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11430..11459 , 11460..11489 , 11490..11519 , 11520..11549 , 11550..11579 , 11580..11609 , 11610..11639 , 11640..11669 , 11670..11699 , 11700..11729 , 11730..11759 , 11760..11789 , 11790..11819 , 11820..11849 , 11850..11879 , 11880..11909 , 11910..11939 , 11940..11969 , 11970..11999 , 12000..12029 , 12030..12059 , 12060..12089 , 12090..12119 , 12120..12149 , 12150..12179 , 12180..12209 , 12210..12239 , 12240..12269 , 12270..12299, >>NextMiscellaneous_Word_Problems/380158: Gerald and John agreed to start from the same point and go in opposite directions every morning for a jog. If Gerald runs at a speed of 3km/hr ans John has a speed of 4km/hr,in how many hrs. will they be 14 km apart?
1 solutions
Answer 269817 by mananth(12270)   on 2010-12-03 00:57:44 (Show Source):
You can put this solution on YOUR website!Gerald runs at a speed of 3km/hr
John has a speed of 4km/hr,
in how many hrs. will they be 14 km apart
..
they are running in opposite directions
add up speeds
4+3=7 km/hr
..
distance = 14 km
...
t= d/r
t= 14/7
t= 2
After 2 hours they will be 14 km apart
...
m.ananth@hotmail.ca
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Travel_Word_Problems/380152: two cars start from points 420 miles apart and travel toward each other. They meet after 3. 5hours. Find the average speed of each car if one travels 30 mph slower than the other
1 solutions
Answer 269815 by mananth(12270) on 2010-12-03 00:47:50 (Show Source):
You can put this solution on YOUR website!Distance = 420 miles
..
speed of 1 car = x
speed of other car = x-30
...
time they meet = 3.5 hours
...
since they are travelling towards each other add up the speeds
x+x-30= 2x-30
..
t= d/r
3.5=420/(2x-30)
multiply by (2x-30)
3.5(2x-30)=420
7x-105=420
+105
7x=420+105
7x=525
/7
x=75 mph ....speed of one car
speed of other car = 75 -30 = 45 mph
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m.ananth@hotmail.ca
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Mixture_Word_Problems/380155: A chemist needs 12 liters of a 40% alcohol solution. She must mix a 20% solution and a 50% solution. How many liters of each well be required to obtain what she needs?
1 solutions
Answer 269814 by mananth(12270) on 2010-12-03 00:42:01 (Show Source):
You can put this solution on YOUR website!A chemist needs 12 liters of a 40% alcohol solution. She must mix a 20% solution and a 50% solution. How many liters of each well be required to obtain what she needs?
...
20% solution .............x liters
50% solution.............12-x liters
40%.......................12 liters (requirement)
...
I have not converted the percentage to 0.2,0.5,0.4.as generally done.
Even if we convert it, we again multiply by 100 for easy calculation
..
20*x+50*(12-x)=40*12
20x+600-50x=480
20x-50x=480-600
-30x=-120
/-30
x= 4 liters 20% solution
12-x = 8 liters of 50% solution.
...
m.ananth@hotmail.ca
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Graphs/380089: y=3x+2
6x-2y=-4
pick between (3,0),(-3,1),infinitely many solutions, or no solution
1 solutions
Answer 269785 by mananth(12270) on 2010-12-02 22:55:36 (Show Source):
You can put this solution on YOUR website!y=3x+2
.....
6x-2y=-4
/2
3x-y=-2
y=3x+2
..
the equations are of the same line.
so there are infintely many solutions
...
m.ananth@hotmail.ca
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Linear_Equations_And_Systems_Word_Problems/380099: 10. You invested your money in a fixed interest junk bond that earns 8.35% per year interest. How many years with simple interest will it take to double your money?
1 solutions
Answer 269784 by mananth(12270) on 2010-12-02 22:50:57 (Show Source):
You can put this solution on YOUR website!Interest rate = 8.35%
Let principal be $ 100
double your money = $200
So interest = $200-100=$100
n = number of years
...
I= p*r*n
100=100*0.0835*n
n= 100/100 *0.0835
n=1/0.0835
n= 11.97 years
Say 12 years
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m.ananth@hotmail.ca
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Rectangles/380097: The area of a rectangle is 15 square feet. The width can be represented by x - 3.5 and the length by 'x'. What are the dimensions of the rectangle?
I've tried this problem a dozen times. I don't know what it is I'm doing wrong.
1 solutions
Answer 269778 by mananth(12270) on 2010-12-02 22:30:59 (Show Source):
You can put this solution on YOUR website!wid th = x-3.5
length =x
..
Area = l*w
x(x-3.5)=15
x^2-3.5x=15
multiply by 2
2x^2-7x=30
-30
2x^2-7x-30=0
2x^2-12x+5x-30=0
2x(x-6)+5(x-6)=0
(2x+5)(x-6)=0
x= 6 feet, the length
x-3.5
=6-3.5 = 2.5 feet, the width.
...
CHECK
Area = l*w
6*2.5 = 15
..
m.ananth@hotmail.ca
...
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Age_Word_Problems/380072: Sarah is two thirds as old as her cousin. The sum of their ages is 45. How old are Sarah and her cousin?
1 solutions
Answer 269763 by mananth(12270) on 2010-12-02 22:00:22 (Show Source):
You can put this solution on YOUR website!cousin = x years
Sarah = 2x/3 years
..
2x/3 +x = 45
LCD = 3
multiply by 3
2x/3 * 3 +3*x=45*3
2x+3x=135
5x=135
/5
x= 135/5
x=27 years cousins age.
..
Sarah = 2*27/3=18 years
..
m.ananth@hotmail.ca
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Rectangles/380068: Shaunice has 36 feet of fence to put around her rectangular flowerbed. How long and how wide will the flowerbed have to be so that she has 72 square feet of area to plant flowers?
1 solutions
Answer 269760 by mananth(12270) on 2010-12-02 21:55:07 (Show Source):
You can put this solution on YOUR website!let length be l
width be w
..
2(l+w)=36
/2
l+w=18
...
Area = l*w = 72
..
12 & 6 are the factors
..
The dimensiona are 12 feet by 6 feet
...
CHECK
Perimeter = 12+12+6+6=36
area = 12*6 = 72
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m.ananth@hotmail.ca
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Graphs/380070: How do I Solve the inequality: -15<5x<20
(Negative Fifteen is less than or equal to five(x) less than twenty.)
1 solutions
Answer 269757 by mananth(12270) on 2010-12-02 21:48:56 (Show Source):
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Linear-equations/379981: so im working on my homework and the equation is slope intercept and it's so confusing. i tried doing it okay, m=1/4 (-2,-3) than i got y-2=1/4(x--3) so you add two to three than 1/4 times x= 1/4x=14? than i can't figure out how to turn that into slope-intercept form.
1 solutions
Answer 269729 by mananth(12270) on 2010-12-02 20:14:00 (Show Source):
You can put this solution on YOUR website!m=1/4 (-2,-3)
...
you have to write the equation in the form y= mx+b
First you have to find the value of b
..
plug value of m and the point(-2,-3)in the equation
..
-3=(1/4 *-2)+b
-3=-1/2 +b
add 1/2
-3+1/2 =b
-5/2 = b
..
Now form the equation
y = 1/4*x -5/2
OR in decimal form
y = 0.25x-2.5
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m.ananth@hotmail.ca
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Travel_Word_Problems/379974: A boat travels 20 miles upstream in 5hours. Going downstream, it can travel 50 miles in the same amount of time. Find the speed of the current and the speed of the boat in still water.
1 solutions
Answer 269727 by mananth(12270) on 2010-12-02 20:06:25 (Show Source):
You can put this solution on YOUR website!A boat travels 20 miles upstream in 5hours. Going downstream, it can travel 50 miles in the same amount of time. Find the speed of the current and the speed of the boat in still water.
...
speed of boat = x mph
speed of current = y mph
..
speed against current = 4 mph
speed with current = x+y mph
...
time downstream = time upstream
..
t=d/r
..
5=50/(x+y)
5(x+y)=50
/5
x+y =10
x-y=4
add the equations
2x=14
/2
x=7
..
speed in still water = 7 mph
speed of current = 3 mph
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m.ananth@hotmail.ca
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Quadratic_Equations/379966: I have to find the zeros or roots of each function or equation by factoring & graphing.
g(x)= 2x^2 - 25x + 12
2(x ) (x )
I know that the multiples of 12 should add up to -25 but there are none so I do not understand how to find the zeros by factoring
1 solutions
Answer 269717 by mananth(12270) on 2010-12-02 19:55:42 (Show Source):
You can put this solution on YOUR website!g(x)= 2x^2 - 25x + 12
...
it is multiples of 24 and not 12. 2*12
..
2x^2-24x-x+12=0
2x(x-12)-1(x-12)=0
(x-12)(2x-1)=0
x=12 OR 1/2
...
...
m.ananth@hotmail.ca
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Triangles/379565: If the longest side of a triangle is 10 centimeters, does the perimeter have to be bigger than 20 centimeters? I think the triangle perimeter has to be bigger than 20 centimeters because each side would be 10 centimeters and the perimeter would be 30. But my mom says it is possible for a triangle could be equal to 20 centimeters if two sides equal 5 centimeters and the longest side is 10 centimeters. Which is correct? Thank you!
1 solutions
Answer 269500 by mananth(12270) on 2010-12-02 08:27:15 (Show Source):
You can put this solution on YOUR website!If the longest side of the three sides is less than the sum of the other two sides, then a triangle could be formed.
..
you should have sum of other two side greater than 10 then a triangle can be drawn.
sum of the other two sides must be >10.
..
It is not necessary that the triangle perimeter be more than 30 cm
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Exponents/379549: I'm very much stuck on this problem. I'm not sure if this is in the right section, but I hope someone can help.
(2^x)^(x+3)=1/4
If I try to simply this using the rules of exponents, I get..
2^(x^2+3x)=1/4
How can I possibly simplify this since x^2 and 3x are not like terms? I thought about making it a logarithm to make it no longer an exponent, but I still can't figure out how I would solve for x. Please help!
1 solutions
Answer 269471 by mananth(12270) on 2010-12-02 06:21:32 (Show Source):
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Linear_Equations_And_Systems_Word_Problems/379547: An airplane can fly 650 miles with the wind in the same amount of time as it can fly 475 miles against the wind. If the wind speed is 40mph, find the speed of the plane in still air.
1 solutions
Answer 269470 by mananth(12270) on 2010-12-02 06:16:06 (Show Source):
You can put this solution on YOUR website!An airplane can fly 650 miles with the wind in the same amount of time as it can fly 475 miles against the wind. If the wind speed is 40mph, find the speed of the plane in still air.
...
wind speed = 40 mph
let plane speed = xmph
..
against wind speed = x-40
with wind speed = x+40
..
time with wind = time against wind
t=d/r
650/(x+40)=475/(x-40)
cross multiply
650(x-40)=475(x+40)
650x-26000=475x+19000
650x-475x=26000+19000
175x=45000
/175
x= 45000/175
257 mph the speed of plane
...
m.ananth@hotmail.ca
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Linear_Equations_And_Systems_Word_Problems/379546: A repairman purchased some washing machine motors for a total of $224. When the unit cost decreased by $4, he was able to buy one extra motor for the same total price. How many motors did he buy originally?
1 solutions
Answer 269469 by mananth(12270) on 2010-12-02 06:05:02 (Show Source):
You can put this solution on YOUR website!let the number of motors he bought be x
he paid $224
so he paid 224/x for each motor.
..
(224/x) -4 is the reduced price.
he got (x+1) motors
((224/x)-4)(x+1)=224
((224-4x)/x)(x+1)= 224
(224-4x)(x+1)/x=224
multiply by x
(224-4x)(x+1)= 224x
224x+224-4x^2-4x=224x
re write
224x-224x+224 -4x^2-4x=0
4x^2+4x-224=0
/4
x^2+x-56=0
x^2+8x-7x-56=0
x(x+8)-7(x+8)=0
(x+8)(x-7)=0
x= 7
The number of motors he bought originally = 7
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m.ananth@hotmail.ca
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Geometry_Word_Problems/379443: write a system of two linear equations in two variables for:a plane flew with a tail wind from madrid to lima, a trip of 1054 km in 93 min, the return trip took 9 more mins.
Let p be the air speed of the plane in km/h and w for the wind speed in km/h.
solve the system and find the air speed of the plane
1 solutions
Answer 269456 by mananth(12270) on 2010-12-02 01:32:05 (Show Source):
You can put this solution on YOUR website!speed of plane = p kmph
speed of wind = w kmph
..
speed with wind = p+w
speed against wind = p-w
..
distance = 1054 km
..
time with wind = 93 minutes = 1.55 hours
time against wind = 102 minutes= 1.7 hours
..
t=d/r
1054/p+w= 1.55
1054 =1.55p+1.55w...............1
...
1054/(p-w)=1.7
1054 = 1.7p+1.7w................2
...
solve these equations (1) & (2) to get the value of p & w
p= 650 km/h
w = 30 km/h
...
m.ananth@hotmail.ca
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Rational-functions/379489: we are graphing quadratic equations and the teacher isn't explaining it in simpler terms it is a function and i need help with the steps to solve the fuction is y=-2x^2-2x+3 and we have to graph it. can you help me and give me the steps?
1 solutions
Answer 269453 by mananth(12270) on 2010-12-02 00:09:33 (Show Source):
You can put this solution on YOUR website!y=-2x^2-2x+3
...
first find the x intercepts.
plug y =0
-2x^2-2x+3=0
...
Find the root of the equation using quadratic formula.
discriminant b^2-4ac= 28
x1=(2+sqrt(28))/-4
x1=-1.82
...
x2=(2-sqrt(28))/-4
x2=0.82
...
The x intercepts are (0,-1.8) & (0,0.82)
..
Using the equation y = -2x^2-2x+3
find the vertex of the parabola
a=-2, b=-2
h=(-b/2a)
h=(2/-4)
h=-1/2
plug the value of (-1/2) in the equation to get the y value of the vertex
y= -2*(1/4)-2*-1/2+3
y=-0.5+1+3
y=3.5
Vertex ( -1/2 , 3.5)
..
since x^2 is negative the parabola opens downwards
.
generate various value of y for different values of x
x=-1, y=3
x=1,y=-1
x=-2,y=3
x=2,y=-9
x=2,y=-9
...
use a calculator or plot points and join the curve.
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Equations/379490: IN 1912, an order by President Taft fixed the width and length of the U.S. flag in the ration 1 to 1.9. If 100 square feet of cloth are to be used to make a U.S. flag, estimate its dimensions to the nearest 1/4 foot.
How can I solve this?
1 solutions
Answer 269444 by mananth(12270) on 2010-12-01 23:30:44 (Show Source):
You can put this solution on YOUR website!Ratio of width to length = 1:1.9
area of flag = 100 sq. ft
...
Let the constant factor be x
(1*x)*(1.9*x)=100
1.9x^2=100
x^2=100/1.9
x= sqrt(100/1.9)
x= 7.25 feet
...
length = 7.25 *1.9 = 13.77
...
The dimensions are 7.25 feet by 13.75 feet
..
m.ananth@hotmail.ca
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