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# Recent problems solved by 'mananth'

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 Money_Word_Problems/475602: A man invested \$2000, part at 8% and part at 6%. He earned \$144 from his investments. How much did he invest at 8%1 solutions Answer 326129 by mananth(12270)   on 2011-07-28 20:36:10 (Show Source): You can put this solution on YOUR website!Investment I 8.00% per annum Investment II 6.00% per annum x+y=2000 ------------------------1 8.00% x + 6.00% y = \$144.00 Multiply by 100 8x+6y= \$14,400.00 --------2 Multiply (1) by -8 we get -8x-8y= -16000.00 Add this to (2) -2y=-\$1,600.00 divide by -2 y=\$800.00 investment at 6.00% Balance \$1,200.00 investment at 8.00% m.ananth@hotmail.com
 Volume/475355: How many gallons of dirt are in a 24" x 24" x 24" square container?1 solutions Answer 325984 by mananth(12270)   on 2011-07-28 09:08:37 (Show Source): You can put this solution on YOUR website!Volume = 13,824 in^3 1 in^3 =0.0043 gallon (US) so 13,824 in^3= = 59.84 gallons m.ananth@hotmail.ca
 Graphs/475339: Line/ goes through the point (5,2) and is perpendicular to the line through(-2,1) and (-4,-2). Find the equation (in slope form) for/.1 solutions Answer 325982 by mananth(12270)   on 2011-07-28 09:03:28 (Show Source): You can put this solution on YOUR website!slope of line passing through (-2,1) & (-4,-2) x1 y1 x2 y2 -2 1 -4 -2 slope m = (y2-y1)/(x2-x1) ( -2 - 1 )/( -4 - -2 ) ( -3 / -2 ) m= 1.50 OR 3/2 The line perpendicular to this line will have a slope of -2/3 Equation of line with slope -2/3 and passing through (5,2) Find the intercept b Plug value of the slope -2/3 and point (5,2) in Y = m x + b 2.00 = -3.75 + b b= 2 +3.75 b= 5.75 So the equation will be Y = -0.75 x + 5.75 m.ananth@hotmail.ca
 Linear-equations/475340: Find the slope if it exists of the line containing the pair of points (1,8) and (9, -6)1 solutions Answer 325980 by mananth(12270)   on 2011-07-28 08:55:01 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 1 8 9 -6 slope m = (y2-y1)/(x2-x1) ( -6 - 8 )/( 9 - 1 ) ( -14 / 8 ) m= -1.75 or -7/4 m.ananth@hotmail.ca
 Circles/475352: When the number 168 is rotated half a turn, it becomes 891. Which of the following numbers when rotated half a turn is decreased by 12? A)81 B)69 C)16 D)981 solutions Answer 325978 by mananth(12270)   on 2011-07-28 08:49:24 (Show Source): You can put this solution on YOUR website!option D 98
 Radicals/475328: 3(2x-1) sqrt =27 1 solutions Answer 325976 by mananth(12270)   on 2011-07-28 08:47:26 (Show Source): You can put this solution on YOUR website! square both sides 3(2x-1)= 27^2 6x-3= 27^2 6x=729+3 6x=732 x=732/6 x=122 m.ananth@hotmail.ca
 Rate-of-work-word-problems/475244: sally can paint a room in 3 hours while it takes steve 9 hours to paint the same room. how long would it take them to paint the room if they worked together?1 solutions Answer 325959 by mananth(12270)   on 2011-07-28 05:26:26 (Show Source): You can put this solution on YOUR website!Painting the house 1 job Sally 3 hours She does 1/ 3 job in 1 hour Steve 9 hours He does 1/ 9 of thejob in 1 hour Together they will do 1/ 3 + 1/ 9 + Together they will do 4/ 9 of the job in one hour So they will take 2 1/4 hours m.ananth@hotmail.ca
 Travel_Word_Problems/475255: amadeus could travel 760 miles in twice the time it took his nemesis Saleri to travel 220 miles. If amadeus's rate exceeded that of Salieri by 40 miles per hour, find the rates and times of both men.1 solutions Answer 325958 by mananth(12270)   on 2011-07-28 05:22:43 (Show Source): You can put this solution on YOUR website!Saleri x 220 miles Amadeus x 40 760 miles t=d/r 2*(220 / x) = 760 / ( x + 40 ) Cross multiply 440 ( x + 40 ) = 760 * x 440 x + 17600 = 760 x 760 x -440 x = 17600 320 x = 17600 / 320 x = 55 Saleri mph 95 Amadeus mph m.ananth@hotmail.ca
 Functions/475266: 2x+y =13 3x + 3y =241 solutions Answer 325955 by mananth(12270)   on 2011-07-28 05:12:04 (Show Source): You can put this solution on YOUR website!2 x + y = 13 .............1 3 x + 3 y = 24 .............2 multiply (1)by -3 Multiply (2) by 1 -6 x -3 y = -39 3 x + 3 y = 24 Add the two equations -3 x = -15 / -3 x = 5 plug value of x in (1) 2 x + y = 13 10 + y = 13 y = 13 -10 y = 3 y = 3
 Functions/475265: 3x-4y=-19 2x+ 4y=141 solutions Answer 325954 by mananth(12270)   on 2011-07-28 05:08:51 (Show Source): You can put this solution on YOUR website!3 x -4 y = -19 .............1 2 x + 4 y = 14 .............2 multiply (1)by 1 Multiply (2) by 1 3 x -4 y = -19 2 x + 4 y = 14 Add the two equations 5 x = -5 / 5 x = -1 plug value of x in (1) 3 x -4 y = -19 -3 -4 y = -19 -4 y = -19 + 3 -4 y = -16 y = 4
 Functions/475268: 3x + 5y -z =11 2x + y - 3z=12 y + 2z = -41 solutions Answer 325953 by mananth(12270)   on 2011-07-28 05:05:12 (Show Source): You can put this solution on YOUR website!3x+5y-z =11 -------------- 1 2x+y-3z =12 -------------- 2 y+2z=-4 -------------- 3 consider equation 1 &2 Eliminate y Multiply 1 by 1 Multiply 2 by -4 we get 3x+5y-z = 11 -8x+y+12z= -48 Add the two -5x+6y+11z= -37 ------------- 4 consider equation 2 & 3 Eliminate y Multiply 2 by -1 Multiply 3 by 1 we get -2 x + -1 y + 3 z = -12 0 x + 1 y + 2 z = -4 Add the two -2x+5z= -16 -------------5 Consider (4) & (5)Eliminate x Multiply 4 by 2 Multiply (5) by -5 we get 2 -10 x + 22 z = -74 10 x + -25 z = 80 Add the two -3 z = 6 / -3 z = -2 Plug the value of z in 5 -2 x + -10 = -16 -2 x = -6 x = 3 plug value of x & z in 1 9 + 5 y + 2 = 11 5 y = -9 + -2 + 11 y= 0 m.ananth@hotmail.ca
 Rectangles/475285: A rectangular swimming pool measures 20 feet by 40 feet. A walk of uniform width surrounds it. The total area of the pool and the walk is 1500 ft². Find the width of the walk.1 solutions Answer 325952 by mananth(12270)   on 2011-07-28 04:54:43 (Show Source): You can put this solution on YOUR website!width = x length of pool + walk = 40+2x with of pool + walk = 20+2x Total area = (40+2x)(20+2x)= 1500 800+80x+40x+4x^2=1500 4x^2+120x+800-1500=0 4x^2+120x-700=0 /4 x^2+30x-175=0 x^2+35x-5x-175=0 x(x+35)-5(x+35)=0 (x+35)(x-5)=0 x= 5 the width. x cannot be -35 m.ananth@hotmail.ca
 Inequalities/475293: 12x-3y=21 4x-y=91 solutions Answer 325950 by mananth(12270)   on 2011-07-28 04:46:54 (Show Source): You can put this solution on YOUR website!12x-3y=21 3y=12x-21 y=4x-7.............1 4x-y=9 y=4x-9.............2 The slope of both lines are 4 so they are parallel. No solution m.ananth@hotmail.ca --------------------------------------------------------------------------------
 Functions/475267: 3x + y = 4 -6x - 2y =61 solutions Answer 325949 by mananth(12270)   on 2011-07-28 04:44:06 (Show Source): You can put this solution on YOUR website!3x + y = 4 y= -3x+4.............1 -6x - 2y =6 2y=-6x-6 y=-3x+2.............2 The slope of both lines are -3 so they are parallel. No solution m.ananth@hotmail.ca
 Geometry_Word_Problems/475295: A circular flower bed is surrounded by a path 4m wide. If the diameter of a flower bed is 66m. Find the area of the path 1 solutions Answer 325946 by mananth(12270)   on 2011-07-28 04:35:22 (Show Source): You can put this solution on YOUR website!Radius of flower bed = 66m Radius of flower bed + path = 70m total area - area of garden = area of path (22/7)*70*70- (22/7) * 66 * 66 =1709.7 m^2 m.ananth@hotmail.ca
 Geometry_Word_Problems/475296: A circular flower garden has an area of 314m^2. A sprinkler at the center of the garden can cover an area that has a radius of 12 cm. Will the sprinkler water the entire garden. (pi = 3.14)1 solutions Answer 325945 by mananth(12270)   on 2011-07-28 04:29:55 (Show Source): You can put this solution on YOUR website!Radius covered by sprinkler =12 m area covered = 3.14*12*12 =452.16 m^2 Yes it will water
 Rectangles/475316: I want ot know the calculation of Area If 1. We have have a piece of Stone Where Length is 29cm Bredth is 19cm & Height is 1.5cm then How we will calculate the Sq Ft of the piece? 2. We have a piece of Stone Where Length is 11.4 inches, Bredth is is 7.5inc and Height is .6Inch then How we will calculate the Sq. Ft of the Piece? Thanks & Best Regards M. R. Siddique1 solutions Answer 325943 by mananth(12270)   on 2011-07-28 04:24:56 (Show Source): You can put this solution on YOUR website!1. We have have a piece of Stone Where Length is 29cm Bredth is 19cm & Height is 1.5cm then How we will calculate the Sq Ft of the piece? I think you need to calculate the surface area. 2lw+2lh+2wh 2*(29*19+19*1.5+1.5*29)=1246 sq.ft 2. We have a piece of Stone Where Length is 11.4 inches, Bredth is is 7.5inc and Height is .6Inch then How we will calculate the Sq. Ft of the Piece? Repeat the formula m.ananth@hotmail.ca
 Travel_Word_Problems/475299: after running for a while at 8mph, Ludwig slowed to a walk at 4mph. If he traveled 68 miles in 12 hours, how far did he run and how far did he walk?1 solutions Answer 325907 by mananth(12270)   on 2011-07-28 01:12:59 (Show Source): You can put this solution on YOUR website!total distance = 68 running distance =x running speed = 8 mph walking distance = 68-x walking speed = 4 mph time running + time walking = 12 t=d/r x/8 + (68-x)/4= 12 LCD = 8 multiply by 8 x+2(68-x)=8*12 x+136-2x=96 -x=96-136 -x=-40 x=40 distance run = 40 miles Balance he walked m.ananth@hotmail.ca
 test/475298: What is 40% off of \$130?1 solutions Answer 325903 by mananth(12270)   on 2011-07-28 00:59:34 (Show Source): You can put this solution on YOUR website! =52
 Travel_Word_Problems/475279: A certain river has a current of 3 miles per hour. A boat takes twice as long to travel upstream between two points as it does to travel downstream between the same two points. What is the speed of the boat in still water? a. 3 miles per hour b. 6 miles per hour c. 9 miles per hour d. 12 miles per hour e. The speed can't be determined from the given information. HELP ME PLS.......... :) & explain it pls.. :) Thanks.1 solutions Answer 325902 by mananth(12270)   on 2011-07-28 00:58:10 (Show Source): You can put this solution on YOUR website!boat speed = x mph current = 3 mph against current speed = x-3 with current speed = x+3 let y be the distance . downstream t= y/(x+3)............1 upstream 2t = y/(x-3)............2 multiply (1) by 2 2t=2y/(x+3) Therefore y/(x-3)=2y/(x+3) 1/(x-3)=2/(x+3) 2(x-3)=x+3 2x-6=x+3 2x-x=6+3 x=9 mph speed of boat m.ananth@hotmail.ca
 Functions/475270: y + 1 = X squared x squared + y = 71 solutions Answer 325900 by mananth(12270)   on 2011-07-28 00:45:13 (Show Source): You can put this solution on YOUR website!........1 ...........2 therefore y+1=7-y 2y=7-1 2y=6 y=3 plug y in (1)
 Rational-functions/475205: x^3-3x^2-5x over x^3-1 + x^3-2x^2+6 over 1-x^3 kindly maam sir /sir answer this? 1 solutions Answer 325864 by mananth(12270)   on 2011-07-27 21:50:17 (Show Source): You can put this solution on YOUR website! LCD = (x^3-1) m.ananth@hotmail.com
 Linear-systems/474992: Use the substitution method to solve the system of equations. Enter your answer as an ordered pair. y = 5x - 17 y = x + 31 solutions Answer 325727 by mananth(12270)   on 2011-07-27 11:48:22 (Show Source): You can put this solution on YOUR website!-5 x + y = -17 .............1 1 y = 3 + x ---------2 y = 3 + x Substitute y in (1) -5x+(3+x)=-17 -5x+3+x =-17 -5x+x=-17-3 -4x=-20 /-4 x= 5 Plug the value of x in (1) -5 x + y = -17 -5 * 5 + y = -17 -25 + y = -17 y = 8 / 1 y= 8 (5,8)
 Complex_Numbers/475011: Please help me solve this equation: Solve the equation (Hint: Set one side of the = to Zero by moving subtracting both sides of the equal by 49) You may use factoring or Quadrtatic Formula to solve this problem. x^2+20x+100=491 solutions Answer 325723 by mananth(12270)   on 2011-07-27 11:21:32 (Show Source): You can put this solution on YOUR website!x^2+20x+100=49 x^2+20x+51=0 x^2+17x+3x+51=0 x(x+17)+3(x+17)=0 (x+17)(x+3)=0 x=-17 OR -3 m.ananth@hotmail.ca
 Complex_Numbers/475012: Please help me to solve this equation: Use the Quadratic Formula to solve the equation. 5x^2-5x-10=01 solutions Answer 325722 by mananth(12270)   on 2011-07-27 11:16:47 (Show Source): You can put this solution on YOUR website! a= 1 b= -1 c= -2 b^2-4ac= 1 - 8 b^2-4ac= 9 = 3 x1=( 1 + 3 )/ 2 x1= 2 x2=( 1 -3 ) / 2 x2= -1 x = 2 OR -1 m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/475004: factor completely 4x^7-32x^6+8x^5 ^means raising to that power1 solutions Answer 325721 by mananth(12270)   on 2011-07-27 11:12:04 (Show Source): You can put this solution on YOUR website!4x^7-32x^6+8x^5 m.ananth@hotmail.ca
 Radicals/475007: solve V5x+21 =x+3 the V is suppose to be the square root symbol, the 5x+21 in under the entire root1 solutions Answer 325718 by mananth(12270)   on 2011-07-27 11:08:01 (Show Source): You can put this solution on YOUR website! square both sides =0 x=-4 , x=3
 Travel_Word_Problems/474989: Two planes leave the same airport and go in opposite directions at the same time, at 600 mph and 350 respectively. In how many hours will they be 2850 miles apart? 1 solutions Answer 325716 by mananth(12270)   on 2011-07-27 11:02:56 (Show Source): You can put this solution on YOUR website!combined speed = 600+350=950 mph distance =2850 time = 2850/950 time= 3 hours m.ananth@hotmail.ca
 Equations/474975: Hi. My name is Hannah. I am going in to 6th grade, and really need help with my math. I am going to be starting really hard equations with algebra next year... Will you help me get over my fear of 6th grade algebra? Thanks so much, Hannah1 solutions Answer 325702 by mananth(12270)   on 2011-07-27 09:31:09 (Show Source): You can put this solution on YOUR website!School algebra is as easy as a pie.Dont fear m.ananth@hotmail.ca
 Linear-equations/474949: Hi, please help me with this: When an airplane flies with a given wind, it can travel 3,000 kilometer in 5 hours. When the same airplane flies in the opposite directions against the wind, it takes 10 hours to fly the same distance. Find the speed of the plane in still air and the speed of the wind. Hint: let x = be the speed of the wind still air y = the speed of the wind1 solutions Answer 325701 by mananth(12270)   on 2011-07-27 09:29:33 (Show Source): You can put this solution on YOUR website!Distance = same= 3000 plane speed =x wind speed =y t=d/r 3000 / ( x - y )= 10.00 10 ( x - y ) = 3,000.00 10 x -10 y = 3000 ....................1 3000 / ( x + y )= 5.00 5.00 ( x + y ) = 3000 5.00 x + 5.00 y = 3000 ...............2 Multiply (1) by 1.00 Multiply (2) by 2.00 we get 10 x + -10 y = 3000 10 x + 10 y = 6000 20 x = 9000 / 20 x = 450 mph plane speed plug value of x in (1) 10 x -10 y = 3000 4500 -10 y = 3000 -10 y = 3000 -4500 -10 y = -1500 y = 150 mph wind speed
 testmodule/474961: Let p, q, and r be the following statements: p: Jamie is on the train. q: Sylvia is at the park. r: Nigel is in the car. Translate the following statement into English: (~p V q) right arrow r 1 solutions Answer 325700 by mananth(12270)   on 2011-07-27 09:20:21 (Show Source): You can put this solution on YOUR website! (~p V q)-> r = If Jamie is not on the train or Sylvia at the park,then Nigel is in the car.