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# Recent problems solved by 'mananth'

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 Circles/363471: Find the distance all the way around the boundary of a 100 degree sector of a circle 6" in radius1 solutions Answer 259163 by mananth(12270)   on 2010-10-29 03:59:58 (Show Source): You can put this solution on YOUR website!Angle = 100 deg full circle = 360 deg .. 100/360 = 0.277 ... circumference of circle with radius 6" pi*D pi*12 37.68 ... length of arc = 37.68*0.277 =10.43 inches ... m.ananth@hotmail.ca =
 Polynomials-and-rational-expressions/363467: Can someone please help me solve this problem? (y+1)/(y+3) - (y-2)/(y-3) = (2)/(y+3) Any help would be so appreciated!!!1 solutions Answer 259162 by mananth(12270)   on 2010-10-29 03:54:18 (Show Source): You can put this solution on YOUR website!(y+1)/(y+3) - (y-2)/(y-3) = (2)/(y+3) (y+1)/(y+3) - (2)/(y+3)-(y-2)/(y-3)=0 first two terms have same denominator (y+1-2)/(y+3)-(y-2)/(y-3)=0 (y-1)/(y+3)-(y-2)/(y-3)=0 LCM = (y+3)(y-3) ((y-1)(y-3)-(y-2)(y+3))/(y+3)(y-3)=0 (y^2-4y+3)-(y^2+y-6)/(y+3)(y-3)=0 (y^2-4y+3-y^2-y+6)=0 -5y+9=0 -5y=-9 y=9/5 ... m.ananth@hotmail.ca
 Mixture_Word_Problems/363470: how much water should be added to 414 ounces of a 21% alcohol solution to get an 18% alcohol solution i set it up this way---.21(414)+W=.18(414 + W) but i came up with a neg answer 86.94 + W = 74.52 + .18W 12.42 = -.82W or .82W = -12.42 === -.1546 I don't think the answer should be negative.1 solutions Answer 259161 by mananth(12270)   on 2010-10-29 03:44:59 (Show Source): You can put this solution on YOUR website!how much water should be added to 414 ounces of a 21% alcohol solution to get an 18% alcohol solution how much water ------------0% alcohol-----------x ounces alcohol ------------------ 21% alcohol----------414 ounces alcohol------------------- 18% alcohol----------(x+414)ounces .. concentration equation ... 0+0.21*414=0.18(x+414) 0+86.94=0.18x+74.52 0.18x=86.94-74.52 0.18x=12.42 x=12.42/0.18 x= 69 ounces of water .. m.ananth@hotmail.ca
 Quadratic_Equations/363466: (a - 1)^1/3 = -31 solutions Answer 259160 by mananth(12270)   on 2010-10-29 03:36:04 (Show Source): You can put this solution on YOUR website! take the cube of the equation (a-1)=-27 a-1=-27 a=-26 ... m.ananth@hotmail.ca
 Systems-of-equations/363445: How can I know how to solve an ecuation for y in slope intercept formula? for exemple if there is 2x+3y=-6 or y=-2-5x etc? what are the rules?1 solutions Answer 259159 by mananth(12270)   on 2010-10-29 02:26:31 (Show Source): You can put this solution on YOUR website!2x+3y=-6 .. add -2x 2x-2x+3y=-6-2x 3y=-2x-6 /3 y= -2/3*x-6/2 y=(-2/3)*x-3 compare with y = mx +b (-2/3) is the slope m y intercept =-3 the line intersects the y axis at -3 ... .. you will see the y intercept =-3 ... m.ananth@hotmail.ca
 Linear-equations/363449: find the slope, if it exists, of the line containing the pair of points (5,4)and(10,-4)1 solutions Answer 259158 by mananth(12270)   on 2010-10-29 02:16:53 (Show Source): You can put this solution on YOUR website!slope m= (y2-y1)/ (x2-x1) m=(-4-4)/(5-10) m=-8/-5 m=8/5 ... m.ananth@hotmail.ca
 Numbers_Word_Problems/363456: one number is 7 more than a second number.Also,the sum of the square of the two numbers is 389.Find the two numbers.1 solutions Answer 259157 by mananth(12270)   on 2010-10-29 02:13:05 (Show Source): You can put this solution on YOUR website!let the number be x & x+7 .. x^2+(x+7)^2=389 .. x^2+x^2+14x+49=389 .. 2x^2+14x+49-389=0 .. 2x^2+14x-340=0 .. /2 x^2+7x-170=0 .. x^2+17x-7x-170=0 x(x+17)-7(x+17)=0 (x+17)(x-7)=0 x=-17 OR x=7 ... The numbers are -17,-10 7,14 does not satisfy the equation ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/363458: I am having a problem simplifying this problem 2x+3/x-4-x-5/x+2 please help me.1 solutions Answer 259156 by mananth(12270)   on 2010-10-29 02:02:44 (Show Source): You can put this solution on YOUR website! LCM= (x-4)(x+2) ... .. ... .. ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/363457: I am having problems understanding how to do this problem. Please help me -x+6/-12x+-x-6/-12x1 solutions Answer 259155 by mananth(12270)   on 2010-10-29 01:45:44 (Show Source): You can put this solution on YOUR website! ... the denominator is common .. =0 ... m.ananth@hotmail.ca
 Travel_Word_Problems/363417: Jim and Joe started on trips from San Francisco and traveled in opposite directions. Jim traveled 15 kph faster than Joe. After 4 hours, they were 420 km apart. How fast was each person traveling?1 solutions Answer 259150 by mananth(12270)   on 2010-10-29 00:02:37 (Show Source): You can put this solution on YOUR website!Jim and Joe started on trips from San Francisco and traveled in opposite directions. Jim traveled 15 kph faster than Joe. After 4 hours, they were 420 km apart. How fast was each person traveling? ... joe - speed =x kmph Jim - speed = x+15 kmph .. they are travelling opposite directions so add the speeds x+x+15 = 2x+15 ... distance = 420 km time = 4 .. t= d/r 420/2x+15=4 420=4(2x+15) 420=8x+60 420-60=10x 360=10x x= 36 kmph speed of Joe x+15 = 16+15 = 31 kmph = speed of Jim ... m.ananth@hotmail.ca
 Expressions-with-variables/363428: Simplify the following expression: b^2+5b+6/3bc / b^2-9/6bc1 solutions Answer 259145 by mananth(12270)   on 2010-10-28 23:46:11 (Show Source): You can put this solution on YOUR website! .. .. .. .. m.ananth@hotmail.ca
 Travel_Word_Problems/363419: Nan and Peg started on trips from New York City and traveled in opposite directions. Nan traveled 10 mph faster than Peg. If they were 450 miles apart after 5 hours, how fast was each person traveling?1 solutions Answer 259144 by mananth(12270)   on 2010-10-28 23:38:00 (Show Source): You can put this solution on YOUR website!Nan and Peg started on trips from New York City and traveled in opposite directions. Nan traveled 10 mph faster than Peg. If they were 450 miles apart after 5 hours, how fast was each person traveling? ... peg speed = xmph Nan speed = x+10 mph ... they travel in opposite directions so speed is added up x+x+10=2x+10 distance = 450 miles .. time = 5 hours ... 450/(2x+10)=5 450=5(2x+10) 450=10x+50 add -50 450-50=10x+50-50 400=10x x=400/10 x= 40 mph Peg's speed Nan's speed = 40+10=50 mph ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/363434: Area of Painting A rectangular painting with a width of x centimeters has an area of x^2+50x centimeters. Find a binomial that represents the length.1 solutions Answer 259140 by mananth(12270)   on 2010-10-28 23:31:55 (Show Source): You can put this solution on YOUR website!Area = L*W .. width = x area = x^2+50x .. x^2+50x = x* length length = (x^2+50x)/x Length = x^2/x + 50x/x Length = x+50 ... m.ananth@hotmail.ca
 Triangles/363431: an isosceles triangel has a perimeter of 34cm. the congurant mesaure (4x-1) cm. the thrid leg is x. what is the lenght of each side?1 solutions Answer 259137 by mananth(12270)   on 2010-10-28 23:28:38 (Show Source): You can put this solution on YOUR website!perimeter = sum of all sides (4x-1)(4x-1)+x=34 8x-2+x=34 9x-2=34 add 2 9x=34+2 9x=36 /9 x=4 ... congruent sides = 4x-1 16-1 = 15 ... 15+15+4 = 34 ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/363437: Area of a sail The area in square meters is trianglar sail is given by A(x) x^2 + 5x + 6. Find A(5) If the height of the sail is x+3 meters, then what is the length of the base of the sail?1 solutions Answer 259134 by mananth(12270)   on 2010-10-28 23:24:13 (Show Source): You can put this solution on YOUR website!The area in square meters is trianglar sail is given by A(x) x^2 + 5x + 6. Find A(5) If the height of the sail is x+3 meters, then what is the length of the base of the sail? ... A(x)= x^2 + 5x + 6. A(5)= 5^2 + 5*5 + 6. A(5)=56 .. A(x)= x^2 + 5x + 6. =(x+3)(x+2) height = (x+3) (x+2) = base ... m.ananth@hotmail.ca
 Age_Word_Problems/363438: kyle is 7 years old. Mike is twice as old. When kyle is 10 years old what will be Mike's age?1 solutions Answer 259131 by mananth(12270)   on 2010-10-28 23:18:31 (Show Source): You can put this solution on YOUR website!Kyle = 7 years Mike =14 ... Kyle will be 10 after 3 years Add 3 years to Mike's present age. Mike will be 14+3 = 17 years after 3 years m.ananth@hotmail.ca
 Travel_Word_Problems/363370: A boat can travel 120 miles upstream against the current in the same amount of time it can travel 180 miles downstream with the current. If the boat's average speed in still water is 20 miles per hour, find the speed of the current.1 solutions Answer 259091 by mananth(12270)   on 2010-10-28 21:15:13 (Show Source): You can put this solution on YOUR website!A boat can travel 120 miles upstream against the current in the same amount of time it can travel 180 miles downstream with the current. If the boat's average speed in still water is 20 miles per hour, find the speed of the current. .. let current speed be x .. upstream speed =20-x distance = 120 miles time = 120/(20-x) .. down stream speed = x+20 distance = 180 miles time = 180/(x+20) ... times are equal 120/(20-x)=180/(x+20) 120(x+20)=180(20-x) 120x+2400=3600-180x 120x+180x=3600-2400 300x=1200 x= 4 mph the speed of current. ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/363375: A ferry leaves a harbor and travels to a resort island at an average speed of 22 mph. On the return trip, the ferry travels at an average speed of 18 mph because of fog. The total time for the trip is 5 h. How far is the island from the harbor1 solutions Answer 259087 by mananth(12270)   on 2010-10-28 21:09:01 (Show Source): You can put this solution on YOUR website!A ferry leaves a harbor and travels to a resort island at an average speed of 22 mph. On the return trip, the ferry travels at an average speed of 18 mph because of fog. The total time for the trip is 5 h. How far is the island from the harbor: .. let distance be x forward speed = 22 mph time = x/22 ... return speed = 18 mph return time = x/18 .. x/18+x/22=5 (22x+18x) / 18*22 =5 40x=5*18*22 x=5*18*22 /40 distance = 49.5 miles ... m.ananth@hotmail.ca
 Expressions-with-variables/363357: A class of 42 students and 2 trachers plan a trip on an observatory. The class has raised \$485 for the trip. Admission is \$5 per person and bus rental is \$230. With the remaining money, the class can invite guests to fill in the remaining seats on the bus. Write and solve an equarion to find thenumber of guests(g) the class can invite1 solutions Answer 259085 by mananth(12270)   on 2010-10-28 21:04:15 (Show Source): You can put this solution on YOUR website!485=5*44 +5x +230 485=220+230+5x 485-450=5x 35=5x x=7 7 guests can be invited. the equation will be 5x+450=485 ... m.ananth@hotmail.ca
 Problems-with-consecutive-odd-even-integers/363360: The average of four consecutive eve integers is 17. Find the integers.1 solutions Answer 259079 by mananth(12270)   on 2010-10-28 20:53:50 (Show Source): You can put this solution on YOUR website!let the even integers be x,x+2,x+4,x+6 sum =4x+10 .. average = 17 17*4= 68 = sum 4x+12 = 68 add-12 4x+12-12=68-12 4x=56 /4 x=14 ... 14,16,18,20 ... m.ananth@hotmail.ca
 Points-lines-and-rays/363362: The equation c=\$.05m+ \$ 4.95 represents the cost (C) of a long didtance telephone call of m minutes. what is the slope of the line? what does the slope represent in this situation? what is the y-intercept (C-intercept)? what does the y-intercept represent in this situation?1 solutions Answer 259073 by mananth(12270)   on 2010-10-28 20:48:10 (Show Source): You can put this solution on YOUR website!The equation c=\$.05m+ \$ 4.95 represents the cost (C) of a long didtance telephone call of m minutes. what is the slope of the line? 0.05 what does the slope represent in this situation? cost/minute what is the y-intercept (C-intercept)? 4.95 what does the y-intercept represent in this situation? a fixed cost ...
 Inequalities/363282: 1.the sum of a number and fourteen is less or equal to three times the number 2.negative three times a number increased by seven is less than negative eleven 3.five times a number decreased by eight is at most ten more than negative three 4.Seven more than five sixths of a number is more than negative three 5.four times the sum of a number and two increased by three is at least twenty seven1 solutions Answer 259061 by mananth(12270)   on 2010-10-28 20:37:20 (Show Source): You can put this solution on YOUR website! I will set up the equations for you. I think then you can work them out. 1.the sum of a number and fourteen is less or equal to three times the number let number be x x+14<=3x 2.negative three times a number increased by seven is less than negative eleven let number be x -3x+7 <-11 3.five times a number decreased by eight is at most ten more than negative three 5x-8<=10+-3 4.Seven more than five sixths of a number is more than negative three 5x/6 +7 >-3 5.four times the sum of a number and two increased by three is at least twenty seven 4(x+2)+3>=27 ... m.ananth@hotmail.ca
 Expressions-with-variables/363058: Solve the following equation: 3t-5/t-1=2+2t/1-t1 solutions Answer 258803 by mananth(12270)   on 2010-10-28 09:22:23 (Show Source): You can put this solution on YOUR website! ... .. (t-1) cancel off t=1 is one solution -1(3t-5)=2+2t -3t+5=2+2t -3t-2t=2-5 -5t=-3 t=3/5 .. (1,3/5) m.ananth@hotmail.ca
 Linear-systems/362921: a rope measures 168 and is cut in three peices and the first peice is one-half bigger than the second peice and the third peice is three time the second peice 1 solutions Answer 258800 by mananth(12270)   on 2010-10-28 09:14:54 (Show Source): You can put this solution on YOUR website!let second piece be x first piece = 1.5x third piece =3x ... add up x+1.5x+3x=168 5.5x=168 11/2x=168 11x=2*168 11x=338 x= 338/11 x=30.7 3x=92.1 1.5x=46.05 ... m.ananth@hotmail.ca
 Age_Word_Problems/363045: 10 years ago brandons mother was 4 times his age 10 yrs later she is twice older son how old is brandon?1 solutions Answer 258792 by mananth(12270)   on 2010-10-28 09:01:09 (Show Source): You can put this solution on YOUR website!Brandon's age = x mother's age =4x .. 10 years later brandon = x+10 years Mother = 4x+10 .. 4x+10=2(x+10) 4x+10=2x+20 4x-2x=20-10 2x=10 x= 5 years--- Brandon .. m.ananth@hotmail.ca
 Rectangles/363028: If the sides of a square are each increased by 4 inches, the area becomes 121 square inches. Find the perimeter of the original square. 1 solutions Answer 258768 by mananth(12270)   on 2010-10-28 07:00:58 (Show Source): You can put this solution on YOUR website!If the sides of a square are each increased by 4 inches, the area becomes 121 square inches. Find the perimeter of the original square. .. let side =x x+4 is the increased length ... Area = L^@ (x+4)^2=121 x^2+8x+16=121 x^2+8x-105=0 x^2+15x-7x-105=0 x(x+15)-7(x+15)=0 (x+15)(x-7)=0 x= 7 perimeter = 4L = 28 inches ... m.ananth@hotmail.ca
 Geometry_Word_Problems/363025: length of each equal side of a triangle is 4m less from the third side.If the perimeter of a triangle is 55m find the dimensions of a triangle.1 solutions Answer 258767 by mananth(12270)   on 2010-10-28 06:55:09 (Show Source): You can put this solution on YOUR website!third side = x equal side = x-4 .. x+x-4+x-4=55 3x-8=55 3x=55+8 3x=63 x= 21 third side other sides = 21-4=17 .. 17+17+21=55 ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/363029: Luis spent 28 minutes more on his math homework than his science homework. If the total time he spent on both subjects was 152 minutes, how much time did he spend on each subject? 1 solutions Answer 258766 by mananth(12270)   on 2010-10-28 06:49:20 (Show Source): You can put this solution on YOUR website!let hime spend x minutes on science homework he spends x+28 minutes on math home work. total = 152 x+x+28 = 152 2x+28=152 2x=152-28 2x=124 x= 62 minutes on science homework .. math home work time = 152 -62=90 minutes .. m.ananth@hotmail.ca
 Travel_Word_Problems/363030: An express train travels 150 miles in the same time that a freight train travels 100 miles. If the express goes 20 miles per hour faster than the freight, find the rate each train travels 1 solutions Answer 258765 by mananth(12270)   on 2010-10-28 06:44:36 (Show Source): You can put this solution on YOUR website!An express train travels 150 miles in the same time that a freight train travels 100 miles. If the express goes 20 miles per hour faster than the freight, find the rate each train travels .. freight train - speed = x , d=100 miles express train speed = (x+20),d= 150miles times are same 100/x= 150/(x+20) 100(x+20)=150x 100x+2000=150x 150x-100x=2000 50x = 2000 x= 40 mph freight train speed express train speed = x+20 = 60 mph ... m.ananth@hotmail.ca
 Reduction-of-unit-multipliers/363032: please help im stuck on 1 kilo and one pound = £12 how do i find the price per pound?1 solutions Answer 258764 by mananth(12270)   on 2010-10-28 06:39:58 (Show Source): You can put this solution on YOUR website!please help im stuck on 1 kilo and one pound = £12 how do i find the price per pound? ... the problem is not very clear. 1kilo & 1 pound = 2.2pounds +1 pound =3.2 pounds 3.2 pounds = 12 1 = 12/3.2 3.75
 Linear_Algebra/363033: Find the value of k if the line through the points (k+1, k-2) and (3,4) is parallel to the line through the points (3,1) and (6,-1).1 solutions Answer 258763 by mananth(12270)   on 2010-10-28 06:36:06 (Show Source): You can put this solution on YOUR website!Find the value of k if the line through the points (k+1, k-2) and (3,4) is parallel to the line through the points (3,1) and (6,-1). .. (k+1, k-2) and (3,4) slope of this line =4-(k-2)/3-(k+1) =6-k/2-k ... (3,1) and (6,-1). slope is -1-1/6-3 =-2/3 .. the lines are parallel so slopes are equal 6-k / 2-k = -2/3 3(6-k)=-2(2-k) 18-3k=-4+2k 18+4=2k+3k 22=5k k=22/5 ... m.ananth@hotmail.ca