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# Recent problems solved by 'mananth'

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 Linear-equations/333725: Let C = Celsius degree and F= Fahrenheit degree scales for temperature. Assuming that relation between C and F is linear and drawing F on vertical axis. Two data points on the line relating C and F are (5, 41), (25, 77) Find the equation relating C and F. Can it be applied for practical purposes?1 solutions Answer 239145 by mananth(12270)   on 2010-08-22 02:14:02 (Show Source): You can put this solution on YOUR website!(5, 41), (25, 77) the slope of the line passing through the above points = 77-41 / 25-5 =36/20 =9/5 = m the slope .. general equation of line = y = mx +b plug value of any point and the slope m in the equation (5,41) 41=9/5 *5 +b 41=9+b 41-9=b b=32 .. so the general equation will be y = 9/5 x + 32 f is drawn on they axis and c on the x axis f= 9/5 c + 32 .. Plot the points and join the points to get a graph as given below.
 Percentage-and-ratio-word-problems/333553: What is 1.35% of 50,000.00 what will I be left with.1 solutions Answer 239005 by mananth(12270)   on 2010-08-21 10:14:30 (Show Source): You can put this solution on YOUR website!1.35% of 50,000.00 = 1.35/100*50000 =675 .. Balance will be 50,000-675 =49325.00
 Rational-functions/333530: Again I find myself confused when it comes to math. I would appreciate any help that i may be able to get. the instructions are solve the equation: 1/(x+4)-1=1/x If you might be able to show me the steps in completing this type of problem i would appreciate it as i have several to solve in this style. thanks in advance Becca1 solutions Answer 238996 by mananth(12270)   on 2010-08-21 06:12:41 (Show Source): You can put this solution on YOUR website! LCM = x(x+4) .. .. x+2=0 x=-2
 Numbers_Word_Problems/333522: the tens digit of certain number is 3 more than the units digit. the sum of the squares of the two digits is 4 more than the number.find the number.1 solutions Answer 238995 by mananth(12270)   on 2010-08-21 06:01:23 (Show Source): You can put this solution on YOUR website!let number be xy x= y+3 x^2+y^2= 10x+y +4 x^2+y^2-10x-y=4 plug value of x in equation (y+3)^2+y^2-10(y+3)-y=4 y^2+6y+9+y^2-10y-30-y=4 2y^2-5y-25=0 2y^2-10y+5y-25=0 2y(y-5)+5(y-5)=0 (2y+5)(y-5)=0 y=5 if y = 5 x= y+3 = 8 the number is 85
 Polynomials-and-rational-expressions/333528: [2(3x-1)+4]-[7(x+4)-8]1 solutions Answer 238994 by mananth(12270)   on 2010-08-21 05:48:03 (Show Source): You can put this solution on YOUR website![2(3x-1)+4]-[7(x+4)-8] .. [6x-2+4]-[7x+28-8] .. [6x+2-7x-20] .. -x-18 ..
 Functions/333424: Solve: 0.9x+9<_1.7x-81 solutions Answer 238992 by mananth(12270)   on 2010-08-21 02:01:05 (Show Source): You can put this solution on YOUR website! .. add -9 to both sides add -1.7x to both sides divide by -0.8
 Functions/333423: Solve by the elimination method: 7r-9s=-35 9r+7s=851 solutions Answer 238991 by mananth(12270)   on 2010-08-21 01:49:34 (Show Source): You can put this solution on YOUR website!7r-9s=-35 9r+7s=85 .. multiply first equation by -9 and equation2 by 7 -63r+81s=315 63r+49s=595 81s+49s=595+315 130s=910 s= 7 .. plug value of s in first equation 7r-9s=-35 7r-63=-35 7x=28 x= 4
 Mixture_Word_Problems/333417: Jodie bicycles 8 km/h faster than Carlos. In the same time it takes Carlos to bicycle 60 km, Jodie can bicycle 84 km. How fast does each bicyclist travel? Carlos travels ____ km/h Jodie travels ____ km/h1 solutions Answer 238990 by mananth(12270)   on 2010-08-21 01:40:59 (Show Source): You can put this solution on YOUR website!Jodie bicycles 8 km/h faster than Carlos. In the same time it takes Carlos to bicycle 60 km, Jodie can bicycle 84 km. How fast does each bicyclist travel? let Carlos speed at x kmph Jodie speed = x+8 kmph .. Carlos distance = 60 km Jodie distance = 84 km .. Carlos time = 60/x Jodie time = 84/(x+8) .. 60/x = 84/(x+8) 84x=60(x+8) 84x=60x+480 84x-60x=480 24x=480 x= 20 kmph x+8 = 20 +8 = 28 kmph Carlos travels _20___ km/h Jodie travels 28____ km/h
 Expressions-with-variables/333516: solve fo r v sub1: P1V1 over T1 = P2V2 over T21 solutions Answer 238989 by mananth(12270)   on 2010-08-21 01:33:54 (Show Source): You can put this solution on YOUR website! ..
 Equations/333520: 2t^2-5t+2=01 solutions Answer 238988 by mananth(12270)   on 2010-08-21 01:26:23 (Show Source): You can put this solution on YOUR website! either 2t=1 or t= 1/2 OR t=2
 Volume/333519: 1.how much of air is there in a 15feet long and 3 feet dia drum 1 solutions Answer 238987 by mananth(12270)   on 2010-08-21 00:30:39 (Show Source): You can put this solution on YOUR website!15feet long and 3 feet dia drum diameter = 3 feet radius = 1.5 feet .. volume = pi*r^2*l volume = pi*(1.5)^2*15 = 106 cu.feet
 Expressions-with-variables/333517: solve for d1: v1 over v2 = sq root d2 over d1 1 solutions Answer 238986 by mananth(12270)   on 2010-08-21 00:28:01 (Show Source): You can put this solution on YOUR website! Take square of both sides ..
 Equations/333489: What is the slope of a line perpendicular to 3x+2y=7?1 solutions Answer 238985 by mananth(12270)   on 2010-08-21 00:21:33 (Show Source): You can put this solution on YOUR website!3x+2y=7 .. add -3x 3x-3x+2y=7-3x 2y= -3x+7 y -3/2 x +7/2 .. the slope of this line = -3/2 slope of perpendicular line will be negative reciprocal = 2/3
 Expressions-with-variables/333515: solve for a: a+b+c=01 solutions Answer 238982 by mananth(12270)   on 2010-08-21 00:07:14 (Show Source): You can put this solution on YOUR website!a+b+c=0 add -b-c to both sides a+b+c-b-c= -b-c a= -b-c
 Travel_Word_Problems/333490: Two cars depart from the same spot for the same destination. Car A travels 60 mph and Car B travels 65 mph. Car B arrives one hour before Car A. How many miles did each car travel?1 solutions Answer 238981 by mananth(12270)   on 2010-08-21 00:05:55 (Show Source): You can put this solution on YOUR website!Car A travels 60 mph and Car B travels 65 mph. Car B arrives one hour before Car A. .. let distance traveled be x car A time = x/60 car B time x/ 65 .. x/60- x/65 = 1 65x-60x /(60*65)=1 5x= 60*65 x= 60*65/5 x=780 miles
 Polynomials-and-rational-expressions/333501: i have a problem it says to multiply as indicated 3y/6y +3 multiplied by 8y+4/7?1 solutions Answer 238980 by mananth(12270)   on 2010-08-20 23:58:17 (Show Source):
 Graphs/333502: How do you graph this equation - 4x-6y=3 Thank you1 solutions Answer 238977 by mananth(12270)   on 2010-08-20 23:52:29 (Show Source): You can put this solution on YOUR website!4x-6y=3 6y=4x-3 y= 4/6 x -3/6 y=2/3 x -1/2. find y for different values of x (1, 1/6) (-1,-7/6) (2, 5/6) (0,-1/2) ..
 Travel_Word_Problems/333507: I need help with the problem: A car traveled for 1/2 hour at r mi/h , then increased the speed by 10 mi/ and traveled for 1 and 1/2 hours more. how far did the car go ( the answer must be expressed in the form of r ) Thank You ! , Any help is appreciated :)1 solutions Answer 238976 by mananth(12270)   on 2010-08-20 23:43:53 (Show Source): You can put this solution on YOUR website!A car traveled for 1/2 hour at r mi/h , then increased the speed by 10 mi/ and traveled for 1 and 1/2 hours more. how far did the car go ( the answer must be expressed in the form of r ) .. the speed of car was r mph it traveled for half hour. distance traveled = 1/2 *r .. then speed was (r+10)mph time driven = 3/2 hours distance traveled = 3/2 * (r+10) .. Total distance traveled = = = = =miles
 Quadratic_Equations/333508: The difference of the present ages of two brothers is 4 years,5years ago,if the product of their ages was 96,find their ages.1 solutions Answer 238975 by mananth(12270)   on 2010-08-20 23:34:19 (Show Source): You can put this solution on YOUR website!let elder brother's age be x the youger brother's age be y .. x-y=4 x=y+4 .. five years ago they were x-5 & y-5 .. (x-5)(y-5)=96 xy-5x-5y+25=96 xy-5x-5y=96-25 xy-5x-5y=71 plug the value of x (y+4)y-5(y+4)-5y=71 y^2+4y -5y-20-5y=71 y^2-6y-91=0 y^2-13y+7y-91=0 y(y-13)+7(y-13)=0 (y-13)(y+7)=0 y =13 ignore negative value. x=y+4 x=13+14=17 The ages are 13 , 17 years CHECK (17-5)(13-5)=96
 Angles/333509: Find the measure of angle B if seven times the complement of angle B exceeds twice the supplement of angle B by 220. edna_albaracin@yahoo.com.ph1 solutions Answer 238974 by mananth(12270)   on 2010-08-20 23:19:58 (Show Source): You can put this solution on YOUR website!let the measure of angle B be x deg the complement will be 90-x 7 time scomplement = 7*(90-x) .. The supplement will be 180-x twice the supplement =2*(180-x) .. 7*(90-x)-2*(180-x)=220 630-7x-360+2x=220 -5x= 220+360-630 -5x=-50 x= -50/-5 x=10 deg
 Linear-equations/333505: application of linear equations Andrew invested a total of Php18,000, part at 5% and part at 9%. If his income for one year from the 9% investment was Php100 less than his income from the 5% investment, how much was invested at each rate?1 solutions Answer 238972 by mananth(12270)   on 2010-08-20 23:10:36 (Show Source): You can put this solution on YOUR website!Andrew invested a total of 18,000, part at 5% . Let this investment be x interest = 0.05x .. part at 9%. this will be 18000-x interest will be (18000-x )*0.09 .. interest from the 9% investment was Php100 less than his income from the 5% .. income from 5% - income from 9% = 100 .. 0.05x - 0.09(18000-x)= 100 0.05x-1620+0.09x=100 0.14x=1620+100 0.14x=1720 x= 1720/0.14 = Php 12,286 .. investment at 9% will be 18000-12286 = Php 5,714 CHECK(0.05*12286) - 0.09(18000-12286)=100
 Mixture_Word_Problems/333345: A chemist has 35% NaCl solution and 50% NaCl solution. How many liters of each should he mix to get 10L of NaCl solution with 40% base concentration?1 solutions Answer 238857 by mananth(12270)   on 2010-08-20 07:48:51 (Show Source): You can put this solution on YOUR website!35% NaCl solution let this be x L 50% NaCl solution. this will be 10-x mix to get 40% 10 L .. 0.35x+0.5(10-x)=0.4*10 0.35x+5-0.5x=4 -0.15x=-1 x=-1/0.15 = 6.66 L 35% solution Balance 3.34 L will be 50% solution CHECK 6.66*35+3.34*50 = 40*10
 Equations/333264: Solve for x and y (2x/3) - (3y/4) = (11/12) and (x/3) + (7y/18) = (1/2) 1 solutions Answer 238852 by mananth(12270)   on 2010-08-20 07:37:06 (Show Source): You can put this solution on YOUR website!(2x/3) - (3y/4) = (11/12) LCM is 12 (4*2x-3*3y) /12 = 11/12 ()8x-9y /12 = 11/12 multiply by 12 8x-9y=11..........................1 (x/3) + (7y/18) = (1/2) LCM =18 (6*x+7y) /18 = 1/2 6x+7y= 18/2 6x+7y=9............................2 .. multiply equation 1 by 7 and equation 2 by 9 and add them to eliminate y 56x-63y+54x+63y=77+81 110x=158 x= 158/110 x=79/55 .. plug value of x in equation 2 6*79/55 +7y=9 474+385y=9*55 385y=495-474 385y=21 y= 21/385 y= 3/55
 Divisibility_and_Prime_Numbers/333329: If the sum of the integers n and n + 1 is greater than 99 and less than 109, what is the only possible prime value of n? 1 solutions Answer 238846 by mananth(12270)   on 2010-08-20 05:31:08 (Show Source): You can put this solution on YOUR website!n+n+1= 2n+1 99<2n+1<109 add-1 99-1<2n<109-1 98<2n<108 divide by 2 98/2 49 .. prime number = 53
 Numbers_Word_Problems/333339: Find four consective intergers if the sum of the second and fourth is 48.1 solutions Answer 238845 by mananth(12270)   on 2010-08-20 05:18:56 (Show Source): You can put this solution on YOUR website!let the consequtive integers be x,x+1,x+2,x+3 x+1+x+3=48 2x+4 = 48 add -4 2x+4-4=48-4 2x=44 divide by 2 x= 22 .. the numbers are 22,23,24,25
 Graphs/333220: Two angles are complimentary The sum of the measure of the first angle and one-fourth the second angle is 88.50. Find the measures of the angles.1 solutions Answer 238837 by mananth(12270)   on 2010-08-20 03:21:18 (Show Source): You can put this solution on YOUR website!let one angle be x the other will be 90-x .. x+1/4(90-x)=88.5 4x+90-x / 4 =88.5 3x+90=4*88.5 3x+90=354 3x=354-90 3x=264 x=264/3 x=88 deg the other angle = 2 deg
 Linear-equations/333326: If the problems asks to rewrite the equation without parentheses and simplify it, the equation (6v+3)^2, should I answer 4v^2+4v+1 or 36v^2+36v+9? 1 solutions Answer 238836 by mananth(12270)   on 2010-08-20 03:15:50 (Show Source): You can put this solution on YOUR website!36v^2+36v+9
 Linear_Equations_And_Systems_Word_Problems/333291: coin bank contains twice as many nickels as dimes and five times as many pennies as dimes. the value of the connection is \$2.00 . how many pennies nickles and dimes are in the collection?1 solutions Answer 238835 by mananth(12270)   on 2010-08-20 02:34:25 (Show Source): You can put this solution on YOUR website!let dimes be x nickels will be 2x pennies will be 5x 5x+5*2x+10x=200 5x+10x+10x=200 25x= 200 x= 8 dimes .. pennies = 5x = 40 nickels = 2*8=16 .. CHECK 40+16*5+8*10 =40+80+80 = 200
 Mixture_Word_Problems/333323: A store mixes coffee A worth \$10. per kilogram and coffee B worth \$12. per kilogram. The mixture is to sell for \$11. per kilogram. Find how much should be used to make a 480 kilogram mixture. How many kilograms of coffee A should be in the mix? How many kilograms of coffee B should be in the mix?1 solutions Answer 238834 by mananth(12270)   on 2010-08-20 02:25:59 (Show Source): You can put this solution on YOUR website!coffee A worth \$10. per kilogram coffee B worth \$12. per kilogram. mixture is to sell for \$11. per kilogram. 480 kilogram mixture. ... coffee A quantity be x kg \$10 coffee B quantity will be 480-x kg. \$12 Mixture \$11 480 kg .. 10x+12(480-x)= 11*480 10x+5760-12x=5280 -2x=5280-5760 -2x=-480 x= 240 kg Coffee A Coffee B = 240 kgs.
 Travel_Word_Problems/333295: One plane took off from the San Fransisco , traveling east. At the same time another plane took off from the same airport, traveling west. The plane traveling east was going 120 miles per hour faster than the plane traveling west. After three hours, the planes were 2,400 miles apart. How fast was each plane going?1 solutions Answer 238833 by mananth(12270)   on 2010-08-20 02:19:12 (Show Source): You can put this solution on YOUR website! traveling east. speed= 120 miles per hour faster than the plane traveling west. After three hours, the planes were 2,400 miles apart. How fast was each let speed of west bound plane be x mph east bound plane speed will be x-120 mph .. distance = speed * time time = 3hours distance traveled by one plane = 3x distance by other plane = (x-120)*3 .. 3x+3(x-120)=2400 3x+3x-360=2400 6x=2760 x=460 speed of west bound plane. East bound plane speed =460-120= 340 mph CHECK effective speed = 340+460 = 800 mph distance = 2400 miles time = distance / speed = 2400/800 = 3 hours
 Linear-equations/333321: This is a silly question, but I'm in doubt for trying to resolve (6v+3)(6v+3). I found it 6v^2+36v+9. Can I simplify this dividing by 3, to 2v^2+12v+3?1 solutions Answer 238832 by mananth(12270)   on 2010-08-20 02:08:53 (Show Source): You can put this solution on YOUR website!(6v+3)(6v+3) = 36v^2+36v+9 ( it is not 6v^2) =9(4v^2+4v+1) =9(2v+1)^2