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# Recent problems solved by 'mananth'

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 Functions/356157: Volume. An open box is constructed from a square 10-inch piece of cardboard by cutting squares of length x inches out of each corner and folding the sides up. Express the volume of the box as a function of x, and state the domain.1 solutions Answer 254237 by mananth(12270)   on 2010-10-14 00:22:29 (Show Source): You can put this solution on YOUR website!the cardboard = 10 by 10 x is cut off from corner so the length of the box will be 10-2x the width also will be 10-2x the height = x ... Volume V = (10-2x)^2*x V=(100-40x+4x^2)*2x V= 8x^3-80x^2+200x .. ... m.ananth@hotmail.ca
 Problems-with-consecutive-odd-even-integers/356065: Find four consecutive integers such that four times the second diminished by twice the fourth is 10.1 solutions Answer 254232 by mananth(12270)   on 2010-10-14 00:00:21 (Show Source): You can put this solution on YOUR website!Find four consecutive integers such that four times the second diminished by twice the fourth is 10. let the integers be x,x+1,x+2,x+3 4(x+1)-2(x+3)=10 4x+4-2x-6=10 2x-2=10 2x=10+2 2x=12 /2 x=6 the integers are 6,7,8,9 .. m.ananth@hotmail.ca
 Travel_Word_Problems/356149: a boat goes 14 km/h in still water. The boat is paddled 6 km downstream in a river in the same time it takes to go 3 km upstream. What is the speed of the river?1 solutions Answer 254228 by mananth(12270)   on 2010-10-13 23:41:10 (Show Source): You can put this solution on YOUR website!a boat goes 14 km/h in still water. The boat is paddled 6 km downstream in a river in the same time it takes to go 3 km upstream. What is the speed of the river? ... speed in still water = 14 km/h speed of current be x .. speed downstream = x+14 spped upstream = 14-x ... Time = distance /speed time upstream = 3/(14-x) speed downstream = 6/x+14 .. the times are same 3/(14-x) =6/(x+14) 3(x+14)=6(14-x) 3x+42=84-6x 9x=84-42 3x+6x=42 9x =42 x=4.66 km/h ... m.ananth@hotmail.ca
 Quadratic_Equations/356155: rewrite the following in simplified form sqt of 281 solutions Answer 254227 by mananth(12270)   on 2010-10-13 23:29:22 (Show Source): You can put this solution on YOUR website!rewrite the following in simplified form sqt of 28 .. sqrt (2*2*7) sqrt(2*2)*sqrt7 2sqrt7 ... m.ananth@hotmail.ca
 Sequences-and-series/356150: Find the sum of two consecutive positive even integers such that the square of the smaller is 4 more than 10 times the larger. I need to know the procces so show steps please.1 solutions Answer 254226 by mananth(12270)   on 2010-10-13 23:27:31 (Show Source): You can put this solution on YOUR website!Find the sum of two consecutive positive even integers such that the square of the smaller is 4 more than 10 times the larger. .. let the numbers be x & x+2 the square of the smaller = x^2 10 times larger = 10(x+2) 4 more 10(x+2)+4 x^2=10(x+2)+4 x^2=10x+20+4 x^2=10x+24 x^2-10x-24=0 x^2-12x+2x-24=0 x(x-12)+2(x-12)=0 (x-12)(x+2) so the number is x=12 which is positive the other number =12+2= 14 12+14=26 their sum ... m.ananth@hotmail.ca
 Problems-with-consecutive-odd-even-integers/356151: Four times the lesser of two consecutive even integers is 12 less than twice the greater number. Find the integers.1 solutions Answer 254225 by mananth(12270)   on 2010-10-13 23:21:24 (Show Source): You can put this solution on YOUR website!Four times the lesser of two consecutive even integers is 12 less than twice the greater number. Find the integers. .. let the numbers be x & x+2 4x=2(x+2)-12 4x=2x+4-12 4x-2x=-8 2x=-8 /2 x=-4 the numbers are -4 & -2 ... m.ananth@hotmail.ca
 Geometry_Word_Problems/356152: two baseball players hit 79 home runs combined last season. the first player hit 7 more home runs than twice the number of home runs hit by the second player. how many home runs did each player hit?1 solutions Answer 254223 by mananth(12270)   on 2010-10-13 23:17:17 (Show Source): You can put this solution on YOUR website!two baseball players hit 79 home runs combined last season. the first player hit 7 more home runs than twice the number of home runs hit by the second player. how many home runs did each player hit? .. let second player hit x home runs first will hit 2x+7.. their sum = 79 x+2x+7=79 3x+7=79 3x=79-7 3x=72 /3 x=72/3 x= 24 scored by second first will score 55 ... m.ananth@hotmail.ca
 Triangles/356143: the sail abc has side length a-b = 5 metres b-c = 6 metres and a-c=7 metres what is the area1 solutions Answer 254216 by mananth(12270)   on 2010-10-13 23:12:35 (Show Source): You can put this solution on YOUR website!the sail abc has side length a-b = 5 metres b-c = 6 metres and a-c=7 metres what is the area sides are 5,6,7 sum of all sides = 18 1/2 perimeter = 9 =s ... area = 14.7 m^2
 Linear-systems/356136: perimeter of a rectangle is 204 inches. the length exceeds the width by 62 inches. what is the length and width?1 solutions Answer 254202 by mananth(12270)   on 2010-10-13 22:25:14 (Show Source): You can put this solution on YOUR website!width be x length = x+62 .. 2*(L+W)=204 2*(x+x+62)=204 2*(2x+62)=204 divide by2 2x+62=102 2x=102-62 2x=40 /2 x= 20 the width length = x+62 = 20+62 =82 ... . m.ananth@hotmail.ca
 test/356137: Solve the equation below by using the addition (elimination) method: 3x-y=13 2x+y=31 solutions Answer 254199 by mananth(12270)   on 2010-10-13 22:21:46 (Show Source): You can put this solution on YOUR website!3x-y=13 2x+y=3 .. 3x+2x-y+y=13+3 5x=16 /5 x=16/5 .. plug value of x in equation 1 3*(16/5)-y=13 48/5 -y =13 y=48/5 -13 y=(48-65)/5 y=-17/5 ... m.ananth@hotmail.ca
 Sequences-and-series/356132: can you explain to me how to do the problem : Find a number whose product with 9 is the same as its usm with 56? step by step1 solutions Answer 254193 by mananth(12270)   on 2010-10-13 22:16:37 (Show Source): You can put this solution on YOUR website!let number be x product with 9 = 9x .. sum with 56 = x+56 .. 9x=x+56 9x-x=56 8x=56 x= 7 ... m.ananth@hotmail.ca
 sets-and-operations/356095: How do you find the average speed of an object. For example: Fly 1200 miles in 4 hours. Thank you for your help. The subject might be wrong. Sorry.1 solutions Answer 254173 by mananth(12270)   on 2010-10-13 21:05:30 (Show Source): You can put this solution on YOUR website!speed = distance/time distance = 1200 miles time = 4hours speed = 1200 miles/4 hours speed = 300 miles/hour ... m.ananth@hotmail.ca
 Pythagorean-theorem/356089: What do I do if I am given the hypotenuse and need to find the length of a leg? And reverse? 1 solutions Answer 254172 by mananth(12270)   on 2010-10-13 21:03:13 (Show Source): You can put this solution on YOUR website! let the legs of the right triangle be leg1 and leg2 the formula is leg1^2 +leg2^2= hypotenuse ^2 just plug the two values to get the third. hypotenuse^2-leg1^2=leg2^2 ... take square root of the calculated value .. m.ananth@hotmail.ca
 Linear-equations/356086: The Eiffel Tower is 497 ft. taller than he Washington Monument. If each of the monuments were 58ft shorter, the Eiffel tower would be twice as tall as the Washington Monument. How tall is each?1 solutions Answer 254170 by mananth(12270)   on 2010-10-13 20:59:39 (Show Source): You can put this solution on YOUR website!WM be x ET = x+497 .. if each were shorter by 58 ft their height would be WM x-58 ET x+497-58 ... x+497-58 = 2(x-58) x+439=2x-116 2x-x=439+116 x= 555 feet the washington Monumnet (WM) ET = x+497 =555+497=1052 feet ... m.ananth@hotmail.ca
 Travel_Word_Problems/356088: A passenger train's speed is 60 miles per hour, and a freight train's speed is 40 miles per hour. The passenger train travels the same distance in 1.5h less time than the freight train. How long does each train take to make the trip. On this problem I am clueless, our teacher did very little to explain this type of problem as our class was short on time. Thank you for your assistance, Devin Price1 solutions Answer 254166 by mananth(12270)   on 2010-10-13 20:51:48 (Show Source): You can put this solution on YOUR website!A passenger train's speed is 60 miles per hour, and a freight train's speed is 40 miles per hour. The passenger train travels the same distance in 1.5h less time than the freight train. How long does each train take to make the trip. passenger train speed = 60 mph freight train speed = 40 mph .. let freight train take x hours the passenger train will take x-1.5 hours .. the distance they travel is the same ... distance = speed * time ... passenger train distance = 60*(x-1.5) freight train distance = 40x .. 40x=60(x-1.5) 40x=60x-90 60x-40x=90 20x=90 /20 x=90/20 x=4.5 freight train 4.5 hours passenger train 4.5-1.5 = 3 hours ... m.ananth@hotmail.ca
 Numbers_Word_Problems/356083: How do you work this? the sum of two and three times the difference of a number and five is equal to four times the differnce a number and one1 solutions Answer 254162 by mananth(12270)   on 2010-10-13 20:45:26 (Show Source): You can put this solution on YOUR website!let number be x 3(x-5)+2 =4(x-1) 3x-15+2=4x-4 3x-13=4x-4 3x-4x=13-4 -x=9 divide by -1 x=-9 m.ananth@hotmail.ca
 Problems-with-consecutive-odd-even-integers/356070: Three consecutive integers are such that their sum has the same value as twice the second integer subtracted from 20. What are the three integers?1 solutions Answer 254160 by mananth(12270)   on 2010-10-13 20:40:08 (Show Source): You can put this solution on YOUR website!let the integers be x ,x+1,x+2 x+x+1+x+2=20-2(x+1) 3x+3=20-2x-2 3x+2x=20-3-2 5x=15 /5 x=3 3,4,5 are the integers ... m.ananth@hotmail.ca
 Equations/356073: Can you please help me find what x is in -x+3=10 ? 1 solutions Answer 254157 by mananth(12270)   on 2010-10-13 20:36:48 (Show Source): You can put this solution on YOUR website!-x+3=10 add -3 -x+3-3=10-3 -x=7 divide by -1 -x/-1=7/-1 x=-7 ... m.ananth@hotmail.ca
 Equations/356072: Factor F(x)= 10a^2-9a+21 solutions Answer 254154 by mananth(12270)   on 2010-10-13 20:34:07 (Show Source): You can put this solution on YOUR website!10a^2-9a+2 10a^2-5a-4a+2 5a(2a-1)-2(2a-1) (2a-1)(5a-2) (2a-1)(5a-2) ... m.ananth@hotmail.ca
 Angles/356046: My thirteen yr. old son is tired and having trouble with this Question Find the number of degrees in the measure of an angle that is 20 degrees less than 4 times it's supplement. Thank You! John 1 solutions Answer 254142 by mananth(12270)   on 2010-10-13 20:05:01 (Show Source): You can put this solution on YOUR website!let angle be x supplement will be 180-x ... x=4(180-x)-20 x=720-4x-20 x+4x=720-20 5x=700 x=140 deg the measure of the angle .. m.ananth@hotmail.ca
 Functions/356045: 10x+3y+2=9x+8 how do you write the equation in a function form? y=? i need help now this is my homework!please help!1 solutions Answer 254137 by mananth(12270)   on 2010-10-13 19:59:32 (Show Source): You can put this solution on YOUR website!10x+3y+2=9x+8 .. add -10x 10x-10x+3y+2=-10x+9x+8 3y+2=-x+8 add -2 3y+2-2=-x+8-2 3y=-x+6 divide by 3 y = -x/3 +2 ... m.ananth@hotmail.ca
 Angles/356034: The measure of an angle exceeds twice the measure of the complement of the angle by 20. What is the measure of half of the complement?1 solutions Answer 254134 by mananth(12270)   on 2010-10-13 19:44:25 (Show Source): You can put this solution on YOUR website!let the angle be x the complement = 90-x x=2(90-x)+20 x=180-2x+20 2x+x=200 3x=200 x=66.66 complement = 23.34 half of complement = 11.67 deg .. m.ananth@hotmail.ca
 Graphs/356035: 1 solutions Answer 254128 by mananth(12270)   on 2010-10-13 19:38:48 (Show Source): You can put this solution on YOUR website!4x^2+8xy-x-2y 4x(x+2y)-1(x+2y) (x+2y)(4x-1) .... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/356027: The greatest recorded temperature change in one 24-hr period occurred between January 23 and January 24, 1916, in Browning, Montana, where the temperature fell from 440F to -560F. By how much did the temperature drop?1 solutions Answer 254127 by mananth(12270)   on 2010-10-13 19:31:53 (Show Source): You can put this solution on YOUR website!it dropped from 440 to 0 then 0 to -560 440+560 =1000F .... m.ananth@hotmail.ca
 Linear-equations/355741: How do i Solve for X? x^(3/2)-26=991 solutions Answer 254023 by mananth(12270)   on 2010-10-13 10:13:11 (Show Source): You can put this solution on YOUR website!x^(3/2)-26=99 x^(3/2)=99+26 x^(3/2)=125 Take the square x^(3/2)^2 = (125)^2 x^3 = 15625 take the cube root x= 25 ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/355720: Okay, I'm trying to help my 9 year old on a participation only math problem. I am not very good at math. My father has given us the steps he believes are necessary, I would like to see what people who obviously LOVE math come up with... The Jaguars scored 35 points in the first half of a basketball game. They scored 3 more points in the fourth quarter than they scored in the third quarter. The opposing team scored 90 points and won. How many points might the Jaguars have scored in the third and fourth quarters? Thanks for the help!1 solutions Answer 254009 by mananth(12270)   on 2010-10-13 09:42:28 (Show Source): You can put this solution on YOUR website!let the jaguars score x points in the third quarter they score x+3 points in the fourth quarter They score 35 points in the first half of the game. Totally they have scored x+x+3 +35 =2x +38 points in the whole game. .. opposite team scored 90 points 2x+38 <90 add -38 to both sides 2x+38-38<90-38 2x<52 divide by 2 x<26 ... third quarter they have scored <26 in the fourth quarter they have scored <29 .... m.ananth@hotmail.ca
 Linear-equations/355721: Write 34392.55 in scientific notation. A. 3.439255 × 104 C. 3.439255 × 103 B. 3.439255 × 10−4 D. 3.439255 × 10−31 solutions Answer 253997 by mananth(12270)   on 2010-10-13 09:21:05 (Show Source): You can put this solution on YOUR website!option A
 Polynomials-and-rational-expressions/355705: Regarding Products of Sums and Differences Multiply and simplify (3xy^2+4y)(-3xy^2+4y) 1) Please show me the steps to solving this. I have tried numberous times and do not get the answer the book shows. 2)Why is commutative law used? How should I know when to use it? Why are they switched? How should I know on my own when to switch them? The book shows the first step goes to (4y+3xy^2) (4y-3xy^2). I do not understand that at all. I appreciate any help. Jill1 solutions Answer 253995 by mananth(12270)   on 2010-10-13 09:19:18 (Show Source): You can put this solution on YOUR website!(4y+3xy^2) (4y-3xy^2) to put in simple terms you have to multiply each term in one bracket with the other terms in the second bracket. ... 4y(4y-3xy^2)+3xy^2(4y-3xy^2) now you have to multiply the term outside the bracket with the terms in the bracket.( distributive law) ... 4y*4y-4y*3xy^2+3xy^2*4y-3xy^2*3xy^2 16y^2-12xy^3+12xy^3-9x^2y^4 16y^2-9x^2y^4 ..
 Expressions-with-variables/355713: \$1043 in the following denominations. hundreds,fifties,wenties,fives,and on. Has 3 times as many fifties as hundreds.12 times as many twenties as hundres,and 4 times as many ones as hundreds. has 9 more 5s than hundress. How many of eaaach denomination of bills are there?1 solutions Answer 253990 by mananth(12270)   on 2010-10-13 09:07:14 (Show Source): You can put this solution on YOUR website!\$1043 in the following denominations. hundreds,fifties,wenties,fives,and on. Has 3 times as many fifties as hundreds.12 times as many twenties as hundres,and 4 times as many ones as hundreds. has 9 more 5s than hundress. How many of eaaach denomination of bills are there? .. let hundreds be x numbers fifties =3x twenties = 12x fives x+9 ones = 4x .. total of all these = 1043 ... 100x +50*3x+20*12x+5(x+9)+4x = 1043 100x+150x+240x+5x+45+4x=1043 499x= 1043-45 499x=998 x= 998/499 x= 2 hundreds fifties = 3x = 6 twenties = 12x=24 fives = x+5 = 7 ones = 4x=8 ... m.ananth@hotmail.ca
 Trigonometry-basics/355714: please help me solve this equation 1 solutions Answer 253984 by mananth(12270)   on 2010-10-13 08:57:16 (Show Source): You can put this solution on YOUR website!2x^3 +2=0 2(x^3+1)=0 2(X+1)(x^2+x+1)............ use a^3+b^3 = (a+b)(a^2+ab+b^2) ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/355708: Regarding Products of Sums and Differences Multiply and Simplify (2t+3)^2 - (t-1)(t+1) Please show me the steps to solving this. What form is used? How do I know what to do first? Thank you, Jill1 solutions Answer 253981 by mananth(12270)   on 2010-10-13 08:53:49 (Show Source): You can put this solution on YOUR website!(2t+3)^2 - (t-1)(t+1) (2t+3)^2-(t^2-1) .............( (a+b)(a-b)= a^2-b^2) here a =t & b =1) (4t^2+12t+9)-(t^2-1)...........( (a+b)^2 = a^2+2ab+b^2; a= 2t and b =3) 4t^2+12t+9-t^2+1 group the similar terms & simplify 4t^2-t^2+12t+9+1 3t^2+12t+10 ... In such problems first solve the terms in the brackets and then simplify .. m.ananth@hotmail.ca