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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659, >>NextEquations/421503: solve by the substitution method.
3x+8y=-5
x=3-5y
the solution is?
or there is no solution? 1 solutions
Answer 294464 by ankor@dixie-net.com(15652) on 2011-03-13 21:23:39 (Show Source):
You can put this solution on YOUR website!solve by the substitution method.
3x + 8y = -5
x = (3-5y); use this for substitution in the 1st equation
:
Replace x with (3-5y)
3(3-5y) + 8y = -5
;
Multiply what's inside the brackets by 3,
9 - 15y + 8y = -5
;
Subtract 9 from both sides
-15y + 8y = -5 - 9
-7y = -14
:
divide both sides by -7
y = 
y = +2
;
Find x using the 2nd equation, replace y with 2
x = 3 - 5(2)
x = 3 - 10
x = -7
;
:
Check solution using the 1st equation
3x + 8y = -5
replace x with -7, y with 2
3(-7) + 8(2) =
-21 + 16 = -5; confirms our solutions of x=-7, y=2
|
Mixture_Word_Problems/421633: To mix weed killer with water correctly, it is necessary to mix 8 teaspoons of weed killer with 2 gallons of water. Find how many gallons of water are needed to mix with the entire box if it contains 36 teaspoons of weed killer. 1 solutions
Answer 294433 by ankor@dixie-net.com(15652) on 2011-03-13 19:36:38 (Show Source):
You can put this solution on YOUR website!To mix weed killer with water correctly, it is necessary to mix 8 teaspoons of weed killer with 2 gallons of water.
Find how many gallons of water are needed to mix with the entire box if it contains 36 teaspoons of weed killer.
:
Let x = amt of water for 36 tsp of weed killer
:
Use a ratio equation
 = 
8x = 2*36
8x = 72
x = 
x = 9 gallons of water
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Rectangles/421710: I am not sure if this is the area to do this question in but here goes. I am doing a practice final, and this question has me stumped.
The owner of a rectangular swimming pool, with dimensions 10 meters by 25 meters, wants to surround the pool with a concrete border of uniform width. The owner has enough concrete mix to cover 74 square meters. How wide should the border be?
I need the equation from beginning to end. So far I have
(2l+25)(2w+10)-250=74
(50l)(20w)
My original answer was 4 meters wide but that's wrong, I already know that the answer needs to be 2 meters wide but I can't figure out the equation to get me to the correct answer.
1 solutions
Answer 294428 by ankor@dixie-net.com(15652) on 2011-03-13 19:07:55 (Show Source):
You can put this solution on YOUR website!he owner of a rectangular swimming pool, with dimensions 10 meters by 25 meters, wants to surround the pool with a concrete border of uniform width. The owner has enough concrete mix to cover 74 square meters. How wide should the border be?
:
Let x = the width of the concrete border
:
The the overall dimensions will be (2x+10) by (2x+25)
:
overall area - pool area = 74 sq/m
(2x+10)(2x+25) - 250 = 74; (which essentially, is what you have)
FOIL
(4x^2 + 50x + 20x + 250) - 250 = 74
4x^2 + 70x - 74 = 0
Simplify, divide by 2
2x^2 + 35x - 37 = 0
Factors to
(2x + 37)(x - 1) = 0
Positive solution
x = 1 meter wide
:
:
You said it should be 2, check this by finding the overall area, subtract this pool area:
(2(1) + 10)(2(1) + 25) - 250 =
(2+10)(2+25) - 250 =
(12 * 27) - 250
324 - 250 = 74, confirms our answer of x = 1
|
Travel_Word_Problems/421658: Kids are one third the way across a bridge when they hear the sound of a train whistle. They see a train coming toward them at 45 miles per hour. Kids figured out they could run ahead to get to the far end of the bridge at the exact same time as the train or they could run back toward the train to the beginning of the bridge at the exact same time as the train arrived at the beginning of the bridge. How fast do the kids have to run to either make it to the beginning of the bridge at the same time as the train or to the end of the bridge at the same time as the train? 1 solutions
Answer 294411 by ankor@dixie-net.com(15652) on 2011-03-13 16:30:00 (Show Source):
You can put this solution on YOUR website!Kids are one third the way across a bridge when they hear the sound of a train whistle.
They see a train coming toward them at 45 miles per hour. Kids figured out they
could run ahead to get to the far end of the bridge at the exact same time as
the train or they could run back toward the train to the beginning of the bridge
at the exact same time as the train arrived at the beginning of the bridge.
How fast do the kids have to run to either make it to the beginning of the
bridge at the same time as the train or to the end of the bridge at the same time as the train?
:
This is a thought problem.
Assume the kids run the same direction that the train is going.
From the information we know that the train will enter the bridge when the kids have run 1/3 of the way
So when the train enters the bridge, the kids are 1/3 way from the far end.
The trains covers the length of the bridge in the same some the kids cover 1/3 of the bridge.
therefore: kids run  * 45 = 15 mph
|
Equations/421439: I am homeschooled and I have worked on this problem for hours. My mom finally gave me the answer but I don't seem to know how to do the steps correctly to get the answer. If I put my work in here it would take up all the space, so here is the question and the answer. I need the steps.
((2x^2 - 10x)/ (x^2 +8x +16)) ((4x + 16)/ (x^2 - 25)) the answer is((8x/ (x +4) (x+5)) but again no matter how many times I try the steps are wrong. 1 solutions
Answer 294392 by ankor@dixie-net.com(15652) on 2011-03-13 13:04:06 (Show Source):
You can put this solution on YOUR website! * 
:
we can do a lot of factoring here, one denominator is a perfect square, one is the difference of squares
 * 
:
Cancel x-5 and x+4, results:
 *
:
 *  =
|
Volume/421407: A monster came to life and ate every plant in its path, causing it to grow out of control. Each day it doubled in volume. At 8 a.m. on January 14th, it was seen by fishermen who estimated its volume to be a blob of about 200 cubic feet. For five days it grew and nothing could stop it. Finally, on January 19th, it died, What was its volume when it died? 1 solutions
Answer 294296 by ankor@dixie-net.com(15652) on 2011-03-12 22:03:56 (Show Source):
You can put this solution on YOUR website!A monster came to life and ate every plant in its path, causing it to grow out of control.
Each day it doubled in volume. At 8 a.m. on January 14th, it was seen by
fishermen who estimated its volume to be a blob of about 200 cubic feet.
For five days it grew and nothing could stop it. Finally, on January 19th,
it died, What was its volume when it died?
:
A = Ao*2^t
Where
Ao = initial amt (200 cu/ft)
t = time in days (5 days)
A = resulting amt after t days
:
A = 200*2^5
A = 6400 cu ft
|
Quadratic_Equations/421216: a sprinkler that sprays water in a circular motion is to be used to water a square garden. If the area of the garden is 920 square feet, find the smallest whole number radius that the sprinkler can be adjusted to so that the entire garden is watered. 1 solutions
Answer 294291 by ankor@dixie-net.com(15652) on 2011-03-12 21:53:28 (Show Source):
You can put this solution on YOUR website!a sprinkler that sprays water in a circular motion is to be used to water a square garden.
If the area of the garden is 920 square feet, find the smallest whole number
radius that the sprinkler can be adjusted to so that the entire garden is watered.
:
The diagonal (d) of the square will = the diameter of the required circle
:
Let x = side of the square
x^2 = 920 sq/ft, the area of the square
and using pythag
d = 
Which is
d = 
d = 
d = 42.895
radius = 
r = 21.4476 ~ 22 ft smallest whole number radius to water the entire garden
|
Travel_Word_Problems/421415: An observer stands 46.0 m behind a marksmen practicing at a rifle range. The marksman fires the rifle horizontally which gives the speed of the bullet to be 985 m/s. How far does each bullet travel before the observer hears the report of the rifle? Assume that the bullet encounter no obstacles during this interval, and ignore both air resistance and vertical component of the bullet's motion. The speed of sound in air is 343 m/s. 1 solutions
Answer 294288 by ankor@dixie-net.com(15652) on 2011-03-12 21:15:11 (Show Source):
You can put this solution on YOUR website!An observer stands 46.0 m behind a marksmen practicing at a rifle range.
The marksman fires the rifle horizontally which gives the speed of the bullet to be 985 m/s.
How far does each bullet travel before the observer hears the report of the rifle?
Assume that the bullet encounter no obstacles during this interval, and ignore
both air resistance and vertical component of the bullet's motion.
The speed of sound in air is 343 m/s.
:
Find how long it takes the report to be heard 46 m away, then how far the bullet travels in that time;
 * 985 = 132.1 meters
|
Radicals/420909: 
This is the problem I am trying to work out. I have tried foiling, quadratic equation, completing the square, but I am not coming up with a good answer. If you could help me I would appreciate it. I don't want to know the answer as much as how to do it. 1 solutions
Answer 294078 by ankor@dixie-net.com(15652) on 2011-03-11 20:18:13 (Show Source):
You can put this solution on YOUR website!
;
square both sides

:
FOIL the Left side
(x+2) -  + (x-3) = (x-6)
:
Combine like terms, move the radical to right
x + x -x + 2 - 3 + 6 = 
;
FOIL inside the radical
x + 5 = 
:
square both sides
x^2 + 10x + 25 = 4(x^2 - x - 6)
x^2 + 10x + 25 = 4x^2 - 4x - 24
:
Combine like terms on the right
0 = 4x^2 - x^2 - 4x - 10x - 24 - 25
:
3x^2 - 14x - 49 = 0
Factors to
(3x + 7)(x - 7) = 0
positive solution is all want here
x = + 7
:
:
Check solution in the original equation

you can see that it checks out
|
Rectangles/420958: If the length of one side of a square is increased by 4 centimeters and the length of an adjacent side is multiplied by 4, the perimeter of the resulting rectangle is 3 times the perimeter of the square. Find the length of a side of the original square. 1 solutions
Answer 294046 by ankor@dixie-net.com(15652) on 2011-03-11 17:17:07 (Show Source):
You can put this solution on YOUR website!If the length of one side of a square is increased by 4 centimeters and the
length of an adjacent side is multiplied by 4, the perimeter of the resulting
rectangle is 3 times the perimeter of the square.
Find the length of a side of the original square.
:
Let x = the side of the square
then
(x+4) = one side of the rectangle
and
4x = the adjacent side of the rectangle
:
Rect perimeter = 3 time sq perimeter
2(x+4) + 2(4x) = 3(4x)
2x + 8 + 8x = 12x
10x + 8 = 12x
8 = 12x - 10x
8 = 2x
x = 4 cm is the side of the original square
:
:
Check this; (rect is 8 by 16)
2(8) + 2(16) = 3(16)
16 + 32 = 48
|
Rate-of-work-word-problems/420854: One copy machine copies twice as fast as another. If both copiers work together, they can finish a particular job in two hours. How long would it take the slower copier to complete the job working alone? 1 solutions
Answer 293979 by ankor@dixie-net.com(15652) on 2011-03-11 10:25:20 (Show Source):
You can put this solution on YOUR website!One copy machine copies twice as fast as another.
If both copiers work together, they can finish a particular job in two hours.
How long would it take the slower copier to complete the job working alone?
:
Let t = time for the slower machine to do the job
then
.5t = time required by the faster machine
:
Let the completed job = 1
:
A typical shared work equation
 +  = 1
multiply thru by .5t, results:
2 + .5(2) = .5t
3 = .5t
t = 6 hrs the slow one alone
:
:
See if that is true
 +  = 1
|
Evaluation_Word_Problems/420547: the sum of louise's age and todd's age is 34 years. five yeras ago, the sum of twice louise's age and three times todd's age was 61 years. how old are they now? 1 solutions
Answer 293910 by ankor@dixie-net.com(15652) on 2011-03-10 21:55:12 (Show Source):
You can put this solution on YOUR website!Here's the equations, you can solve
:
the sum of louise's age and todd's age is 34 years.
L + T = 34
L = (34-T), use this form for substitution
:
five yrs ago, the sum of twice louise's age and three times todd's age was 61 yrs.
2(L-5) + 3(T-5) = 61
how old are they now?
|
Miscellaneous_Word_Problems/420750: Here is a problem that all my helpers say is not solvable, as do I.
Teacher says all problems are solvable
Three people own company shares. A and B together own 1/2, A and C own 1/3,
B and C own 1/5. What fraction do each own?
Can it be solved?
Thanks. 1 solutions
Answer 293906 by ankor@dixie-net.com(15652) on 2011-03-10 21:50:03 (Show Source):
You can put this solution on YOUR website!Three people own company shares.
A and B together own 1/2,
A and C own 1/3,
B and C own 1/5.
What fraction do each own?
:
I don't think this is possible, let say there are a total of 120 shares
then
A + B = 60
A + C = 40
B + C = 24
:
If A + B own 60, then C has to own the other 60
But it says that A + C = 40, we just decided that C has to own 60 ???
|
Age_Word_Problems/420706: A father is 60 years old and his son is half his age. How old was the boy when his father was four times his age? 1 solutions
Answer 293895 by ankor@dixie-net.com(15652) on 2011-03-10 20:52:52 (Show Source):
You can put this solution on YOUR website!A father is 60 years old and his son is half his age.
How old was the boy when his father was four times his age?
:
let y = years ago when dad's age was 4 times son's age
:
60 - y = 4(30 - y)
60 - y = 120 - 4y
-y + 4y = 120 - 60
3y = 60
y = 
y = 20 years ago
:
Then 30 - 20 = 10 yrs old, boy's age when his dad was 40 yrs old
|
Miscellaneous_Word_Problems/420633: Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 80 miles per hour and Train B is traveling at 100 miles per hour. Train A passes a station at 9:20 am. If Train B passes the same station at 9:32 am, at what time will Train B catch up to Train A? 1 solutions
Answer 293878 by ankor@dixie-net.com(15652) on 2011-03-10 20:05:13 (Show Source):
You can put this solution on YOUR website!Trains A and B are traveling in the same direction on parallel tracks.
Train A is traveling at 80 miles per hour and Train B is traveling at 100 miles per hour.
Train A passes a station at 9:20 am.
If Train B passes the same station at 9:32 am, at what time will Train B catch up to Train A?
:
From the given information, we know that train B is 12 min (1/5 hr) behind
train A, when train A passes the station
:
The distance between the trains at this time:  * 100 = 20 mi
:
Let t = time required for train B to catch train A
:
write a distance equation: Dist = speed * time
:
Train B travel dist = Train A travel dist + 20 mi
100t = 80t + 20
100t - 80t = 20
20t = 20
t = 
t = 1 hr for B to catch A
:
9:20 AM + 1.00 = 10:20 AM, B catches A
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Quadratic_Equations/420591: a father and son are chatting when the son poses this question "Dad,Im 22 but just how old are you? the father replies,"You want to know how old your old man is,eh? Hmm, well, I tell you what. im as old as your age, plus half of my age."
How old is the father? explain. 1 solutions
Answer 293870 by ankor@dixie-net.com(15652) on 2011-03-10 19:55:38 (Show Source):
|
Travel_Word_Problems/420509: Ian is standing 1.4 miles across a 2 mile railroad bridge when he sees a train approaching at a constant speed. Astonishingly enough, he can just get off the bridge by either running toward or away from the train at his constant speed of running. Find the number of miles that the train is from the bridge when Ian sees the train. (d=rt) 1 solutions
Answer 293868 by ankor@dixie-net.com(15652) on 2011-03-10 19:49:51 (Show Source):
You can put this solution on YOUR website!Ian is standing 1.4 miles across a 2 mile railroad bridge when he sees a train approaching at a constant speed.
Astonishingly enough, he can just get off the bridge by either running toward
or away from the train at his constant speed of running.
Find the number of miles that the train is from the bridge when Ian sees the train. (d=rt)
:
Assume he is .6 mi from end of the bridge where the train enters and
1.4 mi from the opposite end.
:
The train will enter the bridge when he has traveled .6 mi, going toward the
opposite end of the bridge, he will be .6 + .6 = 1.2 mi from the train when
it enters the bridge.
We can say that he travels .8 mi while the train travels 2 mi, to the end of the bridge.
:
Let d = distance train is from the bridge when he see's the train
Train travels d miles while he travels .6 mi
Using a ratio equation
 = 
.8d * .6 * 2
.8d = 1.2
d = 
d = 1.5 mi from the bridge
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Age_Word_Problems/420199: The sum of the digits of a two-digit number is 7. With the digits reversed the number is 5 times the tens digit of the original number. Find the original number. Thanks for the help. 1 solutions
Answer 293719 by ankor@dixie-net.com(15652) on 2011-03-10 07:54:41 (Show Source):
You can put this solution on YOUR website!The sum of the digits of a two-digit number is 7.
With the digits reversed the number is 5 times the tens digit of the original number.
Find the original number.
:
Let x = the 10's digit
Let y = the units
then
10x + y = the original number
:
"The sum of the digits of a two-digit number is 7."
x + y = 7
x = (7-y); use this form for substitution
:
"With the digits reversed the number is 5 times the tens digit of the original"
10y + x = 5x
10y = 5x - x
10y = 4x
Substitute (7-y) for x
10y = 4(7-y)
10y = 28 - 4y
10y + 4y = 28
14y = 28
y = 28/14
y = 2
then
7 - 2 = 5 is x
:
52 is the original number
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Proportions/420042: if 3 chickens can lay a dozen eggs in 2 days, how many eggs can 5 chicken lay in 9days? 1 solutions
Answer 293635 by ankor@dixie-net.com(15652) on 2011-03-09 21:57:06 (Show Source):
You can put this solution on YOUR website!if 3 chickens can lay a dozen eggs in 2 days, how many eggs can 5 chicken lay in 9 days?
:
Find the number of chicken-days per egg
 = .5 chicken days per egg
:
how many eggs can 5 chicken lay in 9 days
 = 90 eggs
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Volume/419918: Hi! can you please help me solve this?
PROBLEM:a cone has a volume of 5 liters. There is a cylinder that has the same hight and a congruent base. What is the volume, in liters, of the cylinder? thank you so much for your time! 1 solutions
Answer 293630 by ankor@dixie-net.com(15652) on 2011-03-09 21:37:54 (Show Source):
You can put this solution on YOUR website!:a cone has a volume of 5 liters.
There is a cylinder that has the same height and a congruent base.
What is the volume, in liters, of the cylinder?
:
We know the vol of a cone is 1/3 the volume of a cylinder with same dimensions
therefore
3 * 5 = 15 liters vol of the cylinder
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Miscellaneous_Word_Problems/420118: Ten times the first number exceeds the second by five.
Represent the numbers by n and 7n + 19.
Find the numbers.
(I dont know how to set up the equation to solve) 1 solutions
Answer 293628 by ankor@dixie-net.com(15652) on 2011-03-09 21:30:48 (Show Source):
You can put this solution on YOUR website!Ten times the first number exceeds the second by five.
Represent the numbers by n and 7n + 19.
Find the numbers.
:
n = the 1st number
and
(7n+19) = the 2nd number
:
The equation
10n = (7n+19) + 5
10n = 7n + 24
10n - 7n = 24
3n = 24
n = 8
:
:
See if that is true in the original equation
10(8) = (7(8) + 19) + 5
80 = 56 + 19 + 5
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Triangles/420001: The sum of three numbers is 32 the difference between the largest and the smallest number is 17. The sum of the two smaller numbers is 13 find the numbers 1 solutions
Answer 293621 by ankor@dixie-net.com(15652) on 2011-03-09 21:15:47 (Show Source):
You can put this solution on YOUR website!Three numbers, x, y, z (x is the smallest)
:
The sum of three numbers is 32
x + y + z = 32
:
the difference between the largest and the smallest number is 17.
z - x = 17
z = (x+17)
:
The sum of the two smaller numbers is 13
x + y = 13
y = (-x+13)
:
find the numbers
Replace z and y in the 1st equation
x + (-x+13) + (x+17) = 32
Combine like terms
x - x + x + 13 + 17 = 32
x + 30 = 32
x = 32 - 30
x = 2 is the smallest number
then
y = -2 + 13
y = 11
and
z = 2 + 17
z = 19 is the largest number
:
:
Check solutions
2 + 11 + 19 = 32
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Rectangles/419983: If the area of a rectangle is 108cm2,and the ratio is 3:4 what is the perimeter? 1 solutions
Answer 293610 by ankor@dixie-net.com(15652) on 2011-03-09 20:58:44 (Show Source):
You can put this solution on YOUR website!If the area of a rectangle is 108cm2,and the ratio is 3:4
what is the perimeter?
:
Let x = the multiplier
then
3x * 4x = 108
12x^2 = 108
:
divide both sides by 12
x^2 = 108/12
x^2 = 9
x = 
x = 3 is the multiplier
therefore
3*3 = 9 is width
3*4 = 12 is length
:
Find the perimeter
2(9) + 2(12) =
18 + 24 = 42 cm is the perimeter
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Mixture_Word_Problems/419977: a 17in piece of steel is cut into 3 pieces so that the second piece is twice as long as the first piece, and the third piece is 3in more than four times the length of the first piece 1 solutions
Answer 293607 by ankor@dixie-net.com(15652) on 2011-03-09 20:51:05 (Show Source):
You can put this solution on YOUR website!a 17in piece of steel is cut into 3 pieces so that the second piece is twice
as long as the first piece, and the third piece is 3in more than four times
the length of the first piece
:
Let x = length of the 1st piece
:
Write an equation for each phrase
:
"the second piece is twice as long as the first piece,"
2x = length of the 2nd piece
:
"the third piece is 3in more than four times the length of the first piece"
4x + 3 = length of the 3rd piece
:
Solve
x + 2x + (4x+3) = 17
7x = 17 - 3
7x = 14
x = 2 inches is the 1st piece.
I'll let you find the length of the other two pieces
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Polynomials-and-rational-expressions/419966: A square quilt has a border that is 1 foot wide on each side. The quilt has an area of 25 square feet. What is the length of the quilt without the border? 1 solutions
Answer 293603 by ankor@dixie-net.com(15652) on 2011-03-09 20:45:12 (Show Source):
You can put this solution on YOUR website!A square quilt has a border that is 1 foot wide on each side.
The quilt has an area of 25 square feet.
What is the length of the quilt without the border?
:
Let x = length of each side without the border
:
A 1' border adds 2' to each dimension of the inner square
:
(x+2)^2 = 25
FOIL
x^2 + 4x + 4 = 25
x^2 + 4x + 4 - 25 = 0
x^2 + 4x - 21 = 0
Factors to
(x+7)(x-3) = 0
positive solution is what we want here
x = 3 ft on each side without the border
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Linear-equations/420079: Could you please help me answer this question? Find the equation for the line that passes through the point (4,-2), and that is perpendicular to the line with the equation 3/4x-3y=-3. I have tried but seem to get stuck when it comes to fractions and solving for y. Any help is much appreciated! Thank you. 1 solutions
Answer 293600 by ankor@dixie-net.com(15652) on 2011-03-09 20:37:05 (Show Source):
You can put this solution on YOUR website!Find the equation for the line that passes through the point (4,-2), and that is perpendicular to the line with the equation 3/4x-3y=-3.
:
Find the slope of the given equation, put it in the slope/intercept form; y= mx+b
 x - 3y = -3
-3y =  x - 3
:
y has to be positive, multiply by -1
3y =  x + 3
divide eq by 3
y =  x + 1
Reduce fraction
y =  x + 1
:
the slope of the given equation: m1 = 
the slope relationship of perpendicular lines: m1*m2 = -1
Find m2
 *m2 = -1
multiply both sides by 4
m2 = -4 is the slope of line perpendicular to the given equation
:
use the point/slope form to find the perpendicular line: y - y1 = m(x - x1)
we have: x1 = 4, y1 = -2, m = -4
y - (-2) = -4(x - 4)
y + 2 = -4x + 16
y = -4x + 16 - 2
y = -4x + 14, is the equation of the perpendicular line
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Age_Word_Problems/419791: A father said to his son, " I was twice as old as you are now on the day that you were born. You will be just what i was then when fourteen years are gone ".
What are the present ages of the father and son. 1 solutions
Answer 293586 by ankor@dixie-net.com(15652) on 2011-03-09 20:08:00 (Show Source):
You can put this solution on YOUR website!A father said to his son, " I was twice as old as you are now on the day that you were born.
You will be just what i was then when fourteen years are gone ".
What are the present ages of the father and son.
:
Let s = son's present age
Father was twice as old when son was born therefore
2s + s = 3s; father's present age
:
"You will be just what i was then when fourteen years are gone ".
2s = s + 14
2s - s = 14
s = 14 yrs is son's present age
then
3(14) = 42 yrs is father's present age
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