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# Recent problems solved by 'mananth'

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 Proportions/381951: w/6=7/21 solutions Answer 270832 by mananth(12270)   on 2010-12-06 19:25:11 (Show Source): You can put this solution on YOUR website!w/6 = 7/2 multiply by 6 w*6/6 = 7*6/2 w=7*3 w=21 ... m.ananth@hotmail.ca
 Linear-systems/381945: write in standard form y=3/4x+61 solutions Answer 270831 by mananth(12270)   on 2010-12-06 19:23:43 (Show Source): You can put this solution on YOUR website!y = (3/4)x + 6 -6 -6 y-6 = 3x/4 multiply by 4 4(y-6)=3x 4y-24=3x -3x -3x -3x+4y-24 =0 -3x+4y=24 multiply by -1 3x-4y=-24 ... m.ananth@hotmail.ca
 Proportions/381943: 24/h=16/41 solutions Answer 270829 by mananth(12270)   on 2010-12-06 19:21:09 (Show Source): You can put this solution on YOUR website! ... multiply by h multiply by 4 24*4 = 16h*4/4 96=16h /16 96/16= h h= 6 ... m.ananth@hotmail.ca
 Travel_Word_Problems/381940: it takes rob 4 hours to paint a room. it takes darrin 3 hours to paint a room the same size. how long it take them to paint a similar sized room together 1 solutions Answer 270828 by mananth(12270)   on 2010-12-06 19:18:04 (Show Source): You can put this solution on YOUR website!Rob 4 hours Darrin 3 hours .. Rob does 1/4 of the job in 1 hour Darrin does1/3 of the job in 1 hour. .. both together will do 1/4 +1/3 of the job in 1 hour .. 1/4 +1/3 = 7/12 of the job in 1 hour. they will take 12 /7 hours to do the job together. =1.7 hours ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/381518: It takes a train the same time to travel 450 km as it takes a bus to travel 300 km. If the bus is traveling 30 km/h slower than the train, find the rate at which each is traveling. Pls. ans. this....1 solutions Answer 270598 by mananth(12270)   on 2010-12-06 08:45:19 (Show Source): You can put this solution on YOUR website!train rate = x bus rate = x-30 .. train distance = 450 miles bus distance = 300 miles .. time bus = time train 450/x= 300/(x-30) cross mulyiply 450(x-30)=300x 450x-13500=300x 450x-300x=13500 150x=13500 /150 x=13500/150 rate of train = 90 mph. rate of bus = 90-30 = 60 mph ... m.ananth@hotmail.ca
 Volume/381437: what is the height of a cylinder that can hold 8,000 litres of water if its diameter is 1.5 meters?1 solutions Answer 270596 by mananth(12270)   on 2010-12-06 08:41:22 (Show Source): You can put this solution on YOUR website!Diameter = 1.5 m radius = 0.75 m .. Volume V of cylinder = pi*r^2*h 8000 liters = 8 m^3 8=pi^0.75^2*h h=8/(0.75^2)*pi h = 4.527 meters .. m.ananth@hotmail.ca
 Quadratic_Equations/381454: i need your help to this problem. can you help me?here's the prob. A man is at a point A on the bank of a straight river. he can row in a still water at a rate which is 20 per cent faster than he can walk. if he rows downstream to a point B, which is 4 mi. below A and on the same side of the river, and then walks, in a direction which is perpendicular to the river, to a point C, 3mi. from B, it takes him the same amount of time that it thus to walk straight from A to c. if he walks back from C to B and then rows upstream to A, the return trip takes him an hour and 36min. longer. find his rate of walking, his rate of rowing in still water, and the rate of the current of the river.1 solutions Answer 270591 by mananth(12270)   on 2010-12-06 08:31:16 (Show Source): You can put this solution on YOUR website!... This is a multi stage problem .. Let walking rate be x mph Rowing rate in still water = 1.2x ( 20% more) .... Let rate of current = y mph Calculate time A---->B-------->C Ato B (down stream) time = 4/(1.2x+y) .. B to C (walk) time = 3/x Time A to B to C =4/(1.2x+y)+3/x ... AC ^2 = AB^2 +BC^2 AC^2=4^2+3^2 AC^2=25 AC = 5 miles Time to walk from A to C = 5/x ... Time from A to B to C = Time from A to C (walking) 4/(1.2x+y) + 3/x = 5/x 4/(1.2x+y)= 5/x-3/x 4/(1.2x+y)= 2/x cross multiply 4x=2(1.2x+y) 4x=2.4x+2y 4x-2.4x=2y 1.6x=2y /2 0.8x= y speed of current ... TIME RETURN 3/x + 4/(1.2x-y)(upstream) ... Time return - time forward = 8/5 hours .. (3/x + 4/(1.2x-y))- (4/(1.2x+y) + 3/x)= 8/5 y=0.8x plug value of y .. (3/x + 4/(1.2x-0.8x))- (4/(1.2x+0.8x) + 3/x)= 8/5 .. (3/x +4/0.4x)-(4/2x+3/x)=8/5 .. (3/x+10/x)-(2/x+3/x)=8/5 ... (13/x)-(5/x)=8/5 8/x=8/5 x=5 mph rate of walk. Rate of rowing in still water = 1.2x = 1.2 * 5 = 6 mph. .. Cheers m.ananth@hotmail.ca
 Travel_Word_Problems/381491: 2 cars leave the same corner at the same time, traveling at right angles to each other. One car is traveling 3 km per hour faster than the other car. After 1 hour they are 15 km apart. How fast is each car traveling?1 solutions Answer 270571 by mananth(12270)   on 2010-12-06 07:35:54 (Show Source): You can put this solution on YOUR website!let speed of one car be x kmph other car = x+3 kmph ... distance traveled by first car in1 hour = x km distance traveled by other car = x+3 km .. they are at distance of 15 km .. apply pythagoras theorem .. x^2+(x+3)^=15^2 x^2+x^2+6x+9=225 2x^2+6x-216=0 /2 x^2+3x-108=0 x^2+12x-9x-108=0 x(x+12)-9(x+12)=0 (x+12)(x-9)=0 x=9 km /h speed of one car. speed of other car = 9+3 = 12 km/h ... m.ananth@hotmail.ca
 Linear-equations/381427: The line through (3,4) that is parallel to the line 5x+3y=9. Write the equation of each line giving answers in standard form.1 solutions Answer 270543 by mananth(12270)   on 2010-12-06 01:02:29 (Show Source): You can put this solution on YOUR website!The line through (3,4) that is parallel to the line 5x+3y=9. Write the equation of each line giving answers in standard form. ... 5x+3y= 9 -5x -5x 3y=-5x+9 /3 y = -5x/3 +3 .. slope = (-5/3) ... The line parallel will have same slope. slope = (-5/3) point = (3,4) .. find b 4=(-5/3)*3 +b 4=-15+b b=19 .. y = -5x/3 + 19 .. standard form multipl;y by 3 3y=-5x+57 5x+3y-57 =0 ... ... m.ananth@hotmail.ca
 Quadratic_Equations/381299: A 60 foot by 80 foot rectangular walk in a park surrounds a flower bed. If the walk is of uniform width and its area is equal to the area of the flower bed, how wide is the walk? Set up a quadratic equation, factor, and solve.1 solutions Answer 270539 by mananth(12270)   on 2010-12-06 00:54:15 (Show Source): You can put this solution on YOUR website!width of walk = 60 feet length = 80 feet .. Area = 4800 ft^2 .. uniform width w .. GARDEN dimensions width = 60-2w length = 80-2w ... Area of garden = (60-2w)(80-2w) FOIL Area = 4800-120w-160w+4w^2 Area = 4w^2-280w+4800 .. Total area / area of garden = 2 4800 / 4w^2-280w+4800 = 2 4800/2 = 4w^2-280w+4800 2400 =4w^2-280w+4800 4w^2-280w+4800-2400=0 4w^2-280w+2400=0 /4 w^2-70w+600=0 w^2-60w-10w+600=0 w(w-60)-10(w-60)=0 (w-60)(w-10)=0 w= 60 OR 10 ignore 60 .. width = 10 feet ... m.ananth@hotmail.ca
 Travel_Word_Problems/381370: When a plane flies into the wind, it can travel 3,000 km in 6 hours. When it flies with the wind, it can travel the same distance in 5 hours. Find the rate of the plane in still air and the rate of the wind.1 solutions Answer 270532 by mananth(12270)   on 2010-12-06 00:25:57 (Show Source): You can put this solution on YOUR website!speed of plane = p speed of wind = w .. tail wind speed = p+w mph against wind speed = p-w .. distance tailwind = 3000 miles time = 5 hours .. t=d/r 5=3000/(p+w) multiply by (p+w) 5(p+w)=3000 /5 p+w = 600...................1 .. Against wind 6=3000/(p-w) 6(p-w)=3000 /6 p-w=500.....................2 .. add 1&2 2p=600+500 2p=1100 /2 p=550 mph ... p+w = 600 550+w=600 w=50 mph .. m.ananth@hotmail.ca
 Equations/381415: Use the quadratic formula to solve 8x^2+3x=-21 solutions Answer 270531 by mananth(12270)   on 2010-12-06 00:22:48 (Show Source): You can put this solution on YOUR website!8x^2+3x=-2 ... 8x^2+3x+2=0 ... discriminant = -55 .. ... x1=-0.1875 + 0.46351240544347893i ... .. x2=-0.1875 -0.46351240544347893i ... m.ananth@hotmail.ca
 Numbers_Word_Problems/381372: seven less than three times some number is the same as twenty nine1 solutions Answer 270529 by mananth(12270)   on 2010-12-06 00:17:20 (Show Source): You can put this solution on YOUR website!let number be x 3 times number = 3x .. 7 less 3x-7 3x-7=29 +7 +7 3x=36 /3 x= 12 the number ... m.ananth@hotmail.ca
 Functions/381390: Write an equation for each of the following situations: (a) Find the area A of a rectangle with a height x and a width twice the height. (b) What is the cost C of going to the movie, if a ticket for each of the x adults is \$6 and a ticket for each of the y children is \$4?1 solutions Answer 270525 by mananth(12270)   on 2010-12-06 00:11:01 (Show Source): You can put this solution on YOUR website!height = x width = 2x L*W= Area 2x*x= Area 2x^2 sq. units .. x adults ---adult = \$6 y children ---- child =\$4 ... C = 6x+4y ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/381395: A boeing 747 flies the 3000 mile distance from Los Angeles to New York, with a tail wind, in 5 hours. The return trip, against the wind, take 6 hours. Find the speed of the plane and the speed of the wind.1 solutions Answer 270522 by mananth(12270)   on 2010-12-06 00:07:12 (Show Source): You can put this solution on YOUR website!speed of plane = p speed of wind = w .. tail wind speed = p+w mph against wind speed = p-w .. distance tailwind = 3000 miles time = 5 hours .. t=d/r 5=3000/(p+w) multiply by (p+w) 5(p+w)=3000 /5 p+w = 600...................1 .. Against wind 6=3000/(p-w) 6(p-w)=3000 /6 p-w=500.....................2 .. add 1&2 2p=600+500 2p=1100 /2 p=550 mph ... p+w = 600 550+w=600 w=50 mph .. m.ananth@hotmail.ca
 Signed-numbers/381412: 9. A number is six times another number. When the numbers are added, their sum is 49. What are the numbers?1 solutions Answer 270521 by mananth(12270)   on 2010-12-06 00:01:43 (Show Source): You can put this solution on YOUR website!let x = one number 6x = other number .. 6x+x=49 7x=49 /7 x=49/7 x= 7 .. 7 & 42 are the numbers .. m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/381396: Short Answer. The length of the side of a rectangular desk is given by 9x - 2y cm. The length of the front is given by 9x + 2y cm. What is an algebraic expression for the area of the top of the rectangular desk? Include correct units as part of your answer.1 solutions Answer 270520 by mananth(12270)   on 2010-12-06 00:00:08 (Show Source): You can put this solution on YOUR website!side of a rectangular desk is given by 9x - 2y cm. The length of the front is given by 9x + 2y cm. ... Area = L*W (9x-2y)(9x+2y)=Area (81x^2-4y^2)cm^2= Area ... m.ananth@hotmail.ca
 Linear-equations/381411: Write the equation of each line, give the answer in slope intercept form. The line through (-1,-2) with slope 3/7.1 solutions Answer 270518 by mananth(12270)   on 2010-12-05 23:55:49 (Show Source): You can put this solution on YOUR website!The line through (-1,-2) with slope 3/7. .. Find b in y= mx+b .. -2=3/7 * -1+b -2=-3/7+b -2+3/7=b -11/7 =b ... y=3x/7 -11/7 ... m.ananth@hotmail.ca ...
 Surface-area/381403: if diameter is 24in n height is 12in, what is the total volume? 1 solutions Answer 270513 by mananth(12270)   on 2010-12-05 23:50:08 (Show Source): You can put this solution on YOUR website!Volume V of cylinder = pi*r^2*h r=12 h=12 V=pi*12^2*12 V= 5428.67 in^3 ... m.ananth@hotmail.ca
 Graphs/381405: Graph 5x+4y=81 solutions Answer 270512 by mananth(12270)   on 2010-12-05 23:47:03 (Show Source): You can put this solution on YOUR website!5x+4y=8 -5x 4y=-5x+8 /4 y=(-5x/4)+2 ... (x=0,y=2) (y=0,x=8/5) ... ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/381407: Short Answer. The length of the side of a rectangular desk is given by 9x - 2y cm. The length of the front is given by 9x + 2y cm. What is an algebraic expression for the area of the top of the rectangular desk? Include correct units as part of your answer.1 solutions Answer 270509 by mananth(12270)   on 2010-12-05 23:39:08 (Show Source): You can put this solution on YOUR website!side of a rectangular desk is given by 9x - 2y cm. The length of the front is given by 9x + 2y cm. ... Area = L*W (9x-2y)(9x+2y)=Area (81x^2-4y^2)cm^2= Area ... m.ananth@hotmail.ca
 Equations/381402: I need to solve this equation: 10/(x^2-2x)+4/x=5/(x-2) so far I have 4x+2/(x^2-2x) = 5x/(x^2-2x) Is this correct so far and where do I go from here?1 solutions Answer 270506 by mananth(12270)   on 2010-12-05 23:36:01 (Show Source): You can put this solution on YOUR website!10/(x^2-2x)+4/x=5/(x-2) .... ) ... ... LCD = x(x-2) multiply by x(x-2) .. .. 10+4*(x-2)-5(x-2)=0 10+4x-8-5x+10=0 -x+12=0 x=12 ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/381381: 1/x-2=2/x+4+2x-1/x^2+2x-8 this is a rational equation!! please help me solve! 1 solutions Answer 270500 by mananth(12270)   on 2010-12-05 22:58:06 (Show Source): You can put this solution on YOUR website! ... ... ... LCD = (x+4)(x-2) multiply by the LCD ... ... ... 2(x-2)+(2x-1)-(x+4)=0 2x-4+2x-1-x-4=0 3x-9=0 3(x-9)=0 x-9=0 x=9 ... m.ananth@hotmail.ca
 Travel_Word_Problems/381374: A Leisure Time Cruises riverboat travels 46 km downstream in 2 hours. It travels 51 km upstream in 3 hours. Find the speed of the boat and the speed of the water.1 solutions Answer 270488 by mananth(12270)   on 2010-12-05 22:16:27 (Show Source): You can put this solution on YOUR website!A Leisure Time Cruises riverboat travels 46 km downstream in 2 hours. It travels 51 km upstream in 3 hours. Find the speed of the boat and the speed of the water. rate of boat = b rate of current = c ... upstream speed = b-c mph downstream speed = b+c mph .. t= d/r Upstream 51/(b-c)=3 multiply by (b-c) 51=3(b-c) /3 17 = b-c b-c = 17............................1 ... downstream 46/(b+c)=2 multiply by (b+c) 46= 2(b+c) /2 b+c=23..............................2 ... add 1 & 2 2b=17+23 2b=40 /2 b=40/2 b=20 mph ... b-c=17 20-c=17 c=3 mph ... m.ananth@hotmail.ca
 Inequalities/381376: -8>5-v1 solutions Answer 270487 by mananth(12270)   on 2010-12-05 22:08:48 (Show Source): You can put this solution on YOUR website!-8>5-v -5 -5 -8-5>-v -13>-v /-1 v>13
 Numbers_Word_Problems/381365: eight times the sum of three consecutive even integers is 98 more than 23 times the smallest of the three integers. what are the integers?1 solutions Answer 270486 by mananth(12270)   on 2010-12-05 22:04:43 (Show Source): You can put this solution on YOUR website!let the integers be n,n+2,n+4 ... 8times the sum 8*(n+n+2+n+4) 8*(3n+6) ... 23 times smallest = 23n add 98 23n+98 ... 8(3n+6)=23n+98 24n+48=23n+98 -23n -23n 24n-23n+48=23n-23n+98 n+48=98 -48 -48 n+48-48=98-48 n=50 ... the numbers are 50, 52,54 .. m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/381316: solve. moolah has 24 coins that are all dimes and quarters.the value of the coins is \$3.75. how many dimes and how many quarters does moolah have? these are the equations i came up with d=10 q=25 d+q=24 10d+25q=\$3.751 solutions Answer 270483 by mananth(12270)   on 2010-12-05 21:48:02 (Show Source): You can put this solution on YOUR website!d=10 q=25 d+q=24 .............................1 10d+25q=\$3.75 3.75 = 375 cents ... 10d+25q=375.........................2 .. solve by addition multiply (1) by -10 -10d-10q=-240 add it to (2) 25q-10q=375-240 15q=135 /15 q=135/15 q= 9 ... plug value of q in 1 d+q=24 d+9=24 d=15 .. CHECK 10*15+9*25 =150+225 =375. m.ananth@hotmail.ca
 Expressions-with-variables/381303: Solve the system of equations by the addition method. x/4-y/12=-1 x/3+y/9=-21 solutions Answer 270447 by mananth(12270)   on 2010-12-05 20:38:00 (Show Source): You can put this solution on YOUR website!x/4-y/12=-1 LCD =12 3x-y /12 =-1multiply by 12 3x-y=-12.........................1 x/3+y/9=-2 lCD=9 (3x+y)/9 = -2 multiply by 9 3x+y=-18.........................2 Add (1)&(2) 6x=-12+-18 6x=-30 /6 x=-5 ... plug value of x in 2 -15+y=-18 +15 +15 y=-3 ... m.ananth@hotmail.ca
 Graphs/381298: 17)Find the slope of the line that is (a)parallel and (b)perpendicular to the line through the pair of points. (-4,-6) and (1,3) For both, type an integer and simplified fraction.1 solutions Answer 270446 by mananth(12270)   on 2010-12-05 20:27:19 (Show Source): You can put this solution on YOUR website!(-4,-6) and (1,3) slope m of the line passing through above points = =y2-y1 / x2-x1 =((3-(-6))/((1-(-4)) =(9/5) ... slope of line parallel to this linewill be the same = 9/5 .. Find the value of b plug x,y, & b in y= mx +b -6=9/5*-4 +b -6+36/5 =b (-30+36)/5 =b b= 6/5 .. equation of line parallel to the line will be y= 9/5 *x +6/5 Y = 1.8 X + 1.20 .... Line perpendicular will have slope of negative reciprocal= -5/9 y= -5/9x +6/5 y=--0.55x+1.20 ... ... m.ananth@hotmail.ca
 Travel_Word_Problems/381297: if a car travels 60mph how long would it take to travel 210 miles1 solutions Answer 270442 by mananth(12270)   on 2010-12-05 20:15:24 (Show Source): You can put this solution on YOUR website! ... t= 210/60 t=3.50 hours ... m.ananth@hotmail.ca
 Expressions-with-variables/381295: The sum of the angle of a triangle is 180〫. If one angle of a triangle measures x and the second angle measures (5x+18)〫, express the measure of the third angle in terms of x. Simplify the expression.1 solutions Answer 270440 by mananth(12270)   on 2010-12-05 20:13:40 (Show Source): You can put this solution on YOUR website!One angle = x second angle = (5x+18) third angle = 180 - (x+5x+18) third angle = 180-(6x+18) third angle = 180 -6x-18 third angle =