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# Recent problems solved by 'mananth'

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 Linear-equations/534961: find the slope of a line parallel to the line that passes through the following points. (4, 0) and (3.8, 2)1 solutions Answer 351708 by mananth(12270)   on 2011-11-21 03:01:44 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 4 * 0 3.8 2 slope m = (y2-y1)/(x2-x1) ( 2 - 0 )/( 3.8 - 4 ) ( 2 / -0.2 ) m= -10 Parallel line will have same slope m.ananth@hotmail.ca
 Finance/534914: How long does it take an \$1100 investment to earn \$200 interest if it is invested at 7% interest compounded quarterly?1 solutions Answer 351707 by mananth(12270)   on 2011-11-21 02:54:51 (Show Source): You can put this solution on YOUR website!Principal P = 1100 Interest = 200 Amount= 1300 years=n compounded (t) 4 times a year Rate = 7 0.02 Amount = P*((n+r)/n)^n 1300 = 1100 *( 1 + 0.02 )^ n*t 1.18 = *( 1 + 0.02 )^ n* 4 ln 1.18 = 4 n *ln 1.02 0.17 = 4 0.02 *n 2.41 = n 2.41 years m.ananth@hotmail.ca
 Travel_Word_Problems/534938: A truck traveled the first 90 miles of a trip at one speed and the last 80 miles at an average speed of 5 miles per hour less. The entire trip took 4 hours. What was the average speed for the first part of the trip?1 solutions Answer 351706 by mananth(12270)   on 2011-11-21 02:43:35 (Show Source): You can put this solution on YOUR website!first part 90 miles second part 80 miles speed in first part x mph speed second part x -5 mph Total rowing time 2 hours Time first part 90 / x Time second part 80 / ( x -5 ) Time first part + time second part = 4 hours 90 / x + 80 /(x -5 ) = 2 LCD = ( x + 0 )* (x -5 ) multiply the equation by the LCD we get 90 * (x -5 )+ 80 x = 2 90 x -450 + 80 x = 2 X^2 180 x -450 = 2 X^2 2 X^2 -180 x 450 = 0 2 X^2+ -180 x+ 450 = / 2 1 X^2 -90 x 225 = Find the roots of the equation by quadratic formula a= 1 b= -90 c= 225 b^2-4ac= 8100 - -900 b^2-4ac= 7200 = 84.85 x1=( 90 + 84.85 )/ 2 x1= 87.43 87 3/7 x2=( 90 -84.85 ) / 2 x2= 2.57 2 4/7 Ignore negative value x = 87.43 mph LCD = speed CHECK Time first part + Time second part 1.03 + 0.97 = 2 m.ananth@hotmail.ca
 Travel_Word_Problems/534944: two trains start in the same place traveling in opposite directions. one train travels 12 mph faster than the other. find the rate of each train if they are 780 miles apart after 6 hours. 1 solutions Answer 351705 by mananth(12270)   on 2011-11-21 02:36:40 (Show Source): You can put this solution on YOUR website!Train I x mph Train II x+ 12 mph .. They are moving away from each other So add up their speed. combined speed = x+ 1 x + 12 ( 2 x + 12 ) Time = 6 hours Distance = 780 miles Distance = speed * time ( 2 x 12 )* 6 = 780 12 x + 72 = 780 12 x = 780 + -72 12 x = 708 / 12 x= 59 mph Train I Train II 59 + 12 = 71 mph m.ananth@hotmail.ca
 Linear-equations/534958: (-3, ____) is a solution of y=4-3x. 1 solutions Answer 351704 by mananth(12270)   on 2011-11-21 02:32:48 (Show Source): You can put this solution on YOUR website!(-3,13) is a solution of y=4-3x.
 Linear-equations/534959: two differnet lines are parallel if thier slopes are ? 1 solutions Answer 351703 by mananth(12270)   on 2011-11-21 02:31:51 (Show Source): You can put this solution on YOUR website!equal slopes
 Linear-equations/534966: find an equation of the line satisfying the conditions given. Express your answer in standard form. parallel to 3x - y = -5 and passing through (-1, 0)1 solutions Answer 351702 by mananth(12270)   on 2011-11-21 02:30:00 (Show Source): You can put this solution on YOUR website!3 x + -1 y = -5 Find the slope of this line make y the subject -1 y = -3 x + -5 Divide by -1 y = 3 x + 5 Compare this equation with y=mx+b slope m = 3 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 , 0 ) Find b by plugging the values of m & the point in y=mx+b 0 = -3.00 + b b= 3 m= 3 Plug value of the slope and b in y = mx +b The required equation is y = 3 x + 3 y = 3 x + 3 3x-y=-3 m.ananth@hotmail.ca
 Linear-equations/534967: find an equation of the line satisfying the conditions given. express your answer in the standard form. parallel to 5x - y =4 and passing through (-2, 0)1 solutions Answer 351701 by mananth(12270)   on 2011-11-21 02:26:54 (Show Source): You can put this solution on YOUR website!5 x + -1 y = 4 Find the slope of this line make y the subject -1 y = -5 x + 4 Divide by -1 y = 5 x -4 Compare this equation with y=mx+b slope m = 5 m= 5 ,point ( -2 , 0 ) Find b by plugging the values of m & the point in y=mx+b 0 = -10.00 + b b= 10 m= 5 Plug value of the slope and b in y = mx +b The required equation is y = 5 x + 10 y = 5 x + 10 -5x+y=10 m.ananth@hotmail.ca
 Functions/534968: find an equation of the line satisfying the conditions given. Express your answer in standard form. parallel to 5x-y=4 and passing through (-2, 0)1 solutions Answer 351700 by mananth(12270)   on 2011-11-21 02:25:52 (Show Source): You can put this solution on YOUR website!5 x + -1 y = 4 Find the slope of this line make y the subject -1 y = -5 x + 4 Divide by -1 y = 5 x -4 Compare this equation with y=mx+b slope m = 5 m= 5 ,point ( -2 , 0 ) Find b by plugging the values of m & the point in y=mx+b 0 = -10.00 + b b= 10 m= 5 Plug value of the slope and b in y = mx +b The required equation is y = 5 x + 10 y = 5 x + 10 -5x+y=10 m.ananth@hotmail.ca
 Proportions/534824: If the cost of x apples is b cents, what is a general formula for the cost, in cents, of y apples? I know the answer is bx/y, but I need to know why????? Thanks for your help!!1 solutions Answer 351644 by mananth(12270)   on 2011-11-20 20:09:42 (Show Source): You can put this solution on YOUR website!if 10 apples cost 15 cents 15 apples will cost 15*15/10 = 22.5 cents Similarly if x apples cost b cents y apples will cost b*y/x m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/534819: factor completely t^2 – 25t + 1141 solutions Answer 351643 by mananth(12270)   on 2011-11-20 20:06:22 (Show Source): You can put this solution on YOUR website!t^2 – 25t + 114 t^2-19t-6t+114=0 t(t-19)-6(t-19)=0 (t-19)(t-6)=0 t=9 , t=6
 Linear-equations/534779: How do I use substitution to get the answer x=0 and y=-4 for these problems: 10x+3y= -12 5x+4y= -16 I've tried quite a few times and keep getting fractions. Please help.1 solutions Answer 351641 by mananth(12270)   on 2011-11-20 20:00:59 (Show Source): You can put this solution on YOUR website!10 x + 3 y = -12 .............1 4 y = -16 -5 x ---------2 / 4 = y = -4 -1.25 x Substitute y in (1) 10x+3(-4-1.25x )= -12 10x-12+ -3.75x = -12 10x-3.75x = -12 12 6.25 x = 0 / 6.25 x= 0 Plug the value of x in (1) 10x+3= -12 10*0+3y = -12 0+3y=-12 3y=-12 / 3 y= -4 m.ananth@hotmail.ca
 Travel_Word_Problems/534796: The hypotenuse of a right triangle is 1.3 units long. The longer leg is 0.7 units longer than the shorter leg. Find the lengths of the legs of the triangle. All I am able to figure out is the formula to use is a^2 + b^2 = c^2. Please help. I am lost from here. Thank you in advance!1 solutions Answer 351639 by mananth(12270)   on 2011-11-20 19:52:40 (Show Source): You can put this solution on YOUR website!let shorter leg be x units longer leg = x+0.7 units Hypotenuse = 1.3 units By Pythagoras theorem x^2+(x+0.7)^2= 1.3^2 x^2+x^2+1.4x+0.49=1.69 2x^2+1.4x-1.2 /2 x^2+0.7x-0.6=0 multiply by 10 to eliminate the decimals 10x^2+7x-6=0 10x^2+12x-5x-6=0 2x(5x+6)-1(5x+6)=0 (5x+6)(2x-1)=0 x=-6/5 OR 1/2 Ignore negative x=1/2
 Mixture_Word_Problems/534456: John bought two horses at rs 20,000 each.he sold one horse at 15% gain. But he had to sell the second horse at a loss.if he had suffered a loss of rs 1800 on the whole transaction,find the s.p of the second horse.1 solutions Answer 351564 by mananth(12270)   on 2011-11-20 04:58:11 (Show Source): You can put this solution on YOUR website! Profit on first horse = 20,000*15% 15/100 * 20000= Rs. 3000 SP = 23000 Loss on the second horse = x SP= CP-loss SP= 20000-x SP of both = 23000+20000-x CP of both = 40000 CP-SP=Loss = 1800 40000-(43000-x)= 1800 40000-43000+x=1800 -3000+x=1800 x= 4800 SP= cp-loss SP= 20000-4800 SP= 15200 He sold second horse for Rs. 15200. 00 m.ananth@hotmail.ca
 Evaluation_Word_Problems/534358: How do I use two variables and two equations to solve this problem. A machine in a pottery factory takes 3 minutes to form a bowl and 2 minutes to form a plate. The material for a bowl costs \$0.25, and the material for a plate costs \$0.20. If the machine runs for 8 hours and exactly \$44 is spent for material, how many bowls and plates can be produced? How do I set it up? 1 solutions Answer 351561 by mananth(12270)   on 2011-11-20 04:36:37 (Show Source): You can put this solution on YOUR website!let number of bowls be x and plates be y time taken 3x+2y= 480 Money spent 0.25x+0.2y = 44 multiply by 100 to eliminate the decimals 25x+20y=4400 bowls x numbers , Price = \$3.00 plates y numbers , Price = \$9.00 Total 345 3 x + 2 y = 480 .............1 25 x + 20 y = 4400 .............2 Eliminate y multiply (1)by -10 Multiply (2) by 1 -30 x -20 y = -4800 25 x 20 y = 4400 Add the two equations -5 x = -400 / -5 x = 80 plug value of x in (1) 3 x + 2 y = 480 240 + 2 y = 480 2 y = 480 -240 2 y = 240 y = 120 bowls 80 numbers plates 120 numbers m.ananth@hotmail.ca
 Money_Word_Problems/534458: An amount is invested in an account that offers 5% (percent) interest which is compounded annually. How long will it take for this amount to double?1 solutions Answer 351560 by mananth(12270)   on 2011-11-20 04:26:54 (Show Source): You can put this solution on YOUR website!Assume principal = 100 Amount = 200 Principal P = 100 Amount= 200 years=n compounded (t) 1 Rate = 5 0.05 Amount = P*((n+r)/n)^n 200 = 100 *( 1 + 0.05 )^ n*t 2 = *( 1 + 0.05 )^ n* 1 ln 2 = 1 n *ln 1.05 0.69 = 1 0.05 *n 14.21 = n 14.21 years m.ananth@hotmail.ca
 Travel_Word_Problems/534440: Boat traveling against the current travels out 2miles, passes a log moving with the current. The boat travels 1hr more, turns around and arrives at shore the same time as the log. What is rate of current?1 solutions Answer 351559 by mananth(12270)   on 2011-11-20 04:19:04 (Show Source): You can put this solution on YOUR website!Let x be the speed of the rower,and y be the speed of the current. The upstream rowing speed is x-y, mph and the downstream rowing speed is x+y. mph Let A be the point where the rower crosses the log. In 1 hour after crossing the log, the rower reached x-y miles. (upstream speed*1) The log reached y miles from A. (current speed * 1) They are separated by distance x miles now. (x-y+y) miles =x miles They are travelling in the same direction so subtract the speeds (x+y-y) .=x mph is the effective speed t=d/r x/x = 1 hr for the rower back to reach the log at the starting point. floating 2 mile for log=====>1+1= 2hrs. Therefore,the speed of current is 2 miles/hr. m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/534134: on a plane, two men together had 135 kilograms of luggage.The first paid \$1.35 for his excess luggage and the second paid S2.70 for his excess luggage. had all the luggage belonged to one person, the excess luggage charge would have been \$8.10. At most how many kilograms of luggage is each person permitted to bring on the plane free of additional charge.1 solutions Answer 351344 by mananth(12270)   on 2011-11-19 08:43:23 (Show Source): You can put this solution on YOUR website!let x kg be the free allowance for both of them the free allowance = 2x 135-2x is the excess luggage 135-2x they paid \$4.05 1 kg they pay how much ? They pay 4.05/(135-2x) per kg excess Single person 135-x is the excess luggage For 135 kg he pays \$8.10 He pays 8.10/(135-x)per kg for excess luggage The rate per kg for excess luggage is the same so equate both 4.05/(135-2x)=8.10/(135-x) 4.05(135-x)=8.10(135-2x) 546.75-4.05x=1093.5-16.2x 12.15x=546.75 /12.15 x=45 kg free luggage allowance m.ananth@hotmail.ca
 test/534155: solve the following system of equations using substiution. Please help! x-4y=4 6x-3y=-181 solutions Answer 351329 by mananth(12270)   on 2011-11-19 08:00:25 (Show Source): You can put this solution on YOUR website!1 x -4 y = 4 .............1 -3 y = -18 -6 x ---------2 / -3 = y = 6 + 2 x Substitute y in (1) 1 x -4 ( 6 + 2 x ) = 4 1 x -24 + -8 x = 4 1 x -8 x = 4 24 -7 x = 28 / -7 x= -4 Plug the value of x in (1) 1 x -4 y = 4 1 * -4 -4 y = 4 -4 -4 y = 4 -4 y = 8 / -4 y= -2 m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/534061: A clothing company borrows \$775,000. Some of the money is borrowed at 8%, some at 9%, and some at 10% simple annual interest. How much is borrowed at each rate if the total annual interest is \$67,500 and the amount borrowed at 8% is four times the amount borrowed at 10%?1 solutions Answer 351316 by mananth(12270)   on 2011-11-19 05:00:39 (Show Source): You can put this solution on YOUR website!8%--------------------x 9%--------------------y 10%-------------------z x=4z therefore 8% -----------4z 4z+y+z=775000 5z+y=775000...................(1) 0.08*4z+0.09y+0.1z=67500 0.32z+0.09y+0.1z=67500 0.42z+0.09y=67500.............(2) 5 z + 1 y = 775000 .............1 0.42 z + 0.09 y = 67500 .............2 Eliminate y multiply (1)by -0.09 Multiply (2) by 1 -0.45 z -0.09 y = -69750 0.42 z 0.09 y = 67500 Add the two equations -0.03 z = -2250 / -0.03 z = 75,000.00 plug value of z in (1) 5 z + 1 y = 775000 375000 + 1 y = 775000 1 y = 775000 -375000 1 y = 400000 y = 400000.00 10% ------------\$75000 9%--------------\$400000 8%--------------4*75000= \$300000 CHECK 75000*0.1+400000*0.09+300000*0.08=67500 m.ananth@hotmail.ca
 Travel_Word_Problems/534124: Two trains leave stations 156 miles apart the same time and travel toward each other. One train travels at 55 miles per hour other travels 75 miles per hour. How long will it take for the two trains to meet?1 solutions Answer 351313 by mananth(12270)   on 2011-11-19 04:27:41 (Show Source): You can put this solution on YOUR website!train I speed = 55 mph Train II speed = 75 mph They are travelling towrads each other. So the effective speed = 75+55= 130 mph distance = 156 miles Time = distance / speed time = 156/130 Time = 1.2 hours
 Travel_Word_Problems/534126: Two trains leave stations 156 miles apart the same time and travel toward each other. One train travels at 55 miles per hour other travels 75 miles per hour. How long will it take for the two trains to meet?1 solutions Answer 351312 by mananth(12270)   on 2011-11-19 04:26:50 (Show Source): You can put this solution on YOUR website!train I speed = 55 mph Train II speed = 75 mph They are travelling towrads each other. So the effective speed = 75+55= 130 mph distance = 156 miles Time = distance / speed time = 156/130 Time = 1.2 hours
 Mixture_Word_Problems/533773: two alcohol substances, a 15% solution and a 45% solution. How much of each solution should be used to obtain 300 milliliters of a 25% solution?1 solutions Answer 351161 by mananth(12270)   on 2011-11-18 04:12:21 (Show Source): You can put this solution on YOUR website!percent ---------------- quantity Alcohol I 15 ---------------- x ml Alcohol II 45 ------ 300 - x ml Mixture 25.00% ---------------- 300 15x+45(300-x)=25*300 15x+13500-45x =7500 15 x - 45 x= 7500 - 13500 -30 x= -6000 / -30 x =200 ml 15.00% Alcohol I 100 ml 45.00% Alcohol II
 Points-lines-and-rays/533607: write the equation of the line that passes through the point (1,1) and is parallel to the graph of y=2x+6. then graph both lines. i dont get this, help???1 solutions Answer 351091 by mananth(12270)   on 2011-11-17 19:48:39 (Show Source): You can put this solution on YOUR website! y = 2 x + 6 Compare this equation with y=mx+b slope m = 2 The slope of a line parallel to the above line will be the same The slope of the required line will be 2 m= 2 ,point ( 1 , 1 ) Find b by plugging the values of m & the point in y=mx+b 1 = 2.00 + b b= -1 m= 2 Plug value of the slope and b in y = mx +b The required equation is y = 2 x -1 y = 2 x -1 m.ananth@hotmail.ca
 Mixture_Word_Problems/533600: How do you solve this: A chemist has 12 liters of a 25% acid solution. How many liters of water must be added to obtain a 20% solution?1 solutions Answer 351090 by mananth(12270)   on 2011-11-17 19:44:19 (Show Source): You can put this solution on YOUR website! --------percent ---------------- quantity Solution I 25 ---------------- 12 liters Water 0 ---------------- x liters Mixture 20 ---------------- 12 + x liters 25*12+0 x =20(12+x) 300= 240 + 20 x -20 x = 240 - -300 -20 x = -60 / -20 x = 3 3 liters of Water
 Travel_Word_Problems/533575: If a car is traveling at a rate of 30 miles in 1 hours, how many feet per second is this?1 solutions Answer 351089 by mananth(12270)   on 2011-11-17 19:36:16 (Show Source): You can put this solution on YOUR website!30 miles /hour 1 mile = 5280 feet 1 hour = 3600 seconds 30 *5280 / 3600 - feet /second = 44 ft/s
 Linear-equations/533593: Whats the equation of a line that is parallel to the equation y=1/2x-8 and goes through the point (-3,8)?1 solutions Answer 351087 by mananth(12270)   on 2011-11-17 19:32:24 (Show Source): You can put this solution on YOUR website!1 y = 0.5 x -8 Divide by 1 y = 1/2 x -8 Compare this equation with y=mx+b slope m = 1/2 The slope of a line parallel to the above line will be the same The slope of the required line will be 1/2 m= 1/2 ,point ( -3 , 8 ) Find b by plugging the values of m & the point in y=mx+b 8 = -1.50 + b b= 9.5 m= 1/2 Plug value of the slope m and b in y = mx +b The required equation is y = 1/2 x + 9.5 (y = 1/ 2 x + 19/ 2) m.ananth@hotmail.ca
 Geometry_Word_Problems/533226: My answer does not work-I am not sure what I did wrong! The length of a rectangle is 3 ft more than twice its width. The area of the rectangle is 35ft^2. Find the dimensions. Thanks for your help!1 solutions Answer 351025 by mananth(12270)   on 2011-11-17 10:34:58 (Show Source): You can put this solution on YOUR website!width = w length = 2w+3 Area = L*W w(2w+3)=35 2w^2+3w=35 2w^2+3w-35=0 2w^2+10w-7w-35=0 2w(w+5)-7(w+5)=0 (w+5)(2w-7)=0 w=-5 OR w=7/2 ignore negative value width = 3.5 length =>2w+3 => 2*3.5 +3 = 10
 Systems-of-equations/533241: Write an equation of the line that passes through the point (1,2) and has the slope, m = 2. I'm very bad at Math so please answer this question! I need all the help I can get. Thank you so much! 1 solutions Answer 351023 by mananth(12270)   on 2011-11-17 10:29:27 (Show Source): You can put this solution on YOUR website!m= 2 Plug value of the slope and point ( 1,2) in Y = m x + b 2.00 = 2 + b b= 2 - 2 b= 0 So the equation will be Y = 2 x m.ananth@hotmail.ca
 Money_Word_Problems/533148: sue rented a car, a one time deposit is required with the first month pay. she paid \$950 the first montb abd a total of \$9600 during the first year. what is the monthly rent and the amount of the deposit sue paid?1 solutions Answer 351015 by mananth(12270)   on 2011-11-17 08:32:24 (Show Source): You can put this solution on YOUR website!Let x be the deposit paid in the first month 9600-x is the rent for 12 months rent for 1 month = (9600-x)/12 = 960-x (9600-x)/12 = 960-x 9600=12(960-x) 9600-x =11520-12x 11x=1920 x=174.5 9600-174.54= 785.5 Deposit = 174.5 Monthly 785.5 m.ananth@hotmail.ca
 test/533210: Find the slope and y-intercept of the line with the equation 4x-2y=32.1 solutions Answer 351011 by mananth(12270)   on 2011-11-17 08:08:42 (Show Source): You can put this solution on YOUR website!4x-2y=32 write it in the slope intercept form 2y=4x-32 /2 y= 2x-16 compare with equation y= mx+b m= xlope = 2 b the y intercept = -16