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# Recent problems solved by 'mananth'

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 Proportions/489650: In direct variation, as one variable increases, does the constant increase, decrease, or remain the same? thak you 1 solutions Answer 333717 by mananth(12270)   on 2011-09-01 09:11:56 (Show Source): You can put this solution on YOUR website!Constant in english dictionary is permanant,steadfast,unchanging how can this change?
 Numbers_Word_Problems/489615: please answered this problem,A bullet is fired at a target and sound of its impact is heard 6 seconds later.If it travels at the rate of 660 meter per second and sound travels at the rate of 330 meter per second, how far away is the target? 1 solutions Answer 333709 by mananth(12270)   on 2011-09-01 07:43:15 (Show Source): You can put this solution on YOUR website!Let the target distance = x m time for the bullet to reach the target = x/660 time for the sound to return = x/330 Total time = 6 seconds x/660 + x/330= 6 (2x+x)/660 = 6 3x=6*660 x=6*660/3 x=6*220 x=1320m
 Linear-equations/489591: Solve the system of equations x + y = 5 x - y = -9 1 solutions Answer 333708 by mananth(12270)   on 2011-09-01 07:28:58 (Show Source): You can put this solution on YOUR website!x + y = 5 x - y = -9 add the two equations 2x=-4 /2 x=-2 plug x=-2 -2+y=5 y=7
 Length-and-distance/489620: If the speed of light is about 300,000 kilometers per second, what is its speed in miles per hour to the nearest thousand miles.? And please give me the conversion tables.. Thanks in advance!1 solutions Answer 333707 by mananth(12270)   on 2011-09-01 07:23:32 (Show Source): You can put this solution on YOUR website!300,000 km/second 1 kilometer/second = 2 236.936 mile/hour
 Proportions/489598: Pipe A can fill in 20 minutes and Pipe B in 30 mins and Pipe C can empty the same in 40 mins.If all of them work together, find the time taken to fill the tank1 solutions Answer 333706 by mananth(12270)   on 2011-09-01 06:27:18 (Show Source): You can put this solution on YOUR website!Emptying the pool is one job 1 job Pipe I 20 minutes She does 1/20 job in 1 hour Pipe II 30 minutes 1/12 He does 1/30 of thejob in 1 hour Pipe III 40 minutes It does 1/40 of the job in 1 hour Together they will do 1/20 + 1/30 + 1/40 Together they will do 9/83 of the job in one minute 0.11 So they will take 9 2/9 minutes So they will take 9.23 minutes
 Quadratic_Equations/489600: During the first part of a trip, a canoeist travels 48 miles at a certain speed. The canoeist travels 5 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 3 hrs. What was the speed on each part of the trip? The speed on the first part of the trip was ?1 solutions Answer 333704 by mananth(12270)   on 2011-09-01 06:14:32 (Show Source): You can put this solution on YOUR website!first part 48 miles second part 5 miles speed in first part x mph speed second part x -5 mph Total rowing time 3 hours Time first part 48 / x Time second part 5 / ( x -5 ) Time first part + time second part = 3 hours 48 / x + 5 /(x -5 ) = 3 LCD = ( x + 0 )* (x -5 ) multiply the equation by the LCD we get 48 * (x -5 )+ 5 x = 3 48 x -240 + 5 x = 3 X^2 68 x -240 = 3 X^2 3 X^2 -68 x 240 = 0 3 X^2+ -68 x+ 240 = / 3 1 X^2 -22.67 x 80 = Find the roots of the equation by quadratic formula a= 1 b= -22.67 c= 80 b^2-4ac= 513.78 - -320 b^2-4ac= 193.78 = 13.92 x1=( 22.67 + 13.92 )/ 2 x1= 18.29 18 2/7 x2=( 22.67 -13.92 ) / 2 x2= 4.37 4 3/8 Ignore negative value x = 18.29 mph speed & 5 less in the second part CHECK Time first part + Time second part 2.62 + 0.38 = 3
 Triangles/489606: the altitude of a triangle is 4m longer than the base. If its area is 126 square meter, find the length of the altitude. can somebody answer this problem..thank you!1 solutions Answer 333703 by mananth(12270)   on 2011-09-01 05:11:11 (Show Source): You can put this solution on YOUR website!base =x altitude= (x+4) 1/2*x*(x+4)=126 x^2+4x=252 x^2+4x-252=0 x^2+18x-14x-252=0 x(x+18)-14(x+18)=0 (x+18)(x-14)=0 x= 14m which is positive. base = 14 height = 14+4=18m
 Travel_Word_Problems/489516: Hank can row a boat 1 mi upstream against the current in 24 minutes. He can row the same distance downstream in 13 min. If the rowing speed and the current speed are constant, what is Hank's rowing speed, and what is the speed of the current? 1 solutions Answer 333681 by mananth(12270)   on 2011-08-31 23:59:01 (Show Source): You can put this solution on YOUR website!boat speed =x mph current speed =y mph against current x-y 0.40 hours with current x+y 0.22 hours Distance = same= 1 miles t=d/r 1 / ( x - y )= 0.40 0.4 ( x - y ) = 1.00 0.4 x -0.4 y = 1 ....................1 1 / ( x + y )= 0.22 0.22 ( x + y ) = 1 0.22 x + 0.22 y = 1 ...............2 Multiply (1) by 0.22 Multiply (2) by 0.40 we get 0.09 x + -0.09 y = 0.22 0.09 x + 0.09 y = 0.4 0.17 x = 0.62 / 0.17 x = 3.55 mph plug value of x in (1) 0.4 x -0.4 y = 1 1.42 -0.4 y = 1 -0.4 y = 1 -1.42 -0.4 y = -0.42 y = 1.05 mph
 Linear-systems/489547: I need help solving this equation using the substitution method. Can you please answer it as detailed as possible. 2x - 3y = 0 -4x + 3y = -11 solutions Answer 333679 by mananth(12270)   on 2011-08-31 23:47:41 (Show Source): You can put this solution on YOUR website!2 x -3 y = 0 .............1 3 y = -1 + 4 x ---------2 / 3 = y = -0.33 + 1.33 x Substitute y in (1) 2x-3 ( -0.33 + 1.33 x ) = 0 2 x + 1 + -4 x = 0 2 x -4 x = 0 -1 -2 x = -1 / -2 x= 0.5 Plug the value of x in (1) 2 x -3 y = 0 2 * 0.5 -3 y = 0 1 -3 y = 0 -3 y = -1 / -3 y= 0.33 m.ananth@hotmail.ca
 logarithm/488980: How would you write the number 12 in "exponential form?" Is it 12^1, or 2^3.5, or 2^2*3, or 3^2.33, or 1.2(10^1) or? Thanks!1 solutions Answer 333498 by mananth(12270)   on 2011-08-31 11:19:50 (Show Source): You can put this solution on YOUR website!1.2*10^1
 Proportions/488864: Lila paid \$45.25 for a pair of jeans. If she spent 8% of that amount in sales tax, how much tax did she pay?1 solutions Answer 333461 by mananth(12270)   on 2011-08-31 00:16:44 (Show Source): You can put this solution on YOUR website!paid \$45.25 sales tax 8% when you pay \$108 the price is 100 when you pay 45.25 the price is ? (100/108) * 45.25 =41.9 45.25-41.9 = \$ 3.35 is the tax
 Linear-equations/487034: find the solution to the system 2x - 5y = -1 and x - 3y = -3 by the substitution method1 solutions Answer 332954 by mananth(12270)   on 2011-08-28 07:47:57 (Show Source): You can put this solution on YOUR website!2 x -5 y = -1 .............1 -3 y = -3 -1 x ---------2 / -3 = y = 1 + 0.33 x Substitute y in (1) 2 x -5 ( 1 + 0.33 x ) = -1 2 x -5 + -1.67 x = -1 2 x -1.67 x = -1 5 0.33 x = 4 / 0.33 x= 12 Plug the value of x in (1) 2 x -5 y = -1 2 * 12 -5 y = -1 24 -5 y = -1 -5 y = -25 / -5 y= 5 m.ananth@hotmail.ca
 Angles/486614: Marissa has \$4.30 in quarters and dimes. If she has 6 more quarters than dimes, how many of each coin does she have? 1 solutions Answer 332720 by mananth(12270)   on 2011-08-27 06:13:34 (Show Source): You can put this solution on YOUR website!dimes x quarters( x + 6 ) Convert dollars to cents Value= 430 10 x 25 x + 150 = 430 35 x = 280 35 x = 280 0 35 x = 280 / 35 x= 8 dimes = 80 cents 8+6 = 14 quarters 14*25 = 350 cents 350+80 =430 cents
 Trigonometry-basics/486694: Two aircraft leave simultaneously from an airport, one flying due north and the other due east. The northbound aircraft averages a speed of 100 miles per hour fater than the eatbound aircraft. After 3 hours, the aircraft are 1500 miles apart. Find the average speed of each aircraft.1 solutions Answer 332718 by mananth(12270)   on 2011-08-27 06:00:05 (Show Source): You can put this solution on YOUR website!they are travelling at right angles to each other. At any given instant they form a right triangle with their starting point speed of one = x other = x+100 using Pythagoras theorem x^2+(x+100)^2 = 1500^2 x^2+x^2+200x+10000=2250000 2x^2+200x-2240000 Find the roots of the equation by quadratic formula a= 2 ,b= 200 ,c= -2240000 b^2-4ac= 40000 - 17920000 b^2-4ac= 17960000 = 4237.92 x1=( -200 + 4237.92 )/ 4 x1= 1009.48 x2=( -200 -4237.92 ) / 4 x2= -1109.48 Ignore negative value 1009.48 mph= speed of one plane add 100 to this speed to get speed of other m.ananth@hotmail.ca
 Graphs/486553: how do you graph this? x + 2y = 61 solutions Answer 332633 by mananth(12270)   on 2011-08-26 21:16:50 (Show Source): You can put this solution on YOUR website!equation1 when x= 0 y= 3 ( 0 , 3 ) when y = 0 x= 6 ( 6 , 0 )
 Inequalities/486624: Please help me with this inequality. I am not quite sure how to do it. 3y+1<=5y-1<4(y+1) First I distributed and got 3y+1<=5y-1<4y+4 This problem has the y variable on all 3 sides, so I am not sure what to do from there.1 solutions Answer 332630 by mananth(12270)   on 2011-08-26 21:06:41 (Show Source): You can put this solution on YOUR website!3y+1<=5y-1<4y+4 3y+1<=5y-1 1<=2y-1 2<=2y 1<=y 5y-1<4y+4 y-1<4 y<5
 Evaluation_Word_Problems/486625: Please help me with this algebra problem. It has me confused! Thanks so much! -(-6n)-(12-5n)1 solutions Answer 332628 by mananth(12270)   on 2011-08-26 21:01:39 (Show Source): You can put this solution on YOUR website!-(-6n)-(12-5n) 6n-12+5n 11n-12
 Expressions-with-variables/486593: This problem evolves using substitution. 0.1x + 0.8y= -2.1 0.9x - 0.9y= 5.4 Couldnt figure out how to start to get an answer. Thank you for your assistance.1 solutions Answer 332627 by mananth(12270)   on 2011-08-26 21:00:24 (Show Source): You can put this solution on YOUR website!0.1x + 0.8y= -2.1 0.9x - 0.9y= 5.4 multiply both equations by 10 to make life easy. x+8y=-21 9x-9y=54 1 x + 8 y = -21 .............1 -9 y = 54 -9 x ---------2 / -9 = y = -6 + 1 x Substitute y in (1) 1 x + 8 ( -6 + 1 x ) = -21 1 x -48 + 8 x = -21 1 x + 8 x = -21 48 9 x = 27 / 9 x= 3 Plug the value of x in (1) 1 x + 8 y = -21 1 * 3 + 8 y = -21 3 + 8 y = -21 8 y = -24 / 8 y= -3 m.ananth@hotmail.ca
 real-numbers/486621: Please help me out with this algebra problem. Thank you Evaluate and please show all work 3b-b^2 for b = 1/31 solutions Answer 332623 by mananth(12270)   on 2011-08-26 20:48:45 (Show Source): You can put this solution on YOUR website! b= 1/3 m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/486618: Write the slope-intercept equation for the line that passes through (-4,6) and (2,-6) please show all of your work1 solutions Answer 332622 by mananth(12270)   on 2011-08-26 20:46:42 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 -4 6 2 -6 slope m = (y2-y1)/(x2-x1) ( -6 - 6 )/( 2 - -4 ) ( -12 / 6 ) m= -2 Plug value of the slope and point ( -4 , 6 ) in Y = m x + b 6.00 = 8 + b b= 6 - 8 b= -2 So the equation will be Y = -2 x -2 m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/486610: Appreciate help in solving a problem and checking the answer: ((6x-3)/x^2-x-12))-((2x-15)/x^2-x-12)) The answer I got is 4/(x-4) but not sure if this is correct and don't know how to check. Thanks much. Diane1 solutions Answer 332621 by mananth(12270)   on 2011-08-26 20:44:56 (Show Source):
 Angles/486613: Miguel is selling tickets to a barbecue. Adult tickets cost \$8.00 and children's tickets cost \$5.00. He sells seven more children's tickets than adult tickets. The total amount of money he collects is \$256.00. How many adult tickets and how many children's tickets did he sell?1 solutions Answer 332620 by mananth(12270)   on 2011-08-26 20:37:25 (Show Source): You can put this solution on YOUR website!adult tickets x children tickets x+7 8x+5(x+7) = 256 8x+5x+35=256 13x=221 x=17 adult tickets
 Travel_Word_Problems/486393: Need help for the following sum: A starts walking north from Point X at 7 a.m. with a speed of 5 km/hr. After 1 hr, B starts from the same point cycling towards the east with a speed of 16 km/hr. At what time will they be at a distance of 52 km from each other? Thanks1 solutions Answer 332506 by mananth(12270)   on 2011-08-26 11:36:53 (Show Source): You can put this solution on YOUR website!A ---- North ---- 5 km/h B----- east ------16km/h (After 1 hour) let the time be t A distance 5t+5 B distance 16 t (5t+5)^2+(16t)^2=52^2 ( I have used x in place of t) 25t^2+50t+25+256t^2=52^2 281t^2+50t-2679 =0 Find the roots of the equation by quadratic formula a= 281 b= 50 c= -2679 b^2-4ac= 2500 - 3011196 b^2-4ac= 3013696 = 1736 x1=( -50 + 1736 )/ 562 x1= 3 3 x2=( -50 -1736 ) / 562 x2= -3.18 -3 1/6 Ignore negative value x = 3 hours m.ananth@hotmail.ca
 Money_Word_Problems/486363: how much will you have in a savings account if you deposit \$4000 for 8 years at 5% interest compounded annually? 1 solutions Answer 332439 by mananth(12270)   on 2011-08-26 01:16:04 (Show Source): You can put this solution on YOUR website!Principal P = 4000 Amount= A years=n 8.00 compounded 1 times a year t Rate = 5.00 0.05 Amount = P*((n+r)/n)^n*t Amount = = 4000 *( 1 + 0.05 )^ 8 * 1 Amount = 4000 *( 1 + 0.05 )^ 8 4000 *( 1.05 )^ 8 Amount = 5909.82 m.ananth@hotmail.ca
 Percentage-and-ratio-word-problems/486354: x^2-7x+__=(x-__)^21 solutions Answer 332435 by mananth(12270)   on 2011-08-26 01:10:22 (Show Source): You can put this solution on YOUR website! m.ananth@hotmail.ca
 expressions/486367: x^2-7x+__=(x-__)^2 complete the square.1 solutions Answer 332434 by mananth(12270)   on 2011-08-26 01:09:45 (Show Source): You can put this solution on YOUR website! m.ananth@hotmail.ca
 expressions/486365: x^2-7x+__=(x-__)^2 complete the square.1 solutions Answer 332432 by mananth(12270)   on 2011-08-26 01:08:58 (Show Source): You can put this solution on YOUR website! m.ananth@hotmail.ca
 Word_Problems_With_Coins/486358: In a collection of 60 coins, the number of half dollars is 1/3 the number of dimes. The number of quarters is 10 less than the number of dimes, find the value of the collection. I am having difficulty dividing the 1/3. Somewhere I am missing a step. I know: D divided 1/3= half dollars D - 10 = Quarters how do I solve D with the 1/3rd fraction?1 solutions Answer 332431 by mananth(12270)   on 2011-08-26 00:51:37 (Show Source): You can put this solution on YOUR website!In a collection of 60 coins, the number of half dollars is 1/3 the number of dimes. The number of quarters is 10 less than the number of dimes, find the value of the collection. total coins ---- 60 dimes = x half dollar = (1/3)*x Quarters ----(x-10) x+x/3 + x-10=60 whenever you have such an addition of fraction the simplest step I will try to teach you Find the LCD of the denominator and multiply the entire equation by the LCD. Here the LCD is 3 3*2x+(x/3)*3 -10*3=60*3 6x+x-30=180 7x-30=180 7x= 210 /7 x=30 the number of dimes Half dollar = 30 * x/3= 10 quarter = x-10 ==> 30-10=20 m.ananth@hotmail.ca
 Mixture_Word_Problems/486346: Bronze which costs \$9.10/kg is made by combining copper which costs \$8.90/kg with tin which costs \$9.50/kg. Find the number of kg of copper and tin required to make 15.3 kg of bronze.1 solutions Answer 332429 by mananth(12270)   on 2011-08-26 00:39:33 (Show Source): You can put this solution on YOUR website!Copper x kg-------- \$8.9 Tin y kg--------\$9.5 1 x + 1 y = 15.3 .............1 8.9 x + 9.5 y = 139.23 .............2 (9.1*15.3) Eliminate y multiply (1)by -9.5 Multiply (2) by 1 -9.5 x -9.5 y = -145.35 8.9 x 9.5 y = 139.23 Add the two equations -0.6 x = -6.12 / -0.6 x = 10.20 kg plug value of x in (1) 1 x + 1 y = 15.3 10.2 + 1 y = 15.3 1 y = 15.3 -10.2 1 y = 5.1 y = 5.10kg
 Numbers_Word_Problems/486317: Vijay bought 11 tickets for a waterslide. The tickets were \$6 for adults and \$4 for children. Vijay paid \$60 for the tickets. For how many adults and how many children did he buy tickets?1 solutions Answer 332425 by mananth(12270)   on 2011-08-25 23:06:50 (Show Source): You can put this solution on YOUR website!Adult x tickets child y tickets 1 x + 1 y = 11 .............1 6 x + 4 y = 60 .............2 Eliminate y multiply (1)by -4 Multiply (2) by 1 -4 x -4 y = -44 6 x 4 y = 60 Add the two equations 2 x = 16 / 2 x = 8 plug value of x in (1) 1 x + 1 y = 11 8 + 1 y = 11 1 y = 11 -8 1 y = 3 y = 3 Adult 8 tickets child 3 tickets m.ananth@hotmail.ca
 Linear-equations/486291: The line passes through points (-2,4) and (3,4) find the equation1 solutions Answer 332424 by mananth(12270)   on 2011-08-25 23:04:06 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 -2 4 3 4 slope m = (y2-y1)/(x2-x1) ( 4 - 4 )/( 3 - -2 ) ( 0 / 5 ) m= 0 Plug value of the slope and point ( -2 , 4 ) in Y = m x + b 4.00 = -0 + b b= 4 - -0 b= 4 So the equation will be Y = 4 m.ananth@hotmail.ca