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# Recent problems solved by 'mananth'

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 Polynomials-and-rational-expressions/337521: 5x^2-8x-41 solutions Answer 241910 by mananth(12269)   on 2010-08-31 22:46:38 (Show Source): You can put this solution on YOUR website!5x^2-8x-4 5x^2-10x+2x-4 5x(x-2)+2(x-4) (5x+2)(x+2)
 Polynomials-and-rational-expressions/337522: 12x^2-5x-31 solutions Answer 241906 by mananth(12269)   on 2010-08-31 22:44:04 (Show Source): You can put this solution on YOUR website!12x^-5x-3 12x^-9x+4x-3 3x(4x-3)+1(4x-3) (4x-3)(3x+1)
 Numbers_Word_Problems/337450: I'm a 2 digit number. If you reverse my digits and add us together, the result is 110. Find as many correct answers as possible. 1 solutions Answer 241841 by mananth(12269)   on 2010-08-31 20:50:03 (Show Source): You can put this solution on YOUR website!let the digits be x , y 10x +y is the number 10x+y+10y+x=110 11x+11y=110 divie by 11 x+y= 10 .. pair values of x & y to add to 10 like 19,28,37,46, 55,64 73,82,91
 Polynomials-and-rational-expressions/337445: Factor: 6r^2t+7rt+t^21 solutions Answer 241838 by mananth(12269)   on 2010-08-31 20:44:12 (Show Source): You can put this solution on YOUR website!6r^2t+7rt+t^2 t(6r^2+7r+t) t(6r^2+6r+r+t) t((6r(r+1)+1(r+1)) t((6r+1)(r+1)
 Angles/337443: The measure of an angle is 28 degrees more than its complement. Find the measure of each angle.1 solutions Answer 241837 by mananth(12269)   on 2010-08-31 20:41:03 (Show Source): You can put this solution on YOUR website!let angle be x complement = 90-x x=(90-x)+28 x=90-x+28 add x to both sides x+x=90-28 2x=62 x= 62/2 x=31 deg
 Miscellaneous_Word_Problems/337440: Casey and Chris want to design an open topped box having a square base and a surface area of 108 square inches. What dimensions would the box of greatest volume have?1 solutions Answer 241835 by mananth(12269)   on 2010-08-31 20:38:39 (Show Source): You can put this solution on YOUR website!square box top open so the surface area will be 5 times the area of each face. since the box is open at top only 5 sides. let lebgth be x area of 1 face of the box = x^2 5x^2 = total area. 5x^2=108 x^2= 108/5 x^2= 21.6 take sqrt x= sqrt 21.6 4.65 inches is the side of the box
 Triangles/337436: what is the hypotenuse of a triangle of sides 12 and 15 units1 solutions Answer 241834 by mananth(12269)   on 2010-08-31 20:31:22 (Show Source): You can put this solution on YOUR website!(12)^2+(15)^2 = hypotenuse ^2 144+225 =369 sqrt of 369 = 19.2 hypotenuse = 19.2
 Polynomials-and-rational-expressions/337427: im not understanding how to translate problems into equations. my first problem is: (1)Luke has \$5 more then Sam (2)Together they have \$73 how much money does each have? (1)there were 12 people on the jury (2)there were 4 more men then women how many men where there? (1)lee bycycled 3km farther than wing (2)the sum of the distances they biked was 25km how far did each bicyclist go?1 solutions Answer 241833 by mananth(12269)   on 2010-08-31 20:28:13 (Show Source): You can put this solution on YOUR website!(1)Luke has \$5 more then Sam if sam has \$x luke = x+5 (2)Together they have \$73 x+x+5 =73 2x+5=73 add -5 to both sides 2x+5-5=73-5 2x=68 divide by 2 2x/2 = 68/2 x= 34 Sam has \$34 Luke has x+5 = 34+5=39 how much money does each have? (1)there were 12 people on the jury (2)there were 4 more men then women how many men where there? let women be x men = x+4 x+x+4=12 2x+4 =12 2x=8 x=4 women (1)lee bycycled 3km farther than wing (2)the sum of the distances they biked was 25km how far did each bicyclist go? wing bikes x km lee bikes x+3 km x+x+3=25 2x+3 = 25-3 add -3 2x=22 divide by 2 x=11 wing lee = 14 km
 Unit_Conversion_Word_Problems/337426: A 100mL graduated cylinder is filled with water several times and poured into a container. When the container is completely filled, the weight of water in the container is 4.4 pounds. How many times was the graduated cylinder emptied into the container?1 solutions Answer 241832 by mananth(12269)   on 2010-08-31 20:16:29 (Show Source): You can put this solution on YOUR website!2.2 pounds = 1 kg. 4.4 pounds = 2 kgs. 2kgs = 2 liters = 2000 ml of water .. 1 measure 100ml 2000 ml = 2000/100 = 20 times
 Unit_Conversion_Word_Problems/337424: A patient needs 0.032 grams of a drug. The stock on hand is in 8mg tablets. How many tablets should be given?1 solutions Answer 241831 by mananth(12269)   on 2010-08-31 20:12:01 (Show Source): You can put this solution on YOUR website!0.032 gms 1 gm = 1000 mg 0.032 * 1000 = 32 mg .. 1 tablet 8 mg 32/8 = 4 tablets
 Geometry_Word_Problems/337421: Leonardo of Pisa (about 1175–1258), also known as Fibonacci (fee buh NAH chee), was born in Italy and educated in North Africa. He was one of the first Europeans known to use modern numerals instead of Roman numerals.The special sequence 1, 1, 2, 3, 5, 8, 13, . . . is known as the Fibonacci sequence. Find the next three terms of this sequence.1 solutions Answer 241830 by mananth(12269)   on 2010-08-31 20:08:56 (Show Source): You can put this solution on YOUR website!1, 1, 2, 3, 5, 8, 13, 21, 34,55,89
 Quadratic_Equations/337017: Use the quadratic formula to determine the x-intercepts (if any) of the following function. Then evaluate the function for several values of x, and use the resulting points to graph the function. f(x) = -2x^2 + 2x - 91 solutions Answer 241576 by mananth(12269)   on 2010-08-31 05:59:06 (Show Source): You can put this solution on YOUR website! -2x^2+2x-9 a= -2, b=2 , c=-9 .. x1= (-2+sqrt(4-72))/2*-2 x1=(-2+sqrt(-68)))/-4 x1=0.5 +sqrt(-68)/4 x2=0.5-sqrt(-68)/4 No x intercepts Plot values for x you will get a graph as below
 Rectangles/337047: can anyone help me to find this answer?? a production editor at a textbook publishing house decided that the pages of abook should have 1-inch margins at the top and bottom and 0.5-inch margins on the side. she further stipulated that the length of a page should be 1.5 times its width and have a printed area of exactly 51 square inches.find the dimensions of a page of the book thank you...1 solutions Answer 241574 by mananth(12269)   on 2010-08-31 05:45:49 (Show Source): You can put this solution on YOUR website!let the width be x the length will be 1.5x .. Side Margin = 0.5 inch. 1 " total Top margin 1 " bottom 1" = 2 inches. Printing area = (x-1)(1.5x-2)=51 1.5x^2-2x-1.5x+2=51 1.5x^2-3.5x+2=51 multiply by 2 3x^2-7x+4=102 3x^2-7x-98=0 3x^2-21+14x-98=0 3x(x-7)+14(x-7)=0 (x-7)(3x+14) x= 7 ignore -14/3 printing dimensions = 7" & 10.5 "
 Problems-with-consecutive-odd-even-integers/337064: If a is an even integer and b is an odd integer, which of the following must be even? (A) ab + 1 (B) a^2 + 3 (C) a^2 + b^2 (D) a^2b^2 +1 (E) b^2 + 3 1 solutions Answer 241573 by mananth(12269)   on 2010-08-31 05:19:23 (Show Source): You can put this solution on YOUR website!E b^2 +3
 Age_Word_Problems/337066: Hi, can I please have your help with the following worded equation? James is twice as old as Andy. Twelves years ago, James was three times as old. How old are they now? I just need help getting it into an equation Thank you Sally1 solutions Answer 241572 by mananth(12269)   on 2010-08-31 05:17:09 (Show Source): You can put this solution on YOUR website!Andy age = x years James = 2x .. 12 years ago their ages were andy x-12 James 2x-12 .. 2x-12= 3(x-12) 2x-12 = 3x -36 add 12 2x-12+12 = 3x-36+12 2x= 3x-24 add -3x 2x-3x= -3x+3x-24 -x = -24 divide by 1 x=24 Andy's age James age = 48
 Mixture_Word_Problems/337048: A hospital needs to dilutea 60% boric acid solution to a 10% solution. If it needs 40 liters of the 10% solution, how much of the 60% solution and how much water should it use?1 solutions Answer 241570 by mananth(12269)   on 2010-08-31 02:43:03 (Show Source): You can put this solution on YOUR website!60% boric acid solution x liters water 40-x liters 10% solution. 40 liters .. 0.6x +0 = 0.1*40 0.6x=4 divide by 0.6 x= 4/0.6 x= 6.66 liters 40-6.66 = 33.34 liters of water
 Mixture_Word_Problems/337054: How much 20% antifreeze solution must be added to 20 liters of 50% antifreeze solution to reduce it to 40% antifreeze?1 solutions Answer 241569 by mananth(12269)   on 2010-08-31 02:34:48 (Show Source): You can put this solution on YOUR website!20% antifreeze solution x liters 20 liters of 50% antifreeze solution 40% antifreeze 20 + x liters .. 0.2x+0.5*20=0.4(20+x) 0.2x+10=8 +0.4x add -0.2x 0.2x-0.2x+10=0.4x-0.2x+8 10=0.2x+8 add -8 10-8 = 0.2x +8-8 2=0.2x divide by 0.2 10=x 10 liters
 Problems-with-consecutive-odd-even-integers/337059: Four times the smallest of three consecutive even integers is ten more than three times the largest integer. Find the integers?1 solutions Answer 241568 by mananth(12269)   on 2010-08-31 02:29:07 (Show Source): You can put this solution on YOUR website!let the integers be x,x+2,x+4 4x = 3(x+4)+10 4x=3x+12+10 4x=3x+22 add -3x 4x-3x=22 x=22 22,24,26
 Travel_Word_Problems/337057: Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 miles per hour and B is traveling at 70 miles per hour. Train A passes the station at 3:15pm. If Train B passes the station at 3:27, what time will Train B catch up to Train A?1 solutions Answer 241567 by mananth(12269)   on 2010-08-31 02:25:52 (Show Source): You can put this solution on YOUR website!let train B meet train A at x miles distance during that time train A travels x-12 miles because it was 12 minutes early at the station. In12 minutes it travels 12 miles. ( 60 mph) x/70 = x-12/60 60x= 70(x-12) 60x= 70x-840 add 840 to both sides 60x+840=70x+840-840 60x+840 =70x add -60x 60x-60x+840 = 70x -60x 10x =840 divide by 10 x= 84 .. train B speed = 70 mph distance = 84 miles time taken = 84/70 =1.2 hours 1 hour 12 minutes train B will catch up with train A at 4:39 pm
 Length-and-distance/337053: an angle is measured at 2.3 radians. a) what is its measure in degrees, minutes and seconds ( to the nearest second)? b) what is its tangent? 1 solutions Answer 241566 by mananth(12269)   on 2010-08-31 01:54:14 (Show Source): You can put this solution on YOUR website!2.3 radians pi radians = 180 degrees. 1 radian = 180/pi 2.3 radians = 2.3 * 180 /pi =131 .78 degrees 0.78 degrees = 0.78*60 = 4. 68 minutes 0.68 minutes = 0.68*60 = 40.8 seconds .. 2.3rad = 131( deg ) 4 (min) 40.8 (sec)
 Miscellaneous_Word_Problems/337043: This is one of our 4th graders math problems. My husband and I are usually good about helping him but for some reason this just confused us. Thanks for your help. He does have to show his work on his paper. Thank you again. Each Morning Jarilyn runs a total distance of 42 city blocks and always chooses a rectangular running path. This morning her rectangular path was twice as long as it was wide. How many blocks long and how many blocks wide was this mornings rectangular path?1 solutions Answer 241561 by mananth(12269)   on 2010-08-30 23:44:03 (Show Source): You can put this solution on YOUR website!Each Morning Jarilyn runs a total distance of 42 city blocks and always chooses a rectangular running path. This morning her rectangular path was twice as long as it was wide. How many blocks long and how many blocks wide was this mornings rectangular path? .. Let width of area covering 42 blocks be x length = 2*x = 2x. .. He runs round the 42 blocks in rectangular path. Perimeter = 42 blocks Perimeter P = 2*(L+W) 2*(x+2x)=42 2*3x=42 6x=42 divide by 6 6x/6 = 42/6 x= 7 blocks width length = 2*x = 2*7 =14 blocks .. CHECK 7+7+14+14==42 Blocks
 Travel_Word_Problems/337035: Two cars traveling in the same direction leave the same point at the same time. Car 1 is going 65 km/h and Car 2 is going 55 km/h. How far must Car 1 travel before it has a 15 min. lead on Car 2.1 solutions Answer 241557 by mananth(12269)   on 2010-08-30 23:34:18 (Show Source): You can put this solution on YOUR website!since the cars are travelling in same direction Car 1 gains 10 km every hour. in 1/4 hour it will gain 10/(1/4)= 2.5 km. .. Let car 1 travel x km at speed of 65 km/h car2 will travel x-2.5 km in the same time .. time = distance /speed .. x/65 = (x-2.5)/55 55x=65(x-2.5) 55x=65x-162.5 add -65x 55x-65x=65x-65x-162.5 -10x=-162.5 divide by -10 x= -162.5/-10 x=16.25 km. the distance car 1 has to travel to be 15 minutes ahead.
 expressions/337027: my expression is.... 4+5(x-7)^3, for x=9 i have the answer but i can't seem to figure it out myself! it's not the only one either but i guess i just don't know how to use parenthesis and exponents together. help??? thank you1 solutions Answer 241552 by mananth(12269)   on 2010-08-30 23:03:38 (Show Source): You can put this solution on YOUR website!4+5(x-7)^3, for x=9 4+5(x-7)^3, plug the value of x in the term. 4+5(9-7)^3 4+5(2)^3 4+(5*8) 4+40 44
 test/337032: A company has 160 employee. The number of part-time is 7:9 to the number of full-time. How many ea do they employ?1 solutions Answer 241551 by mananth(12269)   on 2010-08-30 22:58:55 (Show Source): You can put this solution on YOUR website!employees = 160 ratio = 7/9 .. total parts = 7+9 =16 7/16 are part time Balance = full time 160-70 = 90
 Equations/337029: Translate each sentence to an equation. 1.The quotient of g and h is the same as seven more than twice the sum of g and h. 2. The quotient of t and forty is the same as twelve minus half of s. 3. The square of m minus the cube of n is sixteen. 4. Two times z is equal to two times the sum of v and w.1 solutions Answer 241550 by mananth(12269)   on 2010-08-30 22:54:22 (Show Source): You can put this solution on YOUR website!1.The quotient of g and h is the same as seven more than twice the sum of g and h. 2. The quotient of t and forty is the same as twelve minus half of s. 3. The square of m minus the cube of n is sixteen. 4. Two times z is equal to two times the sum of v and w.
 Travel_Word_Problems/336979: You and a friend each drive 50.0 km. You travel at 83.0 km/h; your friend travels at 92.0 km/h. How long will your friend wait for you at the end of the trip? 1 solutions Answer 241526 by mananth(12269)   on 2010-08-30 21:08:02 (Show Source): You can put this solution on YOUR website! Time = Distance / speed time taken by me = 50km speed = 83 km/h time = 50/83 hours = 0.60 hours .. Friend 's speed = 92km/h time = 50 /92 = 0.54 hours. Time he has to wait = 0.6 - 0.54 =0.06 hours = 0.06 * 60 = 3.6 minutes
 Travel_Word_Problems/336980: Sally can jog at a rate of 6.5 miles per hour. If she continues on a straight path at this rate, what distance would she travel in 24 minutes?1 solutions Answer 241525 by mananth(12269)   on 2010-08-30 21:00:25 (Show Source): You can put this solution on YOUR website!24 minutes = 24/60 hours = 0.4 hours speed = 6.5 mph time =0.4 hours Distance = speed * time =6.5*0.4 =2.6 miles
 Polynomials-and-rational-expressions/336981: Hi, my name is Whitney and I have the answer to my math question, I just can't figure out how to get there. Here's the problem: I understand that I need to find the least common denominator so I multiply (4)/(3-x) by (x-3)/(x-3) and (2x)/(x-3) by (3-x)/(3-x), after that, I am missing something. I end up with 2(5x-6-x^2)/(3-x)(x-3) and I don't see any way to factor it further. I am clearly wrong since the answer is suppose to be 2(x-2)/(x-3). Any help and explanation of what I'm not getting would be very appreciated. 1 solutions Answer 241521 by mananth(12269)   on 2010-08-30 20:56:17 (Show Source): You can put this solution on YOUR website! LCD = (x-3) ..
 Money_Word_Problems/336943: An insurance agent receives a 12% fee on each new policy payment and a 3% fee on each renewal payment. If the agent received \$1350 fee on total payments of \$26250, how much were the payments for new policies and renewal payments?1 solutions Answer 241518 by mananth(12269)   on 2010-08-30 20:48:59 (Show Source): You can put this solution on YOUR website!Let \$ x be the new policies \$26250 -x will be the renewals. .. 12% on new 3 % on renewal. Amount received = \$1350 .. 0.12x+0.03(26250-x)= 1350 0.12x+787.5-0.03x = 1350 0.09x = 1350-787.5 0.09x = 562.5 divide by 0.09 x= \$6,250 new policies renewals will be 26250-6250=20,000
 Travel_Word_Problems/336967: Please help show me how to answer this word problem: You ride your bike up a steep mountain road at 5 miles per hour. How far do you go in 3 hours?1 solutions Answer 241510 by mananth(12269)   on 2010-08-30 20:35:17 (Show Source): You can put this solution on YOUR website!In 1 hour you go 5 miles So in 3 hours you go 3*5 =15 miles
 Rectangles/336964: length of a rectangle is 3cm greater then its width. the perimeter is 24 cm. what is the dimensions of the rectangle1 solutions Answer 241508 by mananth(12269)   on 2010-08-30 20:33:43 (Show Source): You can put this solution on YOUR website!width = x length = x+3 perimeter p = 2*(L+W) p=2*(x+x+3) p=2*(2x+3) p=4x+6 4x+6 =24 4x =24-6 4x=18 divide by 4 4x/4 = 18/4 x=4.5 cm. width .. Length = x+3 =4.5+3=7.5 cm.