by mananth(12270)   on 2012-01-25 19:53:53 (Show Source): You can put this solution on YOUR website!y= mx+b is the equation of line passing through (x,y) m= slope b = y intercept