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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659, >>NextHuman-and-algebraic-language/98828: the smaller of two numbers is 10 less than 4times the greater number.the greater number is 19 more than the smaller.find the two numbers.
1 solutions
Answer 71901 by ankor@dixie-net.com(15651)   on 2007-09-17 21:29:22 (Show Source):
You can put this solution on YOUR website!
Let x = the smaller number & y = the larger
:
the smaller of two numbers is 10 less than 4 times the greater number.
x = 4y - 10
:
the greater number is 19 more than the smaller.
y = x + 19
:
find the two numbers.
:
Substitute (4y-10) for x in the above equation
y = (4y-10) + 19
y - 4y = 19 - 10
-3y = +9
y = 9/-3
y = -3, the larger number
:
x = 4y - 10
x = 4(-3) -10
x = -12 - 10
x = -22, the smaller number
:
:
Check solution in the 2nd equation:
y = x + 19
-3 = -22 + 19
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Linear-systems/98808: Richard has 22 coins with a total value of $4. If the coins are all quarters and dimes, how many of each type of coin does he have?
1 solutions
Answer 71881 by ankor@dixie-net.com(15651) on 2007-09-17 20:14:17 (Show Source):
You can put this solution on YOUR website!Richard has 22 coins
d + q = 22
d = (22 - q)
:
with a total value of $4.
.10d + .25q = 4
:
If the coins are all quarters and dimes, how many of each type of coin does he have?
:
Substitute (22-q) for d in the above equation:
.10(22-q) + .25q = 4
2.2 - .10a + .25q = 4
-.10q + .25q = 4 - 2.2
.15q = 1.8
q = 1.8/.15
q = 12 quarters
:
That would give us: 22 - 12 = 10 dimes
:
:
Check solutions
.10(10) + .25(12) =
1.00 + 3.00 = 4.00
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Quadratic_Equations/98632: During rush hour, Fernando can drive 40 miles using the side roads in the same time that it takes to travel 30 miles on the freeway. If Fernando's rate on the side roads is 7 mi/h faster than his rate on the freeway, find his rate on the side roads.
1 solutions
Answer 71871 by ankor@dixie-net.com(15651) on 2007-09-17 18:43:47 (Show Source):
You can put this solution on YOUR website!: During rush hour, Fernando can drive 40 miles using the side roads in the same time that it takes to travel 30 miles on the freeway. If Fernando's rate on the side roads is 7 mi/h faster than his rate on the freeway, find his rate on the side roads.
:
Let s = speed on the side-road
then
(s-7) = speed on the freeway
:
Time = dist/speed
:
Side-road time = Freeway time
 = 
:
Cross multiply and you have:
40(s-7) = 30s
40s - 280 = 30s
40s - 30s = +280
10s = 280
s = 280/10
s = 28 mph on the side-roads
:
:
Check our solution by finding the times, they should be equal
40/28 = 1.42857
30/21 = 1.42857, confirms our solution
:
Did this help? Not that hard, right?
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Linear_Equations_And_Systems_Word_Problems/98643: I have no idea how to go about this problem, could you please help me with the set up and finding the answer?
The word problem is, Tom leaves Eddie's house to go home for dinner. He pedals his bike at a speed of 10 mph. Eddie notices that Tom left his wallet behind and gets on his bike to return the wallet. Eddie leaves his house 5 minutes after Tom left, but pedaled fast enough to reach Tom's house at exactly the same time that Tom does. Assuming that Tom's house is 4 miles away from Eddie's house, how fast did Eddie pedal his bike?
thank you for the help
1 solutions
Answer 71852 by ankor@dixie-net.com(15651) on 2007-09-17 16:22:13 (Show Source):
You can put this solution on YOUR website! Tom leaves Eddie's house to go home for dinner. He pedals his bike at a speed of 10 mph. Eddie notices that Tom left his wallet behind and gets on his bike to return the wallet. Eddie leaves his house 5 minutes after Tom left, but pedaled fast enough to reach Tom's house at exactly the same time that Tom does. Assuming that Tom's house is 4 miles away from Eddie's house, how fast did Eddie pedal his bike?
:
Let s = Eddie's speed on the bike
:
We know they both pedaled the same distance, but Eddie's trip took 5 min less.
:
Write a time equation: Time = Dist/speed
Since the speed is in mph, change 5 min to hrs: 5 min = 5/60 = 1/12 hr
:
Tom's time = Eddie's time + (1/12)hr
 =  + 
Multiply equation by 60s to get rid of the denominators
60s* = 60s* + 60s*
:
Cancel out the denominators, and you have simple equation:
6s(4) = 60(4) + 5s
24s = 240 + 5s
24s - 5s = 240
19s = 240
s = 240/19
s = 12.63 mph is Eddie's speed
:
Check solution by finding the time in minutes for each:
4/10 = .4 * 60 = 24 min
4/12.6 = .3174 * 60 = 19.0 min (five minutes less)
:
Did this make sense to you? Any questions?
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Age_Word_Problems/98690: Mary is half Tom's age. In seven more years she will be two thirds Tom's age. When Mary is as old as Tim is now he will be 3 times as old as she is now. How old are mary and tom now?
1 solutions
Answer 71843 by ankor@dixie-net.com(15651) on 2007-09-17 15:24:23 (Show Source):
You can put this solution on YOUR website!Mary is half Tom's age.
M = .5T
:
In seven more years she will be two thirds Tom's age.
(M+7) = (2/3)(T+7)
Multiply equation by 3 to get rid of the denominator
3(M+7) = 2(T+7)
3M + 21 = 2T + 14
Substitute.5T for M:
3(.5T) + 21 = 2T + 14
1.5T - 2T = 14 - 21
-.5T = -7
T = 14 is Tom's age, Then Mary is 7 yrs old now
:
When Mary is as old as Tim is now he will be 3 times as old as she is now. How old are Mary and Tom now
:
Now Tim enters the problem, but we already know the age of Mary & Tom??
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Square-cubic-other-roots/98203: Can someone help me to solve the equation?
square root of x + 5 + x = 1
1 solutions
Answer 71771 by ankor@dixie-net.com(15651) on 2007-09-16 21:31:42 (Show Source):
You can put this solution on YOUR website!Can someone help me to solve the equation?
square root of x + 5 + x = 1
:
One reason that some students do not get an answer from the tutors here is that
they do not say exactly what the problem is.
:
Like in this one, is it:
Sqrt(x) + 5 + x = 1
or is it:
Sqrt(x+5) + x = 1
:
I am going to assume it is:
Sqrt(x+5) + x = 1
:
Sqrt(x+5) = 1 - x; subtracted x from both sides
:
Squaring both sides gets rid of the radical:
x + 5 = (1 - x)^2
:
x + 5 = 1 - 2x + x^2; FOILed (1-x)(1-x)
:
Arrange as a quadratic equation:
x^2 - 2x - x + 1 - 5 = 0
:
x^2 - 3x - 4 = 0
:
This factors to:
(x - 4)(x + 1) = 0
:
Two solutions:
x = +4
x = -1
:
It is important to substitute both solutions in the original problem
Often only one of the solutions is valid, when a radical is involved.
Solution 1:
Sqrt(4+5) + 4 = 1
3 + 4 does not = 1, not a solution:
:
Solution 2
Sqrt(-1+5) - 1 = 1
Sqrt(4) - 1 = 1;
2 - 1 = 1; a good solution
:
Did this help you?
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Equations/98533: I am a mother trying to help her child solve equations, and find linear relations and linear function when given four tables with X and Y columns, each table having a different set of numbers. It asks to write an equation, describe the linear relation and the function. Please help...Thanks
1 solutions
Answer 71753 by ankor@dixie-net.com(15651) on 2007-09-16 20:52:12 (Show Source):
You can put this solution on YOUR website!I am a mother trying to help her child solve equations, and find linear relations and linear function when given four tables with X and Y columns, each table having a different set of numbers. It asks to write an equation, describe the linear relation and the function.
;
This involves finding the slope(designated as "m")from two pairs of the x,y values
Take these two pair and assign them as x1, y1 and x2, y2
:
Find the slope using the following formula: m = 
:
Once you have the value for m, write the equation from the following
formula: y - y1 = m(x - x1), note that you do not use x2 and y2 here.
:
Substitute the same values for x1 and y1 and m, then simpilfy until you
have y = mx - b form of the equation, this describes the relationship between x and y.
:
If this does not help you, submit an actual table along with the specific question and someone will take you through it.
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logarithm/98595: log (x+7) - log (x-2) = 1
1 solutions
Answer 71748 by ankor@dixie-net.com(15651) on 2007-09-16 20:35:45 (Show Source):
You can put this solution on YOUR website!log (x+7) - log (x-2) = 1
:
Same as:
log  = 1
:
Find the anti-log of both sides
 = 10
:
x + 7 = 10(x - 2)
x + 7 = 10x - 20
7 + 20 = 10x - x
9x = 27
x = 27/9
x = 3
:
:
Check solution, substitute 3 for x in original equation you have:
log(10) - log(1)
1 - 0 = 1
:
Did this help:
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Mixture_Word_Problems/98496: This question is from textbook College Algebra and Trigonometry
A radiator contains 6 liters of 25% antifreeze solution. How much should be drained and replaced with pure antifreeze to produce a 33% antifreeze solution?
So far, I know that the first solution contains 6 liters and I need to multiply that by 25%. Then since we are "replacing" pure antifreeze to the mixture that is 100% that I need to multiply to the unknown mixture of x+6 (which is my second solution) so that I can produce a 33% solution. Does this make any sense? I'm not sure how to do this. Thank You
1 solutions
Answer 71726 by ankor@dixie-net.com(15651) on 2007-09-16 19:47:16 (Show Source):
You can put this solution on YOUR website!A radiator contains 6 liters of 25% antifreeze solution. How much should be drained and replaced with pure antifreeze to produce a 33% antifreeze solution?
:
It looks like they want you to start with 6 and end up with 6.
We could do it like this:
:
Let x = amt to be drained and replaced
:
The % antifreeze equation:
:
.25(6) - .25(x) + 1.0(x) = .33(6)
1.5 - .25x + 1x = 1.98
-.25x + 1x = 1.98 - 1.5
.75x = .48
x = .48/.75
x = .64 liters of pure antifreeze to replace .64 liters of the 25% solution
:
:
Check our solution for x.
:
25% amt is now: 6 - .64 = 5.36
:
.25(5.36) + 1.0(.64) = .33(6)
1.34 + .64 = 1.98; confirms our solution
:
Did this help?
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Numeric_Fractions/98163: what fraction lies exactly halfway between x over two and x over three
1 solutions
Answer 71712 by ankor@dixie-net.com(15651) on 2007-09-16 18:42:14 (Show Source):
You can put this solution on YOUR website!what fraction lies exactly halfway between x over two and x over three
:
halfway between  and 
:
Put over a common denominator, and subtract:
 -  =  ; the difference between the two fractions
:
 * =  ; half the difference between the two fractions
:
Halfway value of the fraction would be:
+ =  + = 
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Linear_Algebra/98500: This question is from textbook Mathematical ideas
I have tried to solve this I can't seem to get it set up right. The force needed to keep a car from skidding on a curve varies inversly as the radius of the curve and jointly as the weight of the car and the square of the speed If 242 pounds of force keep a 2000 pound car from skidding on a curve of radius 500 feet at 30 miles per hour, what force would keep the same car from skidding on a curve radius 750 feet at 50 miles per hour?
1 solutions
Answer 71671 by ankor@dixie-net.com(15651) on 2007-09-16 13:51:58 (Show Source):
You can put this solution on YOUR website! The force needed to keep a car from skidding on a curve varies inversely as the radius of the curve and jointly as the weight of the car and the square of the speed
Force =  k
:
If 242 pounds of force keep a 2000 pound car from skidding on a curve of radius 500 feet at 30 miles per hour,
:
Find k
 k = 242
:
 k = 242
:
 k = 242
:
3600k = 242
:
k = 242/3600
:
k = .0672
:
:
what force would keep the same car from skidding on a curve radius 750 feet at 50 miles per hour?
:
Using .0672 for k in the same formula
:
F = .0672 
:
F = .0672
:
F = .0672 
:
F = .0672 * 6666.67
:
F = 448 lb
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Travel_Word_Problems/98431: A sink is filling at the rate of 1 liter in 5 seconds. It is draining at the rate of 1 liter in 11 seconds. How long for the time it is empty will it take the sink to fill, if its capacity is 8 liters?
1 solutions
Answer 71624 by ankor@dixie-net.com(15651) on 2007-09-15 21:46:36 (Show Source):
You can put this solution on YOUR website!A sink is filling at the rate of 1 liter in 5 seconds. It is draining at the rate of 1 liter in 11 seconds. How long for the time it is empty will it take the sink to fill, if its capacity is 8 liters?
:
Let's look the two devices individually
The faucet alone fills the sink: 8 * 5 = 40 sec
The drain alone empties a full sink: 8 * 11 = 88 sec
:
Let t = time to fill the sink when both devices are on
Let the full sink = 1
Filling is +
Draining is -
:
 -  = 1
:
Multiply equation by 880
880* - 880* = 880(1)
:
CAncel out the denominators and you have:
22t - 10t = 880
:
12t = 880
:
t = 880/12
:
t = 73.33 seconds
:
:
Check using t = 73.33 :
 -  = 1
1.83 - .83 = 1
:
How about this? Was it understandable?
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Polynomials-and-rational-expressions/98190: Each of the three dimensions of a cube with a volume of y^3 cubic centimeters is decreased by a whole number of centimeters. If the new volume is y^3-13y^2+54y-72 cubic centimeters and the new width is y-6 centimeters, then what are the new length and height?
1 solutions
Answer 71602 by ankor@dixie-net.com(15651) on 2007-09-15 19:16:34 (Show Source):
You can put this solution on YOUR website!Each of the three dimensions of a cube with a volume of y^3 cubic centimeters is decreased by a whole number of centimeters. If the new volume is y^3-13y^2+54y-72 cubic centimeters and the new width is y-6 centimeters, then what are the new length and height?
:
Divide (y-6) into y^3 - 13y^2 + 54y - 72 using synthetic division:
:
....____________________
6 |1 - 13 + 54 - 72
.....0 + 6 - 42 + 72
....------------------
.....1 - 7 + 12 + 0
:
This gives us a quotient of:
y^2 - 7y + 12
:
Which factors to:
(y - 3)(y - 4); the new height and length
:
:
you can check solution by (y-6)*(y-3)*(y-4)
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Surface-area/98162: This question is from textbook
I have tried to do this problem but no luck. It seems simple but I can't find the answer. The question is: A rectangle has a length that is twice as long s the width. If the area is 24m squared what is the length and width of the rectangle. I know all the multiples of 24, but nothing seems to work.
Thanks,
Tanner
1 solutions
Answer 71569 by ankor@dixie-net.com(15651) on 2007-09-15 16:18:34 (Show Source):
You can put this solution on YOUR website!A rectangle has a length that is twice as long as the width. If the area is 24m squared what is the length and width of the rectangle. I know all the multiples of 24, but nothing seems to work.
:
Let x = width of the rectangle
Then
2x = length of the rectangle
:
Length * width = 24
2x * x = 24
:
2x^2 = 24
:
x^2 = 24/2
:
x^2 = 12
:
x = sqrt(12)
:
x = sqrt(4*3)
:
x = 2*sqrt(3) is the width of rectangle
then
2(2*sqrt(3))
:
4*sqrt(3) = length of the rectangle
:
:
Check solution: 4*sqrt(3) * 2*sqrt(3) = 8 * 3 = 24
:
Did this help?
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Linear-equations/98155: how do you graph using intercept
4x-3y=12
1 solutions
Answer 71521 by ankor@dixie-net.com(15651) on 2007-09-15 11:37:15 (Show Source):
You can put this solution on YOUR website! How do you graph using intercept
:
4x - 3y = 12
:
Put the graph in the slope intercept form:
4x - 3y = 12
-3y = -4x + 12
We want y to be positive, multiply equation by -1
3y = +4x - 12
Divide equation by 3 to get 1y
y = (4/3)x - (12/3)
y = (4/3)x - 4, is the slope/intercept form
:
Graph by making a table assigning a value to x and solving for y:
x | y
--------
-3 |-8
0 |-4
+3 | 0
+6 |
+9 |
You should be able to finish this table
:
This is a linear equation so you really only need to have two points, a 3rd
point, will confirm it as a straight line. should look like this
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Linear-equations/98156: how do you find an equation of a line?
1.) (2,5),m=5
1 solutions
Answer 71517 by ankor@dixie-net.com(15651) on 2007-09-15 11:23:03 (Show Source):
You can put this solution on YOUR website!how do you find an equation of a line?
1.) (2,5),m=5
:
You use the point/slope formula: y - y1 = m(x - x1)
:
In the above problems: x1 = 2, y1 =5, m = 5
:
y - 5 = 5(x - 2)
y - 5 = 5x - 10
y = 5x - 10 + 5
y = 5x - 5, is the equation of the line with a slope of 5 and point 2, 5
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Rectangles/98129: Please help me solve this word problem.
Geometry. The length of a rectangle is 2 cm more than 3 times its width. If the
area of the rectangle is 95 cm2, find the dimensions of the rectangle.
Thank you
1 solutions
Answer 71512 by ankor@dixie-net.com(15651) on 2007-09-15 11:00:34 (Show Source):
You can put this solution on YOUR website!The length of a rectangle is 2 cm more than 3 times its width. If the
area of the rectangle is 95 cm2, find the dimensions of the rectangle.
:
Let x = width of the rectangle
:
It says,"The length of a rectangle is 2 cm more than 3 times its width." Therefore
Length = (3x + 2)
:
"area of the rectangle is 95 cm2,"
L * W = 95
Therefore:
(3x+2) * x = 95
:
3x^2 + 2x = 95
:
3x^2 + 2x - 95 = 0; a quadratic equation, solve using the quadratic formula
a = 3; b = 2; c = -95
:
:
:
:
 ; minus a minus is a plus
:
Two solutions, but it's the positive solution we want here
x = 5.305 is the width
:
Length = 3(5.305) + 2 = 17.915 is the length
:
:
Check solution:
5.305 * 17.915 = 95.0
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Triangles/98335: Just a quick question.
I built a shelf. Its going to be 24" from the wall at a height of 38". How long do I make my braces from the front edge to the back at floor level?
1 solutions
Answer 71500 by ankor@dixie-net.com(15651) on 2007-09-15 09:58:08 (Show Source):
You can put this solution on YOUR website!It's going to be 24" from the wall at a height of 38". How long do I make my braces from the front edge to the back at floor level?
:
The brace would be the hypotenuse. (c)
:
c = Sqrt(a^2 + b^2)
:
c = Sqrt(24^2 + 38^2)
:
c = Sqrt(576 + 1444)
:
c = Sqrt(2020)
:
c = 44.9 inches, say 45 inches
:
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Miscellaneous_Word_Problems/98127: Could you please help me solve this word problem?
Crafts. A solar collector is 2.5 m long by 2.0 m wide. It is held in place by a frame of uniform width around its outside edge. If the exposed collector is 4m^2, what is the width of the frame to the nearest tenth of a centimeter?
Thank you
1 solutions
Answer 71430 by ankor@dixie-net.com(15651) on 2007-09-14 19:31:04 (Show Source):
You can put this solution on YOUR website!A solar collector is 2.5 m long by 2.0 m wide. It is held in place by a frame of uniform width around its outside edge. If the exposed collector is 4m^2, what is the width of the frame to the nearest tenth of a centimeter?
:
Let x = width of the outside frame (in meters)
:
Dimensions of the exposed collector, (2.5 - 2x) by (2 - 2x) = 4
Area:
(2.5 - 2x) * (2 - 2x) = 4
FOIL
5 - 5x - 4x + 4x^2 = 4
:
4x^2 - 9x + 5 - 4 = 0
:
4x^2 - 9x + 1 = 0
:
Use the quadratic formula for this: a = 4, b = -9, c = 1
:
:
:
:
Solution 1:
:
x = 
x = 2.13278 meters * 100 = 213.3 cm, not a possible solution
:
Solution 2:
:
x = 
x = .11721 meters * 100 = 11.7 cm, a reasonable answer
:
:
Check solution by finding the area of exposed collector
2x = 2(.117) = .234 m
(2.5 - .234) * (2 - .234) =
2.266 * 1.766 = 4.00 sq m confirms our solution
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Linear_Equations_And_Systems_Word_Problems/98151: Write qn equation of the line that passes through (9, 6) and is perpendicular to the line whose equation is y=-1/3x+7.
So far I have:
y=3x7/3
y-(6)=7/3 (x-9)
y+6=7/3x3
This is as far as I can go. I am trying to assist my niece and at the age of 55, my brain is not what it use to be.
1 solutions
Answer 71415 by ankor@dixie-net.com(15651) on 2007-09-14 17:54:38 (Show Source):
You can put this solution on YOUR website!Write an equation of the line that passes through (9, 6) and is perpendicular to the line whose equation is y =-(1/3)x + 7.
:
The relationship for the slopes of perpendicular lines is: m1*m2 = -1
m1 = -1/3, find m2
(-1/3)*m2 = -1
multiply by -1
m2 = +3; it looks like you got that part OK
:
Use the point slope equation: y - y1 = m(x - x1)
:
In this equation: m = +3; x1 = 9; y1 = 6
:
y - 6 = 3(x - 9)
y - 6 = 3x - 27
y = 3x - 27 + 6
y = 3x - 21 is perpendicular to y = -(1/3)x + 7
:
Check by substituting 9 for x in the above equation
y = 3(9) - 21
Y = 27 - 21
Y = 6
:
Should look like this:
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Age_Word_Problems/98055: The sum of Anne's, Bert's and Chris's age is 60. Anne is older than Bert by the same number of years that Bert is older than Chris. When Bert is as old as Anne is now, Anne will be three times as old as Chris is now. Set up the equations to solve this problem.
1 solutions
Answer 71414 by ankor@dixie-net.com(15651) on 2007-09-14 16:39:45 (Show Source):
You can put this solution on YOUR website!The sum of Anne's, Bert's and Chris's age is 60.
a + b + c = 60
:
Anne is older than Bert by the same number of years that Bert is older than Chris.
a - b = b - c = x
Let x = difference between a & b, and b & c
Then:
b = a-x
c = a-2x
When Bert is as old as Anne is now, Anne will be three times as old as Chris is now.
b + x = a (now)
then find a in terms of x:
(a + x) = 3c
a + x = 3(a-2x); substituted (a-2x) for c
a + x = 3a - 6x
a - 3a = -6x - x
-2a = -7x
2a = 7x
a = 3.5x
:
a + b + c = 60
Substitute for b and c,
a + (a-x) + (a-2x) = 60
3a - 3x = 60
a - x = 20
:
3.5x - x = 20; substituted 3.5x for a, find x
2.5x = 20
x = 20/2.5
x = 8 is the difference
:
a = 3.5x; find a from knowing x
a = 3.5(8)
a = 28 yrs old, then, b = 20 yrs old, and, c = 12 yrs old
:
Check solution from the statement:
"When Bert is as old as Anne is now, Anne will be three times as old as Chris is now.
When B is 28(A's age now), A(28+8) = 3(12(C's age now))
:
Hope this made sense.
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Quadratic_Equations/98170: find two positive real numbers that differ by 1 and have a product of 1
1 solutions
Answer 71385 by ankor@dixie-net.com(15651) on 2007-09-14 08:13:01 (Show Source):
You can put this solution on YOUR website!ind two positive real numbers that differ by 1 and have a product of 1
:
The two numbers x, (x-1)
:
The product = 1
x(x-1) = 1
x^2 - x = 1
x^2 - x - 1 = 0, a quadratic equation, solve using formula
:
:
:
Two solutions
and
:
The two numbers, approx, +1.618 and +.618
or
The two numbers, approx, -.618 and -1.618
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Travel_Word_Problems/97959: Jenne drives to her son's house in 5 hours when there is heavy traffic. When there is no traffic, the same tri takes 4 hours. She can drive an average of 12 m.p.h faster when there is no traffic than when there is heavy traffic. What is her average speed when there is no traffic? What is the distance from her house to her son's house?
1 solutions
Answer 71352 by ankor@dixie-net.com(15651) on 2007-09-13 21:42:13 (Show Source):
You can put this solution on YOUR website!Jenne drives to her son's house in 5 hours when there is heavy traffic. When there is no traffic, the same trip takes 4 hours. She can drive an average of 12 m.p.h faster when there is no traffic than when there is heavy traffic. What is her average speed when there is no traffic? What is the distance from her house to her son's house?
:
Let x = no traffic speed
Then
(x-12) = traffic speed
:
Write a distance equation: distance = time * speed
:
traffic dist = no traffic dist
5(x-12) = 4x
5x - 60 = 4x
5x - 4x = +60
x = 60 mph with no traffic
:
Find the distance:
4 * 60 = 240 mi
:
5(60-12) = 240 also, (checks the solution of x = 60)
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Linear_Algebra/98009: how to solve 4(2n-1)=(6n+4)+1?
1 solutions
Answer 71347 by ankor@dixie-net.com(15651) on 2007-09-13 21:25:51 (Show Source):
You can put this solution on YOUR website!how to solve
:
4(2n-1) = (6n+4)+1
:
Multiply what's inside the brackets:
8n - 4 = 6n + 4 + 1
:
8n - 4 = 6n + 5
:
Add 4 to both sides
8n - 4 + 4 = 6n + 5 + 4
:
8n = 6n + 9
:
Subtract 6n from both sides:
8n - 6n = 6n - 6n + 9
:
2n = 9
:
n = 9/2 or 4.5
:
:
Check solution, substitute 4.5 for n in the original equation:
4(2(4.5) - 1) = (6(4.5) + 4) + 1
4(9 - 1) = (27 + 4) + 1
4(8) = 27 + 5
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Radicals/98075: Please help me I am not sure how to sovel this. Please need some help. Evaluate if possible.
1 solutions
Answer 71336 by ankor@dixie-net.com(15651) on 2007-09-13 21:10:33 (Show Source):
You can put this solution on YOUR website!Assume you mean evaluate:
:
CubeRt(-8/27)
:
You know the cube root of -8 is -2. (-2*-2*-2 = -8)
and
the cube root of 27 is 3, (3*3*3 = 27)
:
Therefore CubeRt(-8/27) = -2/3
:
Check it:
 * * = 
:
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Travel_Word_Problems/97985: This question is from textbook
In a bicycle race, Lionel gives Robert a 500m advantage. Also, Lionel agrees to start 15min after Robert. If Lionel bikes at 17km/h and Robert at 14km/h, how long will it take Lionel after he starts biking to overtake Robert?
I already know that you have to convert 500m to 0.5km and 15min to 0.25hours. I have to make an equation out of this but I don't know how. Please help.
1 solutions
Answer 71322 by ankor@dixie-net.com(15651) on 2007-09-13 20:22:45 (Show Source):
You can put this solution on YOUR website!In a bicycle race, Lionel gives Robert a 500m advantage. Also, Lionel agrees to start 15min after Robert. If Lionel bikes at 17km/h and Robert at 14km/h, how long will it take Lionel after he starts biking to overtake Robert?
:
When L overtakes R, L will have traveled .5 km further than
:
Let t = travel time for L to overtake R
Then
(t+.25) = travel time of R (had a 15 min head start)
:
Distance = speed * time
:
L's distance = R's distance + .5 (R had a 500 m head start)
17t = 14(t+.25) + .5
:
17t = 14t + 3.5 + .5
:
17t - 14t = 4
:
3t = 4
:
t = 4/3 hr for L to overtake R
:
:
Check the distance of both:
17*(4/3) = 22.68 mi
14*(4/3 + 1/4) = 22.17, .5 mi difference because of the head start
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Equations/97963: the perimeter of a rectangle is 30 meters. If the length is 5 meters more than the width, then what is the length and the width of the rectangle. Make a picture.
Please show me how to solve this problem? thanks!
1 solutions
Answer 71303 by ankor@dixie-net.com(15651) on 2007-09-13 19:29:06 (Show Source):
You can put this solution on YOUR website!the perimeter of a rectangle is 30 meters. If the length is 5 meters more than the width, then what is the length and the width of the rectangle.
:
Let x = the width
Then
(x+5) = length
:
Perimeter:
2W + 2L = 30
2x + 2(x+5) = 30
:
Simplify, divide equation by 2:
x + (x + 5) = 15
2x = 15 - 5
2x = 10
x = 5 m is the width
then
5 + 5 = 10 m is the length
:
:
you can draw the picture. Let 1 cm = 1 m
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Human-and-algebraic-language/97895: A cyclist traveled at a rate of 24 mph to visit a nearby town. The cyclist averaged 18 mph on the return trip. If the round trip took 4.9 hours, find the distance to the nearby town.
1 solutions
Answer 71299 by ankor@dixie-net.com(15651) on 2007-09-13 19:18:54 (Show Source):
You can put this solution on YOUR website!: A cyclist traveled at a rate of 24 mph to visit a nearby town. The cyclist averaged 18 mph on the return trip. If the round trip took 4.9 hours, find the distance to the nearby town.
:
Let d = one-way distance to the town
:
Write a time equation, Time = dist/speed
:
 +  = 4.9
:
Multiply the equation by the least common multiple, 72:
72 + 72 = 72(4.9)
:
Cancel out the denominators:
3d + 4d = 352.8
:
7d = 352.8
:
d = 352.8/7
:
d = 50.4 miles
:
:
Check solution:
 +  = 4.9
:
2.1 + 2.8 = 4.9
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