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# Recent problems solved by 'mananth'

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 Travel_Word_Problems/421372: Two buses leave a station at the same time and travel in opposite directions. One bus travels 10km/h slower than the other. If the two buses are 1200km apart after 6 hours, what is the rate of each bus?1 solutions Answer 294282 by mananth(12270)   on 2011-03-12 20:30:00 (Show Source): You can put this solution on YOUR website!first bus x second bus x-10 .. They are going away from each other. So add up their speed. combined speed = x+x-10= 2x-10 Time = 6 hours Distance = speed * time (2x-10)6=1200 12x-60=1200 12x=1200+60 12x=1260 /12 x= 105 the second bus speed = 105 -10 = 95 mph
 Graphs/421389: graph the inequality on a plane 3x+4y<12 the arrow has a line under it1 solutions Answer 294279 by mananth(12270)   on 2011-03-12 20:20:55 (Show Source): You can put this solution on YOUR website!3x+4y<12 /4 The boundary The inequality
 Graphs/421398: solve then graph 8x>48 there is a line under the arrow chose the correct soluton. a. {x|x<6} b. {x|x>6} the arrow has a line under it c. {x|x>6} d. {x|x<6} arrow has a line under it choose the correct graph of the solution a. 6 going to the righ all shaded and closed shaded circle b. 6 going to left all shaded and closed shaded circle c. 6 going to left open unshaded circle d. 6 going to right open unshaded circle1 solutions Answer 294277 by mananth(12270)   on 2011-03-12 20:12:14 (Show Source): You can put this solution on YOUR website!b. {x|x>6} the arrow has a line under it .....
 Human-and-algebraic-language/421001: a rectagular the perimeter is 218 ft and the length is 3 times the width what is the dimension 1 solutions Answer 294134 by mananth(12270)   on 2011-03-12 00:41:46 (Show Source): You can put this solution on YOUR website!Perimeter =218 Length 3x Width =x cm Perimeter = 2*3x +2x 218 = 8x /8 x=27.25 ft Width Length =81.75 ft
 Rectangles/421139: b) Length of a rectangle is 3 more than its width. The perimeter of the rectangle is 30. Find the length and width. 1 solutions Answer 294133 by mananth(12270)   on 2011-03-12 00:34:12 (Show Source): You can put this solution on YOUR website!Perimeter = 30 Length =x+3 Width =xcm Perimeter =2((x +3)+x) Perimeter =2(2x+ 3) Perimeter =4x +6 30=4x+6 30-6=4x 24=4x x=6 Width Length =9
 test/421015: If 6 boys and 15 men together earn \$7,128 a week and if each man earns 4 times as much as each boy, how much does each boy earn in a week?1 solutions Answer 294131 by mananth(12270)   on 2011-03-12 00:25:48 (Show Source): You can put this solution on YOUR website!let each boy earn \$x-------------6 Man earns 4x--------------------15 6x+15*4x=7128 66x=7128 /66 x=7128/66 x=\$108 --- boy's earning
 Graphs/420999: What would be the equation of the a line with a slope of 3/5 and going through the point (-10, 2)? a. y=3/5x+2 b. y=3/5x+8.8 c. y=3/5x-10 d. y=3/5x+81 solutions Answer 294128 by mananth(12270)   on 2011-03-12 00:13:16 (Show Source): You can put this solution on YOUR website!m= 0.6 ,point ( -10 , 2 ) Find b by plugging the values of m & the point in y=mx+b 2 = -6 + b b= 8 The required equation is y =0.6x +8 Option D 0.6=3/5
 test/421135: solve v^2-4v-21=01 solutions Answer 294126 by mananth(12270)   on 2011-03-12 00:06:21 (Show Source): You can put this solution on YOUR website!v^2-4v-21=0 v^2-7v+3v-21=0 v(v-7)+3(v-7)=0 (v-7)(v+3)=0 v=7 OR v=-3
 test/421136: factor completely 49w^2+1-14w1 solutions Answer 294125 by mananth(12270)   on 2011-03-12 00:04:41 (Show Source): You can put this solution on YOUR website!49w^2+1-14w 49w^2-14w+1 49w^2-7w-7w+1 7w(7w-1)-1(7w-1) (7w-1)(7w-1) (7w-1)^2
 test/421134: solve 3/w=7/w-1/51 solutions Answer 294123 by mananth(12270)   on 2011-03-12 00:02:45 (Show Source): You can put this solution on YOUR website! add -7/w cross multiply -w=-20 /-1 w=20
 Evaluation_Word_Problems/421063: a wire is need to support a vertical pole 14 feet high. the cable will be anchored to a stake 10 feet from the base of the pole. how much cable is needed?1 solutions Answer 294115 by mananth(12270)   on 2011-03-11 22:47:18 (Show Source): You can put this solution on YOUR website!cable , pole and the ground form a right triangle. cable = hypotenuse .. 14^2+10^2=hyp^2 196+100=hyp^2 296=hyp^2 hyp= sqrt 296 17.2 m of cable
 Functions/421096: find the slope and the y-intercept of the line. Write the fractional answer in lowest terms. y = -6/5x - 5/6 the slope is ? the y-intercept is (0,?)1 solutions Answer 294112 by mananth(12270)   on 2011-03-11 22:42:01 (Show Source): You can put this solution on YOUR website!y = -6/5x - 5/6 compare with y= mx+b m= slope b= y intercept m=-6/5 b=-5/6
 Money_Word_Problems/421106: If I wanted to have \$150000.00 when I retire in 10 years and I'm investing into a high yield bond that pays 7% compounded annually, what do I have to invest today to achieve my goal? can someone tell me the formula to solve the equation?1 solutions Answer 294110 by mananth(12270)   on 2011-03-11 22:37:44 (Show Source): You can put this solution on YOUR website!Amount = 150,000 p=? r=7 n=10 .. 150,000/ (1+0.07)^10 = Principal Principal = 76,252.39
 Numeric_Fractions/421108: May I have the steps for solving this problem - 1/2+(2/3÷3/4)-(4/5∙5/6? 1 solutions Answer 294108 by mananth(12270)   on 2011-03-11 22:30:24 (Show Source): You can put this solution on YOUR website!(1/2)+((2/3)÷(3/4))-((4/5)-(5/6)) LCD =270
 Evaluation_Word_Problems/420867: If I have a 20 qt radiator containing a 80% antifreeze solution. How much of the solution should I drain and replace with pure water to get a solution that is 50% antifreeze?1 solutions Answer 293968 by mananth(12270)   on 2011-03-11 08:02:36 (Show Source): You can put this solution on YOUR website!Let 82% solution required be x percent ---------------- quantity 82 ---------------- x water 0% ---------------- 20-x 50.00% ---------------- 20 ... 82x+0(20 -x)=50*20 82x=1000 / 82 x=12.2 qt. of82.00% Balance 7.8 qt of water. 7.8 qt. of 82% will have to be drained and replaced with water
 Linear_Equations_And_Systems_Word_Problems/420849: If the bill for 5 apple juices and 4 salads is \$9.50, but the bill for 4 apple juices and 5 salads is \$10.30, then how much would 1 apple juice and 1 salad cost?1 solutions Answer 293957 by mananth(12270)   on 2011-03-11 05:47:24 (Show Source): You can put this solution on YOUR website!Cost of Apple juice---- x Cost of Salad-----------y 5x+4y=9.5.............1 4x+5y=10.3.............2 multiply (1)by -5 Multiply (2) by 4 -25x-20y =-47.5 16x+20y= 41.2 Add the two equations -9x=-6.3 /-9 x= 5/7= \$0.70 Apple juice plug value of x in (1) 5x+4y =9.5 3.5+4y=9.5 4y=9.5-3.5 4y=6 /4 y=\$1.50 Salad
 Linear-systems/420835: Graph the following equations and solve the system. y=-1 3x-y=41 solutions Answer 293943 by mananth(12270)   on 2011-03-11 01:20:07 (Show Source): You can put this solution on YOUR website!Y=-1 y=3x-4 ... The solution is (1,-1)
 Travel_Word_Problems/420774: The speed of train X is 14 km/h faster than the speed of train Y. Train X travels 400 km in the same time it takes train Y to travel 330 km. Find the speed of each.1 solutions Answer 293941 by mananth(12270)   on 2011-03-11 01:13:13 (Show Source): You can put this solution on YOUR website! speed of Y---- x-----------------------------330 miles speed of X---- x +14------------------------400 miles t=d/r Time is same 330/x=400/(x+14) Cross multiply 330(x+14 )=400*x 330x+4620=400x 400x-330 x=4620 70x=4620 /70 x=66 speed of Y 80= speed of X
 Expressions-with-variables/420810: solve 6x-3y=5 x+2y=01 solutions Answer 293916 by mananth(12270)   on 2011-03-10 22:46:35 (Show Source): You can put this solution on YOUR website!6x-3y=5.............1 x+2y=0 .............2 multiply (1)by 2 Multiply (2) by 3 12x-6y=10 3x+6y=0 Add the two equations 15 x=10 /15 x= 2/3 plug value of x In (1) 6x-3y= 5 4-3y= 5 -3y=5-4 -3y=1 y=- 1/3
 test/420755: THE EQUATION OF 2 lines xxx + 2 y = 3 , 4 x-y = 12 what are the coordinates of the point of intersections1 solutions Answer 293897 by mananth(12270)   on 2011-03-10 20:58:30 (Show Source): You can put this solution on YOUR website!1 x + 2 y = 3 .............1 4 x + -1 y = 12 .............2 multiply (1)by 1 Multiply (2) by 2 1 x + 2 y = 3 8 x + -2 y = 24 Add the two equations 9 x + 0 y = 27 / 9 x = 3 plug value of x In (1) 1 x + 2 y = 3 3 + 2 y = 3 2 y = 3 + -3 2 y = 0 y = 0
 Linear-systems/420741: Please help me solve this equation 4x + 4y + z = 2 -x + 2y + 3z = 5 x + y + 4z = -71 solutions Answer 293896 by mananth(12270)   on 2011-03-10 20:54:19 (Show Source): You can put this solution on YOUR website!4x+4y+1z = 2-------------- 1 -1x +2y+3z =5-------------- 2 1x+ 1y +4z=-7--------------3 consider equation 1 &2 Multiply 1 by 1 Multiply 2 by -2 we get 4 x + 4 y + 1 z = 2 2 x + -4 y + -6 z = -10 Add the two 6 x + 0 y + -5 z = -8 ------------- 4 consider equation 2 & 3 Multiply 2 by 1 Multiply 3 by -2 we get -1 x + 2 y + 3 z = 5 -2 x + -2 y + -8 z = 14 Add the two -3 x + 0 y + -5 z = 19 ------------- 5 Consider (4) & (5) Multiply 4 by 1 Multiply (5) by 2 we get 6 x + -5 z = -8 -6 x + -10 z = 38 Add the two 0 x + -15 z = 30 / -15 z = -2 Plug the value of z in 5 -3 x + 10 = 19 -3 x = 9 x = -3 plug value of x & z in 1 -12 + 4 y + -2 = 2 4 y = 12 + 2 + 2 4 y = 16 y= 4
 Linear-systems/420736: i am having trouble with trying to figure out how to graph y=x-1,y=-x+3 to get (2,1)1 solutions Answer 293893 by mananth(12270)   on 2011-03-10 20:41:42 (Show Source): You can put this solution on YOUR website!-1 x + 1 y = -1 .............1 x=0,y=-1 (0,-1) y=0,x=1 (1,0) 1 x + 1 y = 3 .............2 x=0, y=3 (0,3) y=0,x=3 (3,0) Plot these points and draw the lines. The point of intersection is the solution. The solution is (2,1) CHECK by solving the equation multiply (1)by -1 Multiply (2) by 1 1 x + -1 y = 1 1 x + 1 y = 3 Add the two equations 2 x = 4 / 2 x = 2 plug value of x in (1) - x + y = -1 -2 + y = -1 y = -1 + 2 y = 1 y = 1
 Equations/420710: solve by the elimination method 7r-8s=-21 8r+7s=89 a.the solution is? b.there are infinitely many solutions c.there is no solution1 solutions Answer 293886 by mananth(12270)   on 2011-03-10 20:26:49 (Show Source): You can put this solution on YOUR website!7r-8s =-21 .............1 8r+7s= 89 .............2 multiply (1)by 7 Multiply (2) by 8 49 r + -56 s = -147 64 r + 56 s = 712 Add the two equations 113 r = 565 / 113 r = 5 plug value of r In (1) 7 r + -8 s = -21 35 + -8 s = -21 -8 s = -21 + -35 -8 s = -56 s = 7
 test/420283: Formula to find three conservative number that sum up to 129.1 solutions Answer 293735 by mananth(12270)   on 2011-03-10 09:34:20 (Show Source): You can put this solution on YOUR website!x+x+1+x+2=129 3x+3=129 3x=126 /3 x=42 42,43,44
 Quadratic_Equations/420301: I need help solving this quadratic equation and leaving it in radical form I don't know how to set it to zero? I know how to use the quadratic formula so I need help on how to set the equation to zero so I can solve using the quadratic formula? (x+8)(x-4)=-3(2x+5) thank you for your help 1 solutions Answer 293734 by mananth(12270)   on 2011-03-10 09:31:27 (Show Source): You can put this solution on YOUR website!(x+8)(x-4)=-3(2x+5) x^2-4x+8x-32=-6x-15 x^2+4x-32+6x+15=0 x^2+10x-17=0 Find the roots of the equation by quadratic formula a= 1 , b =10 , c =-17 . b^2-4ac=168 x1=1.48 ... x2=-11.48
 Linear_Equations_And_Systems_Word_Problems/420252: The sum of a number and eight is equal to half the product of that number and twelve. Find the number.1 solutions Answer 293710 by mananth(12270)   on 2011-03-10 05:05:51 (Show Source): You can put this solution on YOUR website!let number be x x+8=1/2 *x*12 x+8=6x 5x=8 x=8/5
 Money_Word_Problems/420261: A movie theater sells children's tickets for \$7.00 and adult tickets for \$9.00. The theater sold 120 tickets and earned \$1,000.00. How many of each ticket did the theater sell? 1 solutions Answer 293709 by mananth(12270)   on 2011-03-10 05:03:01 (Show Source): You can put this solution on YOUR website!Children's Tickets x Adult tickets ------------ y x + y = 120 .............1 7 x + 9 y =1000 .............2 multiply (1)by -9 Multiply (2) by 1 -9 x + -9 y = -1080 7x + 9 y = 1000 Add the two equations -2 x = -80 /-2 x=40 Children's Tickets plug value of x in (1) x + y = 120 40+y = 120 y = 120-40 y = 80 y = 80 Adult tickets
 test/420251: Use the quadratic formula to solve the equation 2x^2-5x=-7 the solution set is1 solutions Answer 293707 by mananth(12270)   on 2011-03-10 03:09:08 (Show Source): You can put this solution on YOUR website! 2x^2-5x=-7 2x^2-5x+7 Find the roots of the equation by quadratic formula a= 2 , b =-5 , c = 7 . b^2-4ac= -31 x1= 1.25 + 1.39194109 i ... x2= 1.25 - 1.39194109 i
 Word_Problems_With_Coins/420183: Sally has 5 more quarters than dimes. She has half as many nickels as dimes . She has an equal number of loonies as dimes. In total she has \$15.00. How many quarters does sally have?1 solutions Answer 293706 by mananth(12270)   on 2011-03-10 02:41:43 (Show Source): You can put this solution on YOUR website!Dimes ------x ------- 10 quarters ---x+5---------25 Nickels-----x/2---------5 Loonies------x---------- 100 ... 10x+25(x+5)+5x/2+100x= 1500 10x+25x+125+5x/2+100x=1500 multiply by 2 20x+50x+250+5x+200x=3000 275x=3000-250 275x=2750 x= 10 dimes Quarters = 10+5 = 15 coins
 Pythagorean-theorem/420202: A small commuter airline flies to three cities whose locations form the vertices of a right triangle. The total flight distance (from city A to city B to city C and back to city A) is 1400 miles. It is 600 miles between the two cities that are furthest apart (city A to city B). Find the other two distances between cities.1 solutions Answer 293704 by mananth(12270)   on 2011-03-10 02:31:26 (Show Source): You can put this solution on YOUR website!Farthest distance = 600 miles will be the hypotenuse the balance 800 is the sum of the two legs of the right triangle. if one side is x other side = 800-x .. x^2+(800-x)^2=600^2 x^2+640000-1600x+x^2=360000 2x^2-1600x+280000=0 /2 x^2-800x+140000=0 solve using quadratic equation b^2-4ac= 120000 one side = 541.4 miles other side =258.6 miles