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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629, >>NextTravel_Word_Problems/408917: At the beginning of the walk, Robert and Juanita are 5.5 miles apart. If you leave at the same time and walk in the same direction, Robert over takes Juanita in 11 hours. If they walk towards each other, they meet in 1 hour. What are their speeds?
Roberto Speed____ mph
Juanita Speed_____mph
1 solutions
Answer 288045 by ankor@dixie-net.com(15638)   on 2011-02-14 17:18:32 (Show Source):
You can put this solution on YOUR website!At the beginning of the walk, Robert and Juanita are 5.5 miles apart.
If they leave at the same time and walk in the same direction, Robert overtakes Juanita in 11 hours.
If they walk towards each other, they meet in 1 hour. What are their speeds?
:
Let r = R's walking speed
Let j = J's walking speed
:
Write a distance equation for each scenario; dist = time * speed
:
11(r - j) = 5.5; (going same direction)
1(r + j) = 5.5; (going toward each other)
:
Divide the 1st equation by 11 and add to the 2nd equation
r - j = .5
r + j = 5.5
-------------adding eliminates j, find r
2r = 6
r = 
r = 3 mph is R's walking speed
then
3 + j = 5.5
j = 5.5 - 3
j = 2.5 mph is J's walking speed
:
:
Check solution in the 1st equation:
11(3 - 2.5) =
11(.5) = 5.5; confirms our solutions
|
Miscellaneous_Word_Problems/408976: One candle will burn up completely in 4 hours, while a second candle of equal length requires 5 hours to burn up completely. If the candles are lit at the same time, how long will they burn before one is exactly three times as long as the other?
1 solutions
Answer 288038 by ankor@dixie-net.com(15638) on 2011-02-14 16:45:06 (Show Source):
You can put this solution on YOUR website!One candle will burn up completely in 4 hours, while a second candle of equal
length requires 5 hours to burn up completely.
If the candles are lit at the same time, how long will they burn before one is
exactly three times as long as the other?
:
Assign a value to the length of the candles, 20"
then
 = 5 in/hr burn rate of candle 1
and
 = 4 in/hr burn rate of candle 2
:
let t = time for candle 2 to be 3 times candle 1
:
Candle 2 = 3 times candle 1
(20 - 4t) = 3(20 - 5t)
20 - 4t = 60 - 15t
-4t + 15t = 60 - 20
11t = 40
t = 
t = 3  hrs; 3 + *60 = 38.2 min
:
3 hrs 38.2 min, Candle 2 will be three times the length of candle 1
|
Evaluation_Word_Problems/408878: A circular mirror is surrounded by a square metal frame. The radius of the circular mirror is 3x. The side length of the metal frame is 15x. What is the area of the metal frame?
1 solutions
Answer 287961 by ankor@dixie-net.com(15638) on 2011-02-14 10:01:31 (Show Source):
You can put this solution on YOUR website!A circular mirror is surrounded by a square metal frame.
The radius of the circular mirror is 3x.
The side length of the metal frame is 15x.
What is the area of the metal frame?
:
Find the area of the whole thing:
(15x)^2 = 225x^2
:
Find the area of the mirror
:
Find the metal area surrounding the mirror
225x^2 - 28.27x^2 = 196.73x^2
|
Human-and-algebraic-language/408821: I read 50 times on these short sentense but still don't get it! Please help me to solve question a and question b
Question a : One number is 3 more than twice another number. find the larger number if their sum is -15
question b: The sum of smallest and largest of 5 consecutive interger is -50. find the middle interger.
1 solutions
Answer 287931 by ankor@dixie-net.com(15638) on 2011-02-14 08:12:52 (Show Source):
You can put this solution on YOUR website!Write exactly what it says
:
Let x = a number
let y = another number
:
a: One number is 3 more than twice another number.
x = 3 + 2y
find the larger number if their sum is -15
x + y = -15
From the 1st statement, replace x with (3+2y)
(3+2y) + y = -15
2y + y = -15 - 3
3y = -18
y = 
y = -6
find x using the 1st equation
x = 3 + 2(-6)
x = 3 - 12
x = -9
Check solutions in the 2nd equation
-9 - 6 = -15; confirms our solution of x=-9, y=-6 (which is the larger number)
:
:
Five consecutive integers: x, (x+1), (x+2), (x+3), (x+4)
b: The sum of smallest and largest of 5 consecutive integer is -50.
x + (x+4) = -50
2x + 4 = -50
2x = -50 - 4
2x = -54
x = 
x = -27 is the 1st integer
:
find the middle integer. That's (x+2), therefore:
-27 + 2 = -25 is the middle integer
:
Did this shed some light on this stuff for you?
|
Systems-of-equations/408718: A wooden box weighs 22kg when it is half full of apples and weighs 15kg when it is one-third full of apples. What is the weight of the box empty?
1 solutions
Answer 287861 by ankor@dixie-net.com(15638) on 2011-02-13 21:45:59 (Show Source):
You can put this solution on YOUR website!A wooden box weighs 22kg when it is half full of apples and weighs 15kg when it is one-third full of apples.
What is the weight of the box empty?
;
let b = weight of empty box
let a = weight of just the apples when box is full
:
b +  a = 22
b +  a = 15
:
multiply the 1st equation by 6, multiply the 2nd equation by 9,
Subtract the 1st from the 2nd equation
9b + 3a = 135
6b + 3a = 132
-----------------subtraction eliminates a, find b
3b = 3
b = 1 kg is the weight of the box
|
Rectangles/408244: if the sides of a square root are lenghtened by 6cm. The area becomes 196cm^2. Find the lenght of a side of the original square. what is the length of side square.
1 solutions
Answer 287859 by ankor@dixie-net.com(15638) on 2011-02-13 21:35:21 (Show Source):
You can put this solution on YOUR website!I think you mean:
if the sides of a square are lengthened by 6 cm. The area becomes 196cm^2.
Find the length of a side of the original square.
what is the length of side square.
:
Let s = the side of the original square
:
Let (s+6) = side of the larger square
:
Area of the new square
(s+6)*(s+6) = 196
FOIL
s^2 + 12s + 36 = 196
s^2 + 12s + 36 - 196 = 0
A quadratic equation
s^2 + 12x - 160 = 0
Factors to
(s - 8)(s + 20) = 0
the positive solution is what we want here:
s = 8 cm, side of the original square
:
Then: 8 + 6 = 14 cm is the side of the larger square
Check this by finding the area: 14 * 14 = 196
|
Miscellaneous_Word_Problems/408325: You want to fill nine 1-lb tins with a holiday snack mix. You want the mix to contain the three following items: dried apple pieces which cost $2.45 per pound., pecans which cost $1.85 per pound, and dried cherry pieces which cost $0.80 per pound. You must spend $15 and want the mix to contain half as many pounds of cherry pieces as dried apple slices and pecans combined. How many pounds of pecans should you buy?
1 solutions
Answer 287857 by ankor@dixie-net.com(15638) on 2011-02-13 21:21:20 (Show Source):
You can put this solution on YOUR website!You want to fill nine 1-lb tins with a holiday snack mix.
You want the mix to contain the three following items:
dried apple pieces which cost $2.45 per pound.,
pecans which cost $1.85 per pound,
and dried cherry pieces which cost $0.80 per pound.
You must spend $15 and want the mix to contain half as many pounds of cherry
pieces as dried apple slices and pecans combined.
How many pounds of pecans should you buy?
:
Let p = lbs of pecans required
Let a = lbs of apples
Let c = lbs of cherrys
:
a + p + c = 9
:
2.45a + 1.85p + .80c = 15
:
"the mix to contain half as many pounds of cherry pieces as dried apple slices and pecans combined.
.5c = a + p
Rearrange as
a + p -.5c = 0
Subtract from the 1st equation
a + p + c = 9
a + p -.5c = 0
-----------------subtracting eliminates a & p, find c
1.5c = 9
c = 
c = 6 lb of cherries
then
a + p = .5(6)
a + p = 3
a = (3-p)
:
In the cost equation: replace a with (3-p), replace c with 6, find p
2.45(3-p) + 1.85p + .80(6) = 15
7.35 - 2.45p + 1.85p + 4.80 = 15
-2.45p + 1.85p + 12.15 = 15
-.60p = 15 - 12.15
-.6p = 2.85
p = 
p = -4.75, a negative means this problem has a major flaw in it. Can't be done with these values|
|
Linear_Algebra/408637: If a ball is dropped from 214 ft above the ground, how long does it take to reach ground level? (Round your answer to two decimal places.)
1 solutions
Answer 287835 by ankor@dixie-net.com(15638) on 2011-02-13 20:38:20 (Show Source):
You can put this solution on YOUR website!If a ball is dropped from 214 ft above the ground, how long does it take to reach ground level?
(Round your answer to two decimal places.)
:
The equation for this is: -16t^2 + 214 = 0 (ground = 0)
-16t^2 = -214
divide both sides by -16
t^2 = 13.375
t = 
t = 3.657 ~ 3.66 seconds
|
Square-cubic-other-roots/408330: can some one help me please and thank you
(4x^2-7xy+y^2)+(-7x^2-6xy-y^2)+(x^2+xy-4y^2)
1 solutions
Answer 287806 by ankor@dixie-net.com(15638) on 2011-02-13 19:13:01 (Show Source):
You can put this solution on YOUR website!(4x^2-7xy+y^2)+(-7x^2-6xy-y^2)+(x^2+xy-4y^2)
Combine like terms (a plus between the sets of brackets, so no sign changes:
4x^2 - 7x^2 + x^2 - 7xy - 6xy + xy + y^2 - y^2 - 4y^2
:
-2x^2 - 12xy - 4y^2
Factor out -2
-2(x^2 + 6xy + 2y^2) about all can do with it
|
Linear-equations/408351: A square platform has a perimeter which is 9 times the length of a side, decreased by 15. Find the length of a side.
1 solutions
Answer 287801 by ankor@dixie-net.com(15638) on 2011-02-13 19:00:31 (Show Source):
You can put this solution on YOUR website!A square platform has a perimeter which is 9 times the length of a side, decreased by 15.
Find the length of a side.
:
Let s = the length of a side
4s = 9s - 15
+15 = 9s - 4s
15 = 5s
s = 
s = 3 units
;
:
Check this
4(3) = 9(3) - 15
12 = 27 - 15
|
Proportions/408517: The world record for the mile in the year 1865 was held by Richard Webster of England when he completed the mile in 4 minutes and 36.5 seconds. The world record in 199 was set by Hicham El Guerrouj when he ran a mile in 3 minutes and 43.13 seconds. If both men ran the mile together, how many feet behind would Richard Webster be when Hichem El Guerrouj crossed the finish line?
1 solutions
Answer 287782 by ankor@dixie-net.com(15638) on 2011-02-13 15:27:23 (Show Source):
You can put this solution on YOUR website!he world record for the mile in the year 1865 was held by Richard Webster of
England when he completed the mile in 4 minutes and 36.5 seconds.
The world record in 199 was set by Hicham El Guerrouj when he ran a mile in 3 minutes and 43.13 seconds.
If both men ran the mile together, how many feet behind would Richard Webster be when Hichem El Guerrouj crossed the finish line?
:
It's hard to tell since Richard W. would be a spirit and spirits can really fly!!
:
Seriously though
:
Find R.W.'s speed in ft/sec
4 min 36.5 sec = 276.5 sec
 = 19.096 ft/sec
:
Find how far R.W. will run in the time it takes HEG to run the mile (223.13 sec)
223.13 * 19.096 = 4260.89 ft
therefore
5280 - 4260.89 = 1019.1 ft behind when HEB crosses the finish line
|
Travel_Word_Problems/408433: traveling at a rate of 60 miles per hour , Teo drives past the Meadville rest area. Thirty minutes later Sierra drives past the same rest area at a rate of 70 miles per hour. If Teo and Sierra continue to travel at their current rate , how long will it take Sierra to catch up with Teo?
1 solutions
Answer 287776 by ankor@dixie-net.com(15638) on 2011-02-13 15:12:23 (Show Source):
You can put this solution on YOUR website!traveling at a rate of 60 miles per hour, Teo drives past the Meadville rest area.
Thirty minutes later Sierra drives past the same rest area at a rate of 70 miles per hour.
If Teo and Sierra continue to travel at their current rate, how long will it take Sierra to catch up with Teo?
:
Let t = time required for S to catch T
:
Change 30 min to .5 hrs
:
From the given information, we know that when T passed the rest area, S is 30 min behind T.
At 70 mph we know; .5 * 70 = 35, therefore, S is 35 mi behind T at this time.
:
When S catches t, S has traveled 35 mi further than T,
:
Write a distance equation; dist = speed * time
:
S dist = T dist + 35 mi
70t = 60t + 35
70t - 60t = 35
10t = 35
t = 
t = 3.5 hrs for S to catch T
:
:
Check this by finding the actual dist each traveled in 3.5 hrs
3.5*70 = 245 mi
3.5*60 = 210 mi
---------------
differ: 35 mi
|
Linear_Equations_And_Systems_Word_Problems/408437: Brenda plans to make blue and purple scarfs in 2 two sizes: medium and large. She has a total of 60 yards of fabric for each color. She will need 1/4 of a yard for medium scarves and will need 1/2 a yard for large scarves. She also wants to add ribbon as a trimming to her scarves. She has a total of 240 yards of ribbon in each color. For the medium scarves, she will need 1 yard of ribbon and for the large, 2 yards. Set up two equations to solve for the number of scarves per color that can be made.
I am unsure of the equation to use.
Thus far, I have:
m=medium scarves and l=large scarves
1/4x+1/2y=60
1x+2y=240
This does not look like the appropriate form. Am I on the right track?
1 solutions
Answer 287757 by ankor@dixie-net.com(15638) on 2011-02-13 13:39:21 (Show Source):
You can put this solution on YOUR website!Brenda plans to make blue and purple scarfs in 2 two sizes: medium and large.
She has a total of 60 yards of fabric for each color.
She will need 1/4 of a yard for medium scarves and will need 1/2 a yard for large scarves.
She also wants to add ribbon as a trimming to her scarves.
She has a total of 240 yards of ribbon in each color.
For the medium scarves, she will need 1 yard of ribbon and for the large, 2 yards.
Set up two equations to solve for the number of scarves per color that can be made.
:
I think you have the right idea here.
Developing what you already have: x = med scarves, y = lg scarves
.25x + .5y = 60; fabric eq:
and
1x + 2y = 240; ribbon eq:
:
If you multiply the 1st equation by 4, both equations are the same, there is no unique solution
:
There are many solutions, we can find the number of each size like this:
x = 240-2y
For example if you have 50 lg scarves, y = 50
x = 240-2(50)
x = 240 - 100
x = 140 med scarves
or
If you have 80 lg scarves, y = 80
x = 240-2(80)
x = 240 - 160
x = 80 med scarves
:
:
You can see that both these x,y values will satisfy your original equations.
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Linear-systems/408453: heyy im amina i was just wondering how do slove this
3x+2y=5
5x-2y=7
1 solutions
Answer 287751 by ankor@dixie-net.com(15638) on 2011-02-13 13:00:45 (Show Source):
You can put this solution on YOUR website!Hey! I'm Amina. I was just wondering, how do you solve this?
:
3x + 2y = 5
5x - 2y = 7
:
These equations lend themselves very well to the "elimination method"
3x + 2y = 5
5x - 2y = 7
---------------adding eliminates y, find x
8x + 0y = 12
x = 
x = 1.5
:
Find y using the 1st equation, replace x with 1.5.
3(1.5) + 2y = 5
4.5 + 2y = 5
2y = 5 - 4.5
2y = .5
y = 
y = .25
:
Check the solutions: x = 1.5 and y = .25; in the 2nd equation.
5(1.5) - 2(.25) = 7
7.5 - .5 = 7
7 = 7; equality reigns, our solutions are correct
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Age_Word_Problems/408305: I am 30 and my daughter is 3 so I was 27 when she was born. At what age will I be 3 times her age?
1 solutions
Answer 287744 by ankor@dixie-net.com(15638) on 2011-02-13 11:01:31 (Show Source):
You can put this solution on YOUR website!I am 30 and my daughter is 3 so I was 27 when she was born.
At what age will I be 3 times her age?
:
Let y = no. of years for this to be true
:
A simple equation:
:
y + 30 = 3(y + 3)
y + 30 = 3y + 9
30 - 9 = 3y - y
21 = 2y
y = 
y = 10.5 yrs
:
In 10.5 years you will be 3 times as old as your daughter
:
:
Confirm this
30 + 10.5 = 3(3 + 10.5)
40.5 = 3(13.5)
40.5 = 40.5; usually these kind of problems have integer solutions but this one does not.
3
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Age_Word_Problems/408347: To train for a marathon, Mei runs an 18-mile course at constant speed. If she doubles her usual speed, she can compete the course in an hour and a half less than her usual time. What is Mei's usual speed and her usual time to compete the course
1 solutions
Answer 287741 by ankor@dixie-net.com(15638) on 2011-02-13 10:52:32 (Show Source):
You can put this solution on YOUR website!Mei runs an 18-mile course at constant speed.
If she doubles her usual speed, she can compete the course in an hour and a half less than her usual time.
What is Mei's usual speed and her usual time to compete the course?
:
Change 1 hr and a half to 1.5 hrs
:
Let s = the normal speed
then
2s = double the normal speed
:
Write a time equation, Time = dist/speed
:
Usual time - faster time = 1.5 hrs
 -  = 1.5
multiply by 2s to clear denominators, results:
2(18) - 18 = 2s(1.5)
36 - 18 = 3s
18 = 3s
s = 
s = 6 mph is the usual speed
:
Find the usual time
= 3 hrs is the usual time
:
:
Check solution by finding the time at the faster speed (12 mph)
 = 1.5 hrs, which is 1.5 hrs faster than the usual time of 3 hrs
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Expressions-with-variables/408284: solve the system by substitution.
1. x+y=-7
x=y+19
show step by step work please
also 2. x^2=5
number 2 is not solving by substitution. It just says solve.
1 solutions
Answer 287689 by ankor@dixie-net.com(15638) on 2011-02-12 21:57:51 (Show Source):
You can put this solution on YOUR website!solve the system by substitution.
x + y =-7
x = y + 19
Use the 2nd equation for substitution in the 1st equation
In the 1st equation replace x with (y+19)
(y+19) + y = -7
2y = -7 - 19
2y = -26
y = 
y = -13
Find x using the 2nd equation, replace y with -13
x = -13 + 19
x = +6
check solutions, substitute for x and y in the 1st equation
6 - 13 = -7
:
:
also 2. x^2=5
Find the square root of both sides
x = +/- 
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Rational-functions/408234: Can someone please help me graph this parabola? -x^2+812x-9600 I have solved for the vertex (406,484908). I know the parabola opens downward. I can get the line of symmetry also. The problem I am having is the question says to "include solutions (roots)". I am not sure what this means or how to do it.
1 solutions
Answer 287685 by ankor@dixie-net.com(15638) on 2011-02-12 21:41:45 (Show Source):
You can put this solution on YOUR website!The roots are the values of x where the graph crosses the x axis (y=0)
:
In this equation find the roots using the quadratic formula:
in this equation a=-1; b=812; c=-9600
you should get two solutions
x=800
x= 12
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Age_Word_Problems/408242: a man is four times older than his wife and five times as old as his son. when the son was born, the age of the wife is six-seventh that of her husband's age. find the age of his wife?
1 solutions
Answer 287672 by ankor@dixie-net.com(15638) on 2011-02-12 21:08:36 (Show Source):
You can put this solution on YOUR website!a man is four times older than his wife and five times as old as his son. when the son was born, the age of the wife is six-seventh that of her husband's age. find the age of his wife?
:
This problem is nonsense, 4 times his wife's age and 5 times his son's age is a
physical impossibility, for example if the man was 80, wife is 20, son is 16 ??
The last statement is even more ridiculous .
Whoever inflicted this on you should be be publicly flogged
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Geometry_Word_Problems/408221: 1. The area of a rectangular room is 300 ft2. The perimeter is 70 ft. What are the dimensions of the room?
i tried to do this, but it doesnt work!!!!
100x3, 2x150, 1x300, 5x60, 6x50
thx!
1 solutions
Answer 287661 by ankor@dixie-net.com(15638) on 2011-02-12 19:08:46 (Show Source):
You can put this solution on YOUR website!1. The area of a rectangular room is 300 ft2.
The perimeter is 70 ft. What are the dimensions of the room?
:
The perimeter:
2L + 2W = 70
Simplify, divide by 2
L + W = 35
W = (35-L); use this form for substitution
:
The area:
L * W = 300
replace W with (35-L)
L*(35-L) = 300
-L^2 + 35L = 300
-L^2 + 35L - 300 = 0
Easier to factor if L^2 is positive, multiply by -1
L^2 - 35L + 300 = 0
Factor this to
(L-15)(L-20) = 0
Two solutions
L = 15
L = 20 ft
choose the larger value for L, 20 ft, find W
W = 35 - 20
W = 15 ft is the width
:
:
See if that is true
2(20) + 2(15) = 70
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Trigonometry-basics/408082: a weather balloon ascends at a rate of 3.86 km/h while moving at an angle of 71.8 degrees with the ground. at the end of an hour what is the horizontal travel (x) of the balloon?
1 solutions
Answer 287659 by ankor@dixie-net.com(15638) on 2011-02-12 19:00:09 (Show Source):
You can put this solution on YOUR website!a weather balloon ascends at a rate of 3.86 km/h while moving at an angle of 71.8 degrees with the ground.
at the end of an hour what is the horizontal travel (x) of the balloon?
:
At the end of an hr the balloon will be 3.86 km high
:
Use the tangent of 71.8 degrees, side opposite = 3.86, side adjacent = x
:
tan(71.8) = 
x = 
x = 1.27 km is the horizontal travel
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Travel_Word_Problems/408091: Jack and Tim were standing in the main street. The distance between the boys was x metres. At the same moment the boys started to move. Jack was running at a m/s and Tim walked at b m/s.
Find the time when the boys met if
a) they moved towards each other,
b) they moved in the same direction, walker in front.
1 solutions
Answer 287636 by ankor@dixie-net.com(15638) on 2011-02-12 17:00:33 (Show Source):
You can put this solution on YOUR website!Jack and Tim were standing in the main street. The distance between the boys was x metres.
At the same moment the boys started to move, Jack was running at a m/s and Tim walked at b m/s.
Find the time when the boys met if:
:
time = dist/speed
dist = x
:
a) they moved towards each other,
time = 
:
b) they moved in the same direction, walker in front.
time = 
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Travel_Word_Problems/408171: Carl can walk from his home to school in 30 minutes. It takes his sister 35 minutes to walk the same distance. How long would it take them to meet, if one started from school and the other at home at the same time and they walked toward each other at their usual speeds.
1 solutions
Answer 287633 by ankor@dixie-net.com(15638) on 2011-02-12 15:57:34 (Show Source):
You can put this solution on YOUR website!Carl can walk from his home to school in 30 minutes.
It takes his sister 35 minutes to walk the same distance.
How long would it take them to meet, if one started from school and the other
at home at the same time and they walked toward each other at their usual speeds
:
let t = time to meet walking towards each other
:
Let d = the distance from home to school
then
 = C's walking speed
and
 = S's walking speed
:
Write a distance equation; dist = speed * time
:
C's dist + S's dist = total dist
t( ) + t( ) = d
:
divide thru by d, we don't need that, results:
(  ) + (  ) = 1
multiply by 210 to clear the denominators
7t + 6t = 210
13t = 210
t = 
t = 16.154 minutes for them to meet
:
:
prove our solution with some real numbers, let d = 210 units
then
210/30 = 7 units per minute is C's walking speed
and
210/35 = 6 units per minute is S's walking speed
:
Find the total distance they walked in 16.154 min
16.154(7) = 16.154(6) =
113.078 + 96.924 = 210.00 confirms our solution of t = 16.154 minutes
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Equations/408184: Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line with a slope of 6.
With 53 gallons of fuel in its tank, the airplane has a weight of 2318 pounds. What is the weight of the plane with 28 gallons of fuel in its tank?
1 solutions
Answer 287627 by ankor@dixie-net.com(15638) on 2011-02-12 15:33:49 (Show Source):
You can put this solution on YOUR website!Suppose that the weight (in pounds) of an airplane is a linear function of the
total amount of fuel (in gallons) in its tank.
When graphed, the function gives a line with a slope of 6.
With 53 gallons of fuel in its tank, the airplane has a weight of 2318 pounds.
:
Use the point/slope formula y - y1 = m(x - x1): where
x1 = 53
y1 = 2318
m = 6
:
y - 2318 = 6(x - 53)
y - 2318 = 6x - 318
y = 6x - 318 + 2318
y = 6x + 2000
:
What is the weight of the plane with 28 gallons of fuel in its tank?
x = 28
y = 6(28) + 2000
y = 168 + 2000
y = 2168 lb with 28 gal of fuel
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Numbers_Word_Problems/408103: when the cube of a number is added to twice its square, the result is equal to 18 more than 9 times the number
1 solutions
Answer 287623 by ankor@dixie-net.com(15638) on 2011-02-12 15:24:10 (Show Source):
You can put this solution on YOUR website!when the cube of a number is added to twice its square,
the result is equal to 18 more than 9 times the number
:
x^3 + 2x^2 = 9x + 18
x^3 + 2x^2 - 9x - 18 = 0
Factor by grouping
x^2(x + 2) - 9(x + 2)
Factor out (x+2) and you have:
(x^2 - 9)(x + 2) = 0
x = -2
and
x^2 - 9 = 0
difference of squares
(x-3)(x+3) = 0
x = 3
x = -3
:
Check all three solutions in original equation
x^3 + 2x^2 = 9x + 18
x=-2
(-2)^3 + 2(-2)^2 = 9(-2) + 18
-8 + 8 = -18 + 18; a good solution
:
x=3
3^3 + 2(3^2) = 9(3) + 18
27 + 18 = 27 + 18; a good solution
:
(-3)^3 + 2(-3^2) = 9(-3) + 18
-27 + 18 = -27 + 18; a good solution also
:
we can say, x = -2, -3, +3, are all solutions of x
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Travel_Word_Problems/408154: a new schedule for a train requires it to go 270 miles in 26 minutes less time than before. To do thsi it must average 4 mpoh faster. What must its new average speed be?
1 solutions
Answer 287618 by ankor@dixie-net.com(15638) on 2011-02-12 15:06:03 (Show Source):
You can put this solution on YOUR website!a new schedule for a train requires it to go 270 miles in 26 minutes less time than before.
To do this it must average 4 mph faster.
What must its new average speed be?
:
Let s = the new average speed
then
(s-4) = the old average speed
:
Change 26 min to  =  hrs
:
write a time equation: time = dist/speed
Old time - new time = 26 min
 -  =
:
Multiply equation by 30s(s-4) to get rid of the denominators, results:
30s(270) - 30(s-4)(270) = 13s(s-4)
8100s - 8100(s-4) = 13s^2 - 52s
8100s - 8100s + 32400 = 13s^2 - 52s
Combine to form a quadratic equation
0 = 13s^2 - 52s - 32400
Solve this using the quadratic formula a=13, b=-52, c=-32400
:
The positive solution: s = 51.963 ~ 52 mph is the new average speed
;
:
Check solution in decimals
270/48 - 270/52 = .4327 * 60 ~ 26.0 min
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