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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.
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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
Becca
1 solutions
Answer 238996 by mananth(12270) on 2010-08-21 06:12:41 (Show Source):
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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
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Functions/333423: Solve by the elimination method:
7r-9s=-35
9r+7s=85
1 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
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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/h
1 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
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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
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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
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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
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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.ph
1 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
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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
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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
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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
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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
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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
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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):
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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
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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.
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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
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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):
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