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# Recent problems solved by 'mananth'

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 Systems-of-equations/404745: 3x+y=2 4y=12-12x1 solutions Answer 286053 by mananth(12270)   on 2011-02-05 20:40:10 (Show Source): You can put this solution on YOUR website!3x+y=2.......(1) 4y=12-12x 4y+12x=12 /4 y+3x=3 multiply by -1 -y-3x=-3 add this to first equation we get 0= -1 There is no solution to the system
 Linear-equations/404717: (0,0) x = -3y - 12 find an equation of the line that passes through the given point and is perpendicular to the given line. write the equation in slope intercept form.1 solutions Answer 286052 by mananth(12270)   on 2011-02-05 20:35:29 (Show Source): You can put this solution on YOUR website!(0,0) x = -3y - 12 x = -3y - 12 3y=-x-12 /3 y=-x/3 -4 compare with y= mx+b m= slope = -1/3 .. The perpendicular line will have slope 3 .. since the line passes through(0,0) the y intercepr = -12. b=-12 y=3x-12 is the equation ...
 Miscellaneous_Word_Problems/404768: The cost of a bus excursion was \$180. This amount was to have been shared equally by all those who said they wished to go. However, 6 people failed to show up so that those who did go each had to pay \$1.50 more. How many people actually went on the trip? I just want to know how to get started I do not need the actual answer.1 solutions Answer 286049 by mananth(12270)   on 2011-02-05 20:21:56 (Show Source): You can put this solution on YOUR website!let x people decide to go initially .. cost per person = 180/x ... 6 persons opt out . number which went = x-6 ... so amount to be paid = 180 /(x-6) ... 180/(x-6) -180/x = 1.5
 Evaluation_Word_Problems/404769: The length of the first side of a triangle is twice the length of the second side, and the length of the third side is 5 more than the length of the second side. Express the perimeter of the triangle in terms of the length of its second side, and use this model to estimate the lengths of the three sides if the perimeter is to be 100 in.1 solutions Answer 286046 by mananth(12270)   on 2011-02-05 20:17:33 (Show Source): You can put this solution on YOUR website!The length of the first side of a triangle is twice the length of the second side, and the length of the third side is 5 more than the length of the second side. Express the perimeter of the triangle in terms of the length of its second side, and use this model to estimate the lengths of the three sides if the perimeter is to be 100 in. ... second side = x first side= 2x third side= x+5 ... x+2x+x+5======> 4x+5 = Perimeter ... 4x+5 =100 4x=95 /4 x=23.75 in 2x= 47.50 in x+5 = 28.75 in
 Travel_Word_Problems/404408: a passenger train leaves a train station four hours after a train leaves the same station. The freight train is traveling ten mph slower than the passenger train. Find the rate of the passenger train if the passenger train overtakes the fright train in 20 hours. 1 solutions Answer 285882 by mananth(12270)   on 2011-02-05 04:51:01 (Show Source): You can put this solution on YOUR website!a passenger train leaves a train station four hours after a train leaves the same station. The freight train is traveling ten mph slower than the passenger train. Find the rate of the passenger train if the passenger train overtakes the fright train in 20 hours. .. Passenger train x mph freight train x-10 mph ... In fours hours freight train has traveled 4(x-10) hours ,.. Catch up distance = 4(x-10) catch up speed = 10 mph Time = distance / speed 4(x-10)/10= 20 4x-40=200 4x=240 x=60 mph. Speed of passenger train = 60 mph
 Linear-systems/404506: How would I graph the following system of inequalities? y≥-1 x≥5 Thank you 1 solutions Answer 285881 by mananth(12270)   on 2011-02-05 04:41:33 (Show Source): You can put this solution on YOUR website!The boundary
 Polynomials-and-rational-expressions/404503: please help which of the following binomials is a factor of 2n^2 - 18 n + 3 n^2 + 9 2n + 3 2n^2 + 91 solutions Answer 285879 by mananth(12270)   on 2011-02-05 04:36:42 (Show Source): You can put this solution on YOUR website!option 1 (n+3) 2(n^2-9) 2(n+3)(n-3)
 Polynomials-and-rational-expressions/404528: The area of a rectangular athletic field is represented by the expression 28y^4 -21y^3 +56y^2 square meters. Write an algebraic expression to represent one possible set of dimensions (in the sense “length times width”) of the athletic field. Include correct units with your solution. 1 solutions Answer 285878 by mananth(12270)   on 2011-02-05 04:34:01 (Show Source): You can put this solution on YOUR website!28y^4 -21y^3 +56y^2 (7y^2)(4y^2-3y+8)= Area
 Miscellaneous_Word_Problems/404529: thirty percent of a number is equals to twenty-five percent of 144.what is the unknown number?1 solutions Answer 285877 by mananth(12270)   on 2011-02-05 04:29:27 (Show Source): You can put this solution on YOUR website!let the number be x 30% 0f x= 25% of 144 x= (100*25*144)/100*30 x=120
 Rectangles/404530: the area of a rectangle is 96 square centimeters. if the width of the rectangle is 4 centimeter less than its length, what are the dimension of the rectangle1 solutions Answer 285876 by mananth(12270)   on 2011-02-05 04:24:11 (Show Source): You can put this solution on YOUR website!length= x width = x-4 ... area = L*W Area = x(x-4)=96 x^2-4x=96 x^2-4x-96=0 x^2-12x+8x-96=0 x(x-12)+8(x-12)=0 *x-12)(x+8)=0 So x= 12 cms===>length width = 12-4=8 cm
 Polynomials-and-rational-expressions/404426: The area of a rectangular swimming pool is given by 3x^2-2x-1ft^2 . One side length of the pool is given by 3x + 1 feet. What is an algebraic expression for the other side length of the pool? Simplify this, and include correct units as part of your answer. 1 solutions Answer 285869 by mananth(12270)   on 2011-02-05 01:18:20 (Show Source): You can put this solution on YOUR website!The area of a rectangular swimming pool is given by 3x^2-2x-1ft^2 . One side length of the pool is given by 3x + 1 feet. What is an algebraic expression for the other side length of the pool? Simplify this, and include correct units as part of your answer. The area = 3x^2-2x-1ft^2 . One side length= 3x + 1 feet. Area = L*W Area / Length = Width Width = (x-1)feet
 Coordinate-system/404446: Show that a square whose diagonal has length d has perimeter 2sqrt2d.1 solutions Answer 285868 by mananth(12270)   on 2011-02-05 01:11:01 (Show Source): You can put this solution on YOUR website!diagonal = d apply pythagoras theorem Let the legs be x each .. d^2= x^+x^2 d^2=2x^2 divide by 2 d^2/2= x^2 Perimeter = 4*length
 Linear-systems/404508: I need to solve the following system of equations x+6y=9 (1) x=7-6y (2) What is the solution to the system? Thank you1 solutions Answer 285866 by mananth(12270)   on 2011-02-05 00:57:57 (Show Source): You can put this solution on YOUR website!x+6y=9 (1) x=7-6y (2) add 6y to both sides x+6y=7... (2) compare (1) & (2) we get 9=7 ... There is no solution to this system
 Linear-equations/404521: find the slope for (9,7) and (19,8)1 solutions Answer 285864 by mananth(12270)   on 2011-02-05 00:51:35 (Show Source): You can put this solution on YOUR website!find the slope for (9,7) and (19,8) slope m = (y2-y1)/(x2-x1) m= (8-7)/(19-9) m=1/10====> slope
 Inequalities/404514: Please assist me with solving the inequality and also could you show me how you came up with the answer: -18t-2<24 Thank you1 solutions Answer 285863 by mananth(12270)   on 2011-02-05 00:49:58 (Show Source): You can put this solution on YOUR website!-18t-2<24 add +2 to both sides -18t-2+2<24+2 -18t<26 divide by -2 -18t/-2 > 26/-2 Because you are dividing by a negative number the sign reverses 9t>-13 divide by 9 t>-13/9
 Pythagorean-theorem/404480: 10. A square has a 40-cm diagonal. How long is each side of the square? Round your answer to the nearest tenth of a centimeter. (1 point1 solutions Answer 285844 by mananth(12270)   on 2011-02-04 22:08:54 (Show Source): You can put this solution on YOUR website!The legs and the diagonal form a right angle. The diagonal is the hypotenuse. apply Pythagoras theorem .. Let l be one leg. since it is a square the other leg is also l. l^2+l^2= 40^2 2l^2=1600 l^2=800 l = sqrt (800) l = 28.28 ... l= 28.3 cm
 Travel_Word_Problems/404209: B is 50% faster than A. If A starts at 9 A.M. and B starts at 10 A.M. A travels at a speed of 50 km/hr. If A and B are 300 kms apart, The time when they meet when they travel in opposite direction is ? 1 solutions Answer 285675 by mananth(12270)   on 2011-02-04 05:49:07 (Show Source): You can put this solution on YOUR website!A 50 km/h ... 50% of A = 25 km/h ... B travels at 75km/h .. B starts at 10 am. A starts at 9 am .. A travels 50 km in 1 hour .. when B starts they are 300 -50 km apart. =250km. Speed together = 50+75 = 125 km/h Time = distance /speed Time =250/125 Time = 2hours to meet. They meet at 12.00 noon
 Geometry_proofs/404128: x-y=-1 3x+y=51 solutions Answer 285664 by mananth(12270)   on 2011-02-03 23:45:05 (Show Source): You can put this solution on YOUR website!x-y=-1.................1 3x+y=5.................2 ... add (1) & (2) x+3x-y+y=-1+5 4x=4 /4 x=1 ,,plug value of x in 1 x-y =-1 1-y=-1 y=1+1 y=2
 Travel_Word_Problems/403742: Stephen left at 6:00am and traveled 470 miles at a rate of 55mph. About when will he arrive at his destination?1 solutions Answer 285453 by mananth(12270)   on 2011-02-03 08:41:43 (Show Source): You can put this solution on YOUR website! distance =470 speed = 55 mph t = 8.54 hours 0.54*60 = minutes====> =32 minutes time = 8 hours 32 minutes reaching time = 2:32 pm
 Money_Word_Problems/403690: Mary two student loans total \$9000. One loan is at 5% simple interest and the other is at 6% simple interest. At the end of 1 yr, Mary owes \$492 in interest. What is the amount of each loan?1 solutions Answer 285452 by mananth(12270)   on 2011-02-03 08:36:23 (Show Source): You can put this solution on YOUR website!Mary two student loans total \$9000. One loan is at 5% simple interest and the other is at 6% simple interest. At the end of 1 yr, Mary owes \$492 in interest. What is the amount of each loan? Mary two student loans total \$9000. 5% simple interest------------\$x 6% simple interest. -----------9000-x \$492 in interest. .. 5x+6(9000-x)=492*100 5x+54000-6x=49200 -x=-54000+49200 -x=-4800 x=\$4800====> 5% balance \$4200 at 6%
 Expressions-with-variables/403723: a sparrow flies to see a friend at a speed of 4km/h. his friend is out,so the sparrow immediately returns home at a speed of 5km/h. the complete journey took 54 minutes. how many far away does his friend Live?1 solutions Answer 285451 by mananth(12270)   on 2011-02-03 08:30:01 (Show Source): You can put this solution on YOUR website! let distance be x km while going to meet 4km/h time taken = x/4 ... return speed = 5km/h time = x/5 ... x/5 +x/4 = 54/60 (4x+5x)/20=54/60 9x=54*20/60 9x=18 /9 x= 2km====> distance friend lives
 Graphs/403740: Use the five step to solve and show. The area of a triangular section of a store cannot be more than 910 sq. ft. If the height of the triangular section is 52 ft, what should the base be?1 solutions Answer 285447 by mananth(12270)   on 2011-02-03 08:25:24 (Show Source): You can put this solution on YOUR website! Height = 52 .. Area of triangle = 1/2 * base * height Area = 1/2*base*52 1/2*base*52<=910
 Graphs/403739: Use the five steps for problem solving to answer the following question. Show all work and solve. Laura found \$2.15 in quarters and nickles in the bottom of her purse. There were seven fewer quarters than nickles. How many nickles and quarters did she have?1 solutions Answer 285443 by mananth(12270)   on 2011-02-03 08:21:20 (Show Source): You can put this solution on YOUR website!nickels-------x quarters--------x-7 total \$ 2.15 = 215 cents ... 5x+25(x-7)=215 5x+25x-175=215 30x=215+175 30x=390 /30 x=13=====> nickels 13-7 = 6 =====> quarters
 Age_Word_Problems/403730: james is 4 years older than danny. 2 years ago, James was 5 years as old as danny. how old was james today?1 solutions Answer 285441 by mananth(12270)   on 2011-02-03 08:17:34 (Show Source): You can put this solution on YOUR website!Danny ---------- x years James ----------- x+4 years .. 2 years ago Danny = x-2 James = (x+4)-2=======> x+2 ... x+2=5(x-2) x+2=5x-10 5x-x=2+10 4x=12 /3 x=4 years===========> Danny's age James============> 4+4 = 8 years
 Graphs/403704: I need to graph the following equation on a plane and I am not sure how to do that. 2x+3y≤6 Thank you1 solutions Answer 285432 by mananth(12270)   on 2011-02-03 00:38:02 (Show Source): You can put this solution on YOUR website! x=0,y=2(0,2) y=0,x=3(3,0) .. The boundary plot the points and draw the line Since y is less than something all points below the line are solutions to the equation. The shaded area
 Polynomials-and-rational-expressions/403614: The length of the side of a rectangular desk is given by 6x - 3y cm. The length of the front is given by 6x + 3y 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 285360 by mananth(12270)   on 2011-02-02 20:06:08 (Show Source): You can put this solution on YOUR website!The length of the side of a rectangular desk is given by 6x - 3y cm. The length of the front is given by 6x + 3y cm. What is an algebraic expression for the area of the top of the rectangular desk? Include correct units as part of your answer. The length of the side of a rectangular desk is given by 6x - 3y cm. The length of the front is given by 6x + 3y cm. ... Area = L*W Area = (6x-3y)(6x+3y) Area = (36x^2-9y^2) cm^2
 Travel_Word_Problems/403604: the length of a rectangular frame is 53cm.for what widths would the perimeter be greater than 160cm? 1 solutions Answer 285359 by mananth(12270)   on 2011-02-02 20:03:30 (Show Source): You can put this solution on YOUR website!the length of a rectangular frame is 53cm.for what widths would the perimeter be greater than 160cm? let width be w .. Perimeter = 2*(L+W) Perimeter = 2(53+W) .. 2(53+W)>160 /2 53+W >80 -53 w>80-53 W>27 cm
 Graphs/403600: Use substitution or elimination to solve each system of equations. 2x + 5y= 16 5x - 2y=111 solutions Answer 285357 by mananth(12270)   on 2011-02-02 19:59:03 (Show Source): You can put this solution on YOUR website!2x + 5y= 16..............1 5x - 2y=11...............2 ... multiply (1) by 2 & (2) by 5 we get 4x+10y=32 25x-10y=55 add them 29x=87 /29 x=3 ... plug value of x in (1) 2x+5y=16 2*3+5y=16 6+5y=16 5y=10 /5 y=2
 Money_Word_Problems/403597: Gunther invested \$10,000 in two mutual funds. One of the funds rose 6 percent in one year and the other rose 9 percent in one year. If Gunthers investment rose a total of \$684 in one year, how much did he invest in each mutual fund? Yes, this is my son's 7th graded algebra homework. He's learning to solve systems of equations so my first inclination is to .06x +.09y=684 and x + y = 10,0001 solutions Answer 285353 by mananth(12270)   on 2011-02-02 19:53:20 (Show Source): You can put this solution on YOUR website!Yes, this is my son's 7th graded algebra homework. He's learning to solve systems of equations so my first inclination is to .06x +.09y=684 and x + y = 10,000 0.06x +0.09y=684 ...........1 x + y = 10,000 ............2 ... multiply (1) by 100 we get 6x+9y=68400................3 Multiply (2) by -6 we get -6x-6y=-60000.............4 Add (3) & (4) 6x-6x+9y-6y=68,400-60,000 3y=8,400 /3 y=2800 So x= 7,200
 Rectangles/403593: Suppose that the width of a certain rectangle is 5 inches less than its length. The area is numerically 16 less than twice the perimeter. Find the length and width of the rectangle. 1 solutions Answer 285349 by mananth(12270)   on 2011-02-02 19:45:55 (Show Source): You can put this solution on YOUR website!Suppose that the width of a certain rectangle is 5 inches less than its length. The area is numerically 16 less than twice the perimeter. Find the length and width of the rectangle. ... length = L width = L-5 .. Area = L(L-5) ... Perimeter = 2(L+L-5) Perimeter = 2(2L-5) ... L(L-5)=2*2(2L-5)-16 L^2-5L=8L-20-16 L^2-5L-8L=-20-16 L^2-13L=-36 L^2-13L+36=0 L^2-9L-4L+36=0 L(L-9)-4(L-9)=0 (L-9)(L-4)=0 So L= 4 OR 9 The dimensions are 9 by 4 feet