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# Recent problems solved by 'mananth'

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 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
 Linear_Equations_And_Systems_Word_Problems/562723: On an interstate highway the maximum speed is 70 miles per hour and the minimum speed is 45 miles per hour. If x represents speed, then write an inequality to express this condition 1 solutions Answer 364654 by mananth(12270)   on 2012-01-25 19:52:06 (Show Source):
 Travel_Word_Problems/562708: Daily rate is \$39 + 0.20 per mile, Rent car for 1 day, the bill is \$95 before taxes. How many miles did you drive. Am I setting this equation up right? Here is what I have. 39+ 0.20 (1) = 95 If not how??1 solutions Answer 364653 by mananth(12270)   on 2012-01-25 19:48:52 (Show Source): You can put this solution on YOUR website!\$39 + 0.20 per mile, if you drive only 1 mile it will cost 39.20 if you drive x miles it will cost (% \$39 + 0.20(x)=95 0.2x=95-39 0.2x=56 /0.2 x=56/0.2 x=280 miles
 Numbers_Word_Problems/562332: find three consecutive numbers such that the sum of the second and the third numbers exceeds the first by 14.1 solutions Answer 364553 by mananth(12270)   on 2012-01-25 09:34:00 (Show Source): You can put this solution on YOUR website!let the three consequtive numbers be x, x+1, x+2 x+1+x+2=x+14 2x+3=x+14 -x 2x-x+3=14 x+3=14 -3 x=11 11,12,13
 Expressions-with-variables/562341: 5x-9y=-3 4x-3y=61 solutions Answer 364552 by mananth(12270)   on 2012-01-25 09:30:36 (Show Source): You can put this solution on YOUR website!5 x -9 y = -3 .............1 4 x -3 y = 6 .............2 Eliminate y multiply (1)by 1 Multiply (2) by -3 5 x -9 y = -3 -12 x 9 y = -18 Add the two equations -7 x = -21 / -7 x = 3 plug value of x in (1) 5 x + -9 y = -3 15 + -9 y = -3 -9 y = -3 -15 -9 y = -18 y = 2 m.ananth@hotmail.ca
 Linear-equations/562342: write the equation of the line that is parallel to the line y=-3+12 and passes through the point (-1,6)1 solutions Answer 364551 by mananth(12270)   on 2012-01-25 09:28:39 (Show Source): You can put this solution on YOUR website!1 y = -3 x + 12 Divide by 1 y = -3 x + 12 Compare this equation with y=mx+b slope m = -3 0.8 The slope of a line parallel to the above line will be the same The slope of the required line will be -3 m= -3 ,point (-1,6 ) Find b by plugging the values of m & the point in y=mx+b 6 = 3 + b b= 3 m= -3 Plug value of the slope and b in y = mx +b The required equation is y= -3x + 3 m.ananth@hotmail.ca
 Mixture_Word_Problems/562337: if 40 liters of an acid solution is 60% acid, how many liters of pure acid are there in the mixture?1 solutions Answer 364548 by mananth(12270)   on 2012-01-25 08:58:43 (Show Source): You can put this solution on YOUR website!60% of 40 liters 0.6*40 = 24 liters
 Money_Word_Problems/562334: 14% interest on borrowing \$5,000 for 3years1 solutions Answer 364547 by mananth(12270)   on 2012-01-25 08:57:14 (Show Source): You can put this solution on YOUR website!if it is simple interest I = P*r*n I=5000*0.14*3 I= \$2100
 Volume/562335: I have two aquariums. One is 12x18x30. The other is 13x24x30. how many gallons of water will fit into each of them.1 solutions Answer 364545 by mananth(12270)   on 2012-01-25 08:55:08 (Show Source): You can put this solution on YOUR website!I presume they are in feet One is 12x18x30. Volume = L*W*H 12x18x30=6480 cu.ft The other is 13x24x30 =9360 9360+6480 =14840 cu.ft 1 cu.ft = 7.48 gallons 14840/7.48= 1984 gallons ( rounded off)
 Travel_Word_Problems/562297: the speed of a freight train is 14 mph slower than that of passanger train.if the passenger train travels 400 miles in the time it take the freight train to travel 70 fewer miles ,what is the speed of the passenger train1 solutions Answer 364543 by mananth(12270)   on 2012-01-25 08:46:08 (Show Source): You can put this solution on YOUR website!Freight train x 330 miles Passenger train x+14 400 miles 330/x=400/(x+14) 330/x-400(x+14) LCD = x(x+14) = Multiply by LCD 330(x+14)-400x= 0 330x+4620-400*x =0 -70x+4620=0 -70x=-4620 /-70 x=66 speed of Freight train x+14=> 80 speed of Passenger train
 Linear-equations/562307: I am needing help setting up this problem and solving. Thank you so much in advance, I'll be sure to leave comments and like your page! Graph the following equations; calculate the slope, x-intercept, and y-intercept, and label the intercepts on the graph. 2x + 3y = 91 solutions Answer 364539 by mananth(12270)   on 2012-01-25 08:16:25 (Show Source): You can put this solution on YOUR website!equation 2x+3y=9 rewrite the equation in slope intercept form 3y=-2x+9 /3 y=(-2/3)x+3 compare equation with y=mx+b m=(-2/3) the slope +3 = y intercept when y = 0 x=4.5 the x intercept when x= 0 y= 3 ( 0 , 3 ) when y = 0 x= 4.5 ( 4.5 , 0 )
 Numbers_Word_Problems/562281: The Square of a number exceeds the number by 110. Find the number 1 solutions Answer 364527 by mananth(12270)   on 2012-01-25 01:40:26 (Show Source): You can put this solution on YOUR website!let the number be x square = x^2 x^2=x+110 x^2-x-110=0 x^2-11x+10x-110=0 x(x-11)+10(x-11)=0 (x+10)(x-11)=0 x= -10 OR 11
 Rate-of-work-word-problems/562282: at 7:00 am joe starts jogging at 6mi/h . At 7:10 Ken starts off after him. How fast must ken run in order to overtake him at 7:301 solutions Answer 364526 by mananth(12270)   on 2012-01-25 01:38:33 (Show Source): You can put this solution on YOUR website!Joe speed = 6 mph Ken speed = x mph Joe starts 10 minutes early so he has run 6*10/60 = 1 mile before ken starts distance Ken has to run to catch up = 6-1=5 miles catchup time = 20 minutes ( from 7:10 to 7:30)= 2/3 hours speed = d/t speed = 5/(2/3) speed = 5 *3/2 speed = 15/2 = 7.5 mph CHECK catchup time = 2/3 Joe started 1/6 hour early so he ran for 2/3 +1/6 = 5/6 hours his speed = 6 mph 5/6 hour *6 = 5 miles
 Reduction-of-unit-multipliers/562249: I need to convert 28.6 lb / ft cu. To kg / m cu. Please help!1 solutions Answer 364523 by mananth(12270)   on 2012-01-25 01:24:45 (Show Source): You can put this solution on YOUR website! 28.6 lb / ft cu. To kg / m cu. 1kg = 2.2 lb 1cu.m = 35.31 cu.ft =459.03kg/m^3
 Polynomials-and-rational-expressions/562259: can 8x to the 3rd power +27y to the 3rd power be simplified1 solutions Answer 364518 by mananth(12270)   on 2012-01-25 01:07:55 (Show Source): You can put this solution on YOUR website! you have to use the identity
 Mixture_Word_Problems/562273: if a chemist has 40 ounces of a 25% acid solution, how much acid should be mixed with it to produce a new solution that is 40%1 solutions Answer 364517 by mananth(12270)   on 2012-01-25 01:04:42 (Show Source): You can put this solution on YOUR website! percent ---------------- quantity Acid solution 25 ----------------40 ounces Pure acid 100 ----------------x ounces Mixture 40 ----------------40+x ounces 25*40+100x=40(40+x) 1000+100x=1600+40x 100x-40x=1600-1000 60x=600 /60 x=10 ounces of Pure acid
 Volume/562264: a cylindrical tin if height 15cm and radius 4cm is filled with sand from a rctangular box. how many times can the tin be filled if the dimensions of the box are 50cm by 40cm by 20cm?1 solutions Answer 364514 by mananth(12270)   on 2012-01-25 01:01:21 (Show Source): You can put this solution on YOUR website!Volume of Box / volume of tin = number of tins required Volume of box =50*40*20= 40000 cu.cm Volume of Tin = pi*r^2*h=pi*4^2*15 = 754 cu.cm 4000/754= 53 tins (rounded off)
 Quadratic_Equations/562173: the solutions are x=-5, x=0 what is the quadratic equation?1 solutions Answer 364502 by mananth(12270)   on 2012-01-24 23:05:49 (Show Source): You can put this solution on YOUR website!x(x+5) x^2+5x
 Money_Word_Problems/562228: chuan invested some money in a savings account earning 6% interest and an equal amount of money in bonds earning 8% interest. How much did he invest altogether if he earned \$210 in a year?1 solutions Answer 364501 by mananth(12270)   on 2012-01-24 23:02:49 (Show Source): You can put this solution on YOUR website!money invested = x in each x+x=2x 6x+8x=210*100 ( percentage converted by multiplying by 100) 14x=21000 x=21000/14 x=1500 1500@6%=90 1500@8%=120 Total = 210
 test/562231: Twice the square of a number is 10 more than the number. What is the number?1 solutions Answer 364500 by mananth(12270)   on 2012-01-24 22:57:26 (Show Source): You can put this solution on YOUR website!number =x 2x^2=x+10 2x^2-x-10=0 2x^2-5x+4x-10=0 x(2x-5)+2(2x-5)=0 (2x-5)(x+2)=0 x=5/2 OR x=-2
 Linear-systems/562146: tell whether the system has one solution infinitely many solutions or no solution 5=1/2x+3y 10-x=6y1 solutions Answer 364457 by mananth(12270)   on 2012-01-24 20:45:14 (Show Source): You can put this solution on YOUR website!5=1/2x+3y multiply by 2 10=x+6y 6y=-x+10 /6 y=-x/6 +10/6 10-x=6y /6 y=-x/6 + 10/6 compare with y= mx+b slopes are same and y intercepts are same so the lines coincide with each other. so they have innumerable solution -
 Exponents/562143: Please help me solve this problem. 1 solutions Answer 364453 by mananth(12270)   on 2012-01-24 20:41:37 (Show Source):
 Miscellaneous_Word_Problems/562122: I need an equation for the tollowing word problem. at your lemonade stand you charge .50 for 1/2 cup and .75 for a full cup at the end of the day you see that 12 cups have been used and you have made 8\$ how name of each size of drink did you sell? 1 solutions Answer 364450 by mananth(12270)   on 2012-01-24 20:39:12 (Show Source): You can put this solution on YOUR website!1/2 cup ---x numbers full cup---y numbers x+y =12 0.5x+0.75y=8 multiply by 100 50x+75y=800 these are the two equations solve for x & y 1 x + 1 y = 12 .............1 50 x + 75 y = 800 .............2 Eliminate y multiply (1)by -75 Multiply (2) by 1 -75 x -75 y = -900 50 x 75 y = 800 Add the two equations -25 x = -100 / -25 x = 4 1/2 cup plug value of x in (1) 1 x + 1 y = 12 4 + 1 y = 12 1 y = 12 -4 1 y = 8 y = 8 full cup
 Linear-equations/562130: what is the slope intercept form for 5x-9y=111 solutions Answer 364446 by mananth(12270)   on 2012-01-24 20:31:33 (Show Source): You can put this solution on YOUR website!5x-9y=11 re write in slope intercept form 9y=5x-11 /9 y=(5/9)x-(11/9) compare with y=mx+b m= slope = (5/9) y intercept = b = 11/9
 Travel_Word_Problems/562106: A plane traveled 1012 miles to go to jacksonville and back. The trip there was with wind. It took 11 hours.The trip back took 22 hours. What is the speed of the plane in still air? What is the speed of the wind? ----------------------------------------------------------------------------------------- I tried drawing a table, but it has been a wile since I have solved any problems. The answer I got was a repeating decimal, so I doubt very much its likelihood of being correct.1 solutions Answer 364444 by mananth(12270)   on 2012-01-24 20:29:18 (Show Source): You can put this solution on YOUR website!plane speed=x mph wind speed=y mph with wind Speed = (x+y) against wind speed= (x-y) t=d/r d= 1012 downstream 1012 / (x+y)= Speed = 11 divide by 11 92 / (x+y)= 1 x+ y 92 ............1 d= against wind 1012 1012 /(x-y)= 22 divide by 22 46 /(x-y) = 1 x - y = 46.00 .............2 add up (1) & (2) 2 x = 138 / 2 x= 69 mph speed of plane in still air plug value of x in (1) we get y= 23 mph speed of wind
 Linear-systems/562104: solve each system using substitution. 2=2y-x 23=5y-4x1 solutions Answer 364440 by mananth(12270)   on 2012-01-24 20:13:17 (Show Source): You can put this solution on YOUR website!2=2y-x x=2y-2 23=5y-4x substitute x in second equation 23=5y-4x 23=5y-4(2y-2) 23=5y-8y+8 23=-3y+8 -3y=23-8 y=-5 plug y in equation to get x x=2y-2 x=-10-2 x=-12
 Mixture_Word_Problems/562081: please help me solve this problem. manuel traveled 4 hours non stop to mexico a total of 166 mles. he took a train part of the way which averaged 50 mph, and then took a bus the remaining distance, which avereged 30 mph. how long was manuel on the train?1 solutions Answer 364438 by mananth(12270)   on 2012-01-24 20:07:21 (Show Source): You can put this solution on YOUR website!First part distance = x--------------speed =50 mph II part will be 166-x----------------------30 mph t=4 time first part + time II part = 4 t=d/r x/50 + (166-x)/30 = 4 LCD = 150 multiply equation by 150 3x+5(166-x)=4*150 3x+830-5x=600 -2x=-230 /-2 x= 115 miles time on train = 115 /50=2.3 hours
 Rectangles/562084: A rectangle has a length of 4x and a width of 4x-2. Its perimeter is 12. What is the length and width? How do you solve this problem? Step by step1 solutions Answer 364437 by mananth(12270)   on 2012-01-24 19:54:27 (Show Source): You can put this solution on YOUR website!length = 4x width = 4x-2 Perimeter 2(L+W) 12= 2(4x-2+4x) 12=2(8x-2) 12=16x-4 12+4 =16x 16=16x x=1 length = 4x =4 width = 4x-2=> 4-2=2
 test/562079: A restaurant manager bought 20 packages of bagels. Some packages contained 6 bagels each, and the rest contained 12 bagels each. There were 168 bagels in all. How many packages of 12 bagels did the manager buy?1 solutions Answer 364436 by mananth(12270)   on 2012-01-24 19:51:28 (Show Source): You can put this solution on YOUR website!6 bagel packages ------- x numbers 12 bagel packages ----------y numbers x+y =20 6x+12y=168 x + y = 20 .............1 6x + 12y = 168 .............2 Eliminate y multiply (1)by -12 Multiply (2) by 1 -12x -12y = -240 6x 12y = 168 Add the two equations -6 x = -72 / -6 x = 12.00 OR 12 plug value of x in (1) 1 x + 1 y = 20 12 + 1 y = 20 1 y = 20-12 1 y = 8 6 pack 12 numbers 12 pack 8 umbers m.ananth@hotmail.ca
 Linear-systems/562073: solve each system using substitution. y=8-x 7=2-y1 solutions Answer 364434 by mananth(12270)   on 2012-01-24 19:46:02 (Show Source): You can put this solution on YOUR website!y=8-x 7=2-y -y=7-2 -y=5 y=-5 plug y in first equation -5=8-x -x=-13 x=13
 Money_Word_Problems/561627: I put \$10000.00 in the bank. In 12 years the principle and interest is \$16000.00. What is the simple interest rate. I am sure the answer is 5.5% but I do not know how to get it through the correct formula. Thank you for your help1 solutions Answer 364330 by mananth(12270)   on 2012-01-24 02:19:51 (Show Source): You can put this solution on YOUR website!P=10000 Interest = 6000 n= number of years = 12 I= p*r*n 6000= 10000*r*12 6000/(10000*12)=r 6000/120000=r 6/120 =0.05 0.05 * 100 = 5%