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# Recent problems solved by 'mananth'

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 Expressions-with-variables/381295: The sum of the angle of a triangle is 180〫. If one angle of a triangle measures x and the second angle measures (5x+18)〫, express the measure of the third angle in terms of x. Simplify the expression.1 solutions Answer 270440 by mananth(12270)   on 2010-12-05 20:13:40 (Show Source): You can put this solution on YOUR website!One angle = x second angle = (5x+18) third angle = 180 - (x+5x+18) third angle = 180-(6x+18) third angle = 180 -6x-18 third angle =
 Travel_Word_Problems/381290: A migrating elephant herd started movin at a rate of six miles per hour.One elephant stood still and was left behind. Then this stray elephant sensed danger andbehan running at a rat of ten miles per hour to reach the herd. The stray caught up in five minutes.How long ( in hours ) did the stray run to catch up?How fardid it run? 1 solutions Answer 270438 by mananth(12270)   on 2010-12-05 20:08:24 (Show Source): You can put this solution on YOUR website!A migrating elephant herd started movin at a rate of six miles per hour.One elephant stood still and was left behind. Then this stray elephant sensed danger andbehan running at a rat of ten miles per hour to reach the herd. The stray caught up in five minutes.How long ( in hours ) did the stray run to catch up?How fardid it run? ... rate = 6 mph. rate of stray elephant = 10 mph. since they are moving in same direction subtract the rates 10-6 = 4mph. is the catch up speed. .. distance = r*t distance = 4 * 5/60 distance = 20/60 distance = 1/3 mile. ... distance run by stray = 1/3 mile. rate = 10 mph time = (1/3) / 10 time = 1/3 * (1/10) time = 1/30 hour time the stray ran = 0.0333 hours .. m.ananth@hotmail.ca ..
 Quadratic_Equations/381287: 2x^2-3x=-5 Use quadratic formula to solve equation1 solutions Answer 270432 by mananth(12270)   on 2010-12-05 19:59:39 (Show Source): You can put this solution on YOUR website!2x^2-3x=-5 +5 +5 2x^2-3x+5=0 ... discriminant = -31 ... x1= ((-(-3)+sqrt(-31))/4 x1= 3/4 +sqrt(-31)/4 x1= 0.75 + 1.3919410907075053i ... x2= ((-(-3)-sqrt(-31))/4 x2= 3/4 -sqrt(-31)/4 x2= 0.75 - 1.3919410907075053i ... m.ananth@hotmail.ca
 Square-cubic-other-roots/380886: Solve the following for x: 5+sqrt3x=171 solutions Answer 270325 by mananth(12270)   on 2010-12-05 05:47:15 (Show Source): You can put this solution on YOUR website! ... -5 ... ... square both sides 3x=144 /3 x=144/3 x=48 ... m.ananth@hotmail.ca
 Square-cubic-other-roots/380884: Multiply and simplify the following: (3+2sqrt7)(6-5sqrt7)1 solutions Answer 270324 by mananth(12270)   on 2010-12-05 05:42:07 (Show Source): You can put this solution on YOUR website! .. ... ... ... m.ananth@hotmail.ca
 Square-cubic-other-roots/380883: Simplify the following: square root of 121x^2 divided by 144x^121 solutions Answer 270321 by mananth(12270)   on 2010-12-05 05:29:35 (Show Source): You can put this solution on YOUR website! ... ... ... ... m.ananth@hotmail.ca
 Sequences-and-series/380955: find a number whose product with 9 is the same as it sum with 561 solutions Answer 270318 by mananth(12270)   on 2010-12-05 05:20:44 (Show Source): You can put this solution on YOUR website!n= number .. 9n = n+56 -n 9n-n=56 8n=56 /8 n=7 ... m.ananth@hotmail.ca
 Equations/380935: Hi can someone please help me solve the following problem? 1/9x -1/3y + 2/3x -1/9y Thank you!1 solutions Answer 270316 by mananth(12270)   on 2010-12-05 05:18:16 (Show Source): You can put this solution on YOUR website! ... Re organize the terms .. ... m.ananth@hotmail.ca
 Equations/380929: Can you please help me solve this problem? 2x^2> -5x + 3 1 solutions Answer 270315 by mananth(12270)   on 2010-12-05 05:11:00 (Show Source): You can put this solution on YOUR website!2x^2> -5x + 3 ... +5x 2x^2+5x>3 -3 2x^2+5x-3>0 2x^2+6x-x-3>0 2x(x+3)-1(x+3)>0 (2x-1)(x+3)>0 ... x>1/2 OR x>-3 ... m.ananth@hotmail.ca
 Inequalities/380953: 1) The sum of two numbers is 89. Their difference is 13. What are the two numbers? Pls indicate the representation,the equation,solution,checking and the cheking. Thank you!1 solutions Answer 270313 by mananth(12270)   on 2010-12-05 05:04:50 (Show Source): You can put this solution on YOUR website!let the numbers be x & y .. x+y =89 x-y =13 ... add the equations 2x=89+13 2x=102 /2 x=51 .. x+y = 89 x=51 y=89-51 y=38 ... 51 & 38 are the numbers .. m.ananth@hotmail.ca
 Numbers_Word_Problems/380940: find three consecutive even integers such that one fourth of the sum of the first and the third is equal to 22 less than the second1 solutions Answer 270311 by mananth(12270)   on 2010-12-05 05:01:51 (Show Source): You can put this solution on YOUR website!let the consequtive even numbers be n,n+2,n+4 ... 1/4(n+n+4)=n+2-22 1/4(2n+4)=n-20 multiply by 4 2n+4 = 4(n-20) 2n+4 = 4n-80 -4n 2n-4n+4 = -80 -2n+4=-80 -4 -2n=-84 /-2 n=42. n+2 = 44 n+4 = 46 ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/380944: Working with your cousin, you can finish a table in 8 hours. Working alone your cousin can complete the job in 10 hours. How long would it take you to refinish the table working alone?1 solutions Answer 270307 by mananth(12270)   on 2010-12-05 04:20:06 (Show Source): You can put this solution on YOUR website!together they can finish in 8 hours. together they do 1/8 of the job in 1hour. ... cousin takes 10 hours. so cousin does1/10 of the job in 1 hour. ... so you can do 1/8 -1/10 of the job in 1 hour. LCD = 40 (5-4)/40 of the job you can do in 1 hour =1/40 of the job. so you will take 40 hours to do the job ... m.ananth@hotmail.ca
 Problems-with-consecutive-odd-even-integers/380930: Find three consecutive odd positive intergers such that 5 times the sum of all three is 66 more then the product of the first and second intergers.1 solutions Answer 270302 by mananth(12270)   on 2010-12-05 02:22:43 (Show Source): You can put this solution on YOUR website!let the integers be x,x+2,x+4 ... 5(x+x+2+x+4)=x(x+2)+66 5(3x+6)=x^2+2x+66 15x+30=x^2+2x+66 -15x 30=x^2+2x-15x+66 30=x^2-13x+66 -30 0=x^2-13x+36 x^2-9x-4x+36=0 x(x-9)-4(x-9)=0 (x-9)(x-4)=0 x= 9 OR 4. reject 4 x= 9 the numbers are 9,11,13. ... m.ananth@hotmail.ca
 Linear-equations/380909: 3x-2y=9 -6x+4y=1 I need to solve special systems. (& if it is infinitely many, only one, or none. I tried to do substitution. Canceling out one variable I think the answer I got was x=6 and y=18. I am not sure it is right. I look at it and it just seems to long compared to the other problems. 3x-2y=9 -3 -3 x-2y=3 -x+x-2y=3+x -2y=3+x ---------- +2 +2 y =6+x 3x+y=6 3x+(6+x)=6 4x+6 =6 4x+6-6=6-6 4x = 0 Now it does not come out the way I had on paper. I did something wrong. Please help. Thank you.1 solutions Answer 270301 by mananth(12270)   on 2010-12-05 02:15:16 (Show Source): You can put this solution on YOUR website!3x-2y=9...............1 -6x+4y=1..............2 .. you will see that 6x is a multiple of 3x. 3x*2=6x so you can eliminate x by multiplying (1) 2 and add it to (2) 3x*2-2*2y=2*9 6x-4y=18. add this to (2) -6x+6x-4y+4y=18+1 0= 19 .. The system has no solution. As you will see from the grah below. The lines are parallel. .. m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/380914: A metal ball is dropped from the top of the 1450 foot high Sears Tower in Chicago. If the distance the ball falls is directly proportional to the square of the time it is allowed to fall and after 1 second, the ball falls 16 feet, find the formula d(t) for the distance the ball has fallen after t seconds. At what time will the ball hit the ground? The speed s of the ball is given by the formula s(t) = 32t . How fast is the ball traveling when it hits the ground?1 solutions Answer 270299 by mananth(12270)   on 2010-12-05 01:26:05 (Show Source): You can put this solution on YOUR website! ... plug value of t=1 & d=16 to find the value of k 16=k*1^2 k=sqrt16 k=+/-4 ... d=4t^2 1450= 4*t^2 1450/4 =t^2 362.5=t^2 t=sqrt362.5 t = 19 .03 seconds ... s(t)=32t s(19)= 32*19 s19)= 608 ft/s ... m.ananth@hotmail.ca
 Money_Word_Problems/380318: Please write equation for problem and solve A friend deposits a total of \$6,000 in two accounts, paying 3% interest and 4% interest respectively. If at the end of the first year the interest earned was \$220, how much money was deposited in each account?1 solutions Answer 270111 by mananth(12270)   on 2010-12-04 04:30:33 (Show Source): You can put this solution on YOUR website!\$x @ 3 % 6000-\$x 4% .. total interest= \$220 ... 0.03x+0.04(6000-x)=220 multiply by 100 3x+4(6000-x)=220*100 3x+24000-4x=22,000 -x=-2000 x=2000 ... \$2000 @ 3 % \$4000@4% ... m.ananth@hotmail.ca
 Linear-equations/380516: Graph the ineqaulity x - 2y is less than or equal to 01 solutions Answer 270110 by mananth(12270)   on 2010-12-04 04:24:45 (Show Source): You can put this solution on YOUR website!x-2y<=0 -x -2y<=-x /-2 y>=x/2 ... the boundary ... y>=x/2 ... m.ananth@hotmail.ca
 Rectangles/380527: find the dimensions of a rectangular lot whose perimeter is 40 meters and whose area is 96 square meters. 1 solutions Answer 270109 by mananth(12270)   on 2010-12-04 04:20:14 (Show Source): You can put this solution on YOUR website!Perimeter P= 40 2*(l+w)=40 /2 l+w = 20 .. Area = 96 l*w=96 w=96/l .. plug value of w in l+w=20 96/l+l=20 (96+l^2)/l=20 96+l^2=20l l^2-20l+96=0 l^2-12l-8l+96=0 l(l-12)-8(l-12)=0 (l-12)(l-8)=0 l=12 Or 8 .. the dimensions are 12 m by 8 m ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/380528: The perimeter of a swimming pool is 91m. The width is 5m more than half the length of the pool. Find the length and width of the pool.1 solutions Answer 270108 by mananth(12270)   on 2010-12-04 04:12:52 (Show Source): You can put this solution on YOUR website!let length be x m width = x/2 +5 m ... Perimeter = 2(l+w) 2*(x+x/2+5)= 91 2x+x+10=91 3x+10=91 -10 3x=91-10 3x=81 /3 x=27 m ... the length ... width = x/2 +5 =27/2 + 5 =13.5 +5 =18.5 m the width ... CHECK 2*(18.5+27)=91 ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/380529: An aluminum plate is made according to the following dimensions. The outer radius is 8 inches and the inner radius is 4 inches. (See diagram below) Use π = 3.14 as an approximate value. (a) How many square inches in area is the aluminum plate (the shaded region)? (b) If the cost to construct the plate is \$6.50 per square inch, what is the construction cost? (Area = ∏ r2 ).1 solutions Answer 270107 by mananth(12270)   on 2010-12-04 04:08:28 (Show Source): You can put this solution on YOUR website!The area of shaded portion = area of larger circle - area of smaller circle. larger circle radius = 8 " Area = pi*8*8 area = 64 pi ... Area of inner circle = pi*4*4 area = 16pi .. difference = 64pi-16pi =48pi =48*3.14 =150.72 in^2 is the shaded area .. 1 in^2 = \$6.50 150.72in^2= 150.72*6.50 =\$ 979.68 is the cost ... m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/380522: The sum of two numbers is -12.43 and their difference is 117.77 (I tried adding two negative numbers to equal -12.43, but nothing large enough to have a difference of 117.77.1 solutions Answer 270102 by mananth(12270)   on 2010-12-04 02:06:53 (Show Source): You can put this solution on YOUR website!x+y = -12.43 ... x-y = 117.77 .. add the two equations 2x=105.34 /2 x=52.67 ... plug value of x in first equation 52.67+y=-12.43 -52.67 y=-12.43-52.67 y = -65.10 ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/380512: I need to factor 12x^2 - 5x -31 solutions Answer 270100 by mananth(12270)   on 2010-12-04 02:01:02 (Show Source): You can put this solution on YOUR website!12x^2 - 5x -3 ... 12x^-9x+4x-3 3x(4x-3)+1(4x-3) (4x-3)(3x+1) ... m.ananth@hotmail.ca
 Travel_Word_Problems/380514: d/550 + 2900-d/600 = 5 I am having trouble getting a LCD. I know that distance is 1100, but I dont know how to make it come out right1 solutions Answer 270094 by mananth(12270)   on 2010-12-04 01:30:52 (Show Source): You can put this solution on YOUR website!d/550 + (2900-d)/600 = 5 multiply by 50 50d/550 + (2900-d)*50/600 = 5*50 .. d/11 +(2990-d)/12= 250 ... LCD = 132 (12d+11(2900-d))/132=250 12d+31900-11d=132*250 d=132*250-31900 d= 1,100 ... m.ananth@hotmail.ca
 Evaluation_Word_Problems/380380: okay so i need help with solving this: Tim and Mary paddled a canoe 6 miles upstream in 4 hours.The trip back took 3hours.Find the rate at which they paddled in still water??1 solutions Answer 270083 by mananth(12270)   on 2010-12-04 00:42:02 (Show Source): You can put this solution on YOUR website!Tim and Mary paddled a canoe 6 miles upstream in 4 hours.The trip back took 3hours.Find the rate at which they paddled in still water?? ... distance = 6 miles time upstream = 4 hours .. speed upstream = 6/4 = 3/2 mph= 1.5 mph ... speed downstream = 6/3 = 2 mph ... (3/2+2)/2 (7/2) /2 7/2 *1/2 = 7/4 =1.75 mph speed in still water 0.25 mph = speed of current. ... m.ananth@hotmail.ca
 Numeric_Fractions/380496: solve for c. 1945.4°=9/5c + 321 solutions Answer 270078 by mananth(12270)   on 2010-12-04 00:21:52 (Show Source): You can put this solution on YOUR website!1945.4°=9/5c + 32 ... -32 1945.4-32=9/5 *c 1913.4=9/5*c multiply by 5 5*1913.4=9c /9 5*1913.4/9 =c c=1063 ... m.ananth@hotmail.ca
 Numeric_Fractions/380494: solve for x x + 0.20x = 987 1 solutions Answer 270077 by mananth(12270)   on 2010-12-04 00:12:54 (Show Source): You can put this solution on YOUR website!x + 0.20x = 987 multiply by 10 10x+2x=9870 12x=9870 /12 12x/12=9870/12 x=822.50 ... m.ananth@hotmail.ca
 Rational-functions/380493: find the equation of the line satisfying the given conditions , giving it in slope intercept form if possible Through(9,5) , Parallel to -7x + 6y = -57 Im confused , please help 1 solutions Answer 270076 by mananth(12270)   on 2010-12-04 00:08:23 (Show Source): You can put this solution on YOUR website!Through(9,5) , Parallel to -7x + 6y = -57 write the equation in slope intercept form +7x 6y=7x-57 /6 y=(7/6)x-(57/6) .. slope = 7/6 .. the slope of line parallel to this line will be the same. so m= 7/6 Point(9,5) Find b in y = mx+b 5=7/6 *9 +b 5=21/2+b b=5-21/2 b=-11/2 ... the equation will be y=(7/6)x-11/2 ... Check with graph ... m.ananth@hotmail.ca
 Human-and-algebraic-language/380382: * Sammy can complete a programming job in 8 hours if he works alone. * Marilyn can complete the same programming job in 12 hours if she works alone. If Sammy and Marilyn work together, how many hours and minutes will they complete the job?1 solutions Answer 270075 by mananth(12270)   on 2010-12-03 23:58:47 (Show Source): You can put this solution on YOUR website! Sammy can complete a programming job in 8 hours if he works alone. So he does 1/8 of the job in 1 hour .. Marilyn can complete the same programming job in 12 hours if she works alone Marilyn can do 1/12 of the job in 1 hour. ... Together they can do 1/8 +1/2 of the job in 1 hour =(3+2)/24 =5/24 of the job in 1 hour .. so they will take 24/5 hours to do the job =4.8 hours =4hours +0.8*60minutes =4hours +48 minutes ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/380455: Solve and check the equation using factoring: 49p^2-112p+64=01 solutions Answer 270074 by mananth(12270)   on 2010-12-03 23:53:39 (Show Source): You can put this solution on YOUR website!49p^2-112p+64=0 ... (7p)^2-2*7p*8+(8)^2=0 ... (7p-8)^2=0 ... take the square root 7p-8=0 +8 7p=8 p=8/7 ... 49(8/7)^2-112*(-8/7)+64=0 64-128+64=0 ... m.ananth@hotmail.ca
 Word_Problems_With_Coins/380397: I have 30 coins, all nickels, dimes, and quarters, worth \$4.60. There are two more dimes than quarters. How many of each kind of coin do I have.1 solutions Answer 270073 by mananth(12270)   on 2010-12-03 23:45:04 (Show Source): You can put this solution on YOUR website!I have 30 coins, all nickels, dimes, and quarters, worth \$4.60. There are two more dimes than quarters. How many of each kind of coin do I have. .. let quarters be x dimes = x+2 ... dimes + quarters = x+x+2=2x+2 ... nickels = 30-(2x+2) ... 5(30-(2x+2))+10(x+2)+25x=460 5(30-2x-2)+10x+20+25x=460 150-10x-10+10x+20+25x=460 160+25x=460 -160 25x=460-160 25x=300 /25 x=300/25 x=12 ---- quarters x+2= 12+2=14 dimes 30-(2x+2)=4 nickels ... check 4*5+14*10+12*25=20+140+300=460 ... m.ananth@hotmail.ca
 Geometry_Word_Problems/380483: total revenue is the total amount of money taken in by a business. an appliance firm determines that when it sells x washing machines the total revenue, R, in dollars, is given by the polynomial R=239.46x-0.1x^2. what is the total revenue from the sale of 165 washers 1 solutions Answer 270072 by mananth(12270)   on 2010-12-03 23:33:28 (Show Source): You can put this solution on YOUR website!R=239.46x-0.1x^2 .. x= 165 plug value of 165 R=(239.46*165)-(0.1*(165)^2) R= \$36,788.40 ... m.ananth@hotmail.ca