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Inequalities/87379: The length of the rectangle is 3 times its width. The perimeter of the rectangle is 160 ft. Find the length and the width of the rectangle. Solve the problem algebraically.
1 solutions
Answer 63319 by Nate(3500)   on 2007-07-06 01:42:24 (Show Source):
You can put this solution on YOUR website!width = w
length = 3w
2*width + 2*length = perimeter
2(w) + 2(3w) = 160
2w + 6w = 160
8w = 160
w = 20
width = 20 feet
length = 60 feet
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Functions/87222: I am not sure if I have the right answer. use f(x) = 5^x find x
f(x)=- 1/125
5^x = -5^-3
x=3
1 solutions
Answer 63167 by Nate(3500) on 2007-07-04 00:14:41 (Show Source):
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Rational-functions/87220: Determine, approximately using a graph, the intervals on which the function
f(x)=x^3 + 3x^2-7x-1 is increasing and decreasing.
1 solutions
Answer 63164 by Nate(3500) on 2007-07-03 23:51:53 (Show Source):
You can put this solution on YOUR website!f(x) = x^3 + 3x^2 - 7x - 1
A function will change from decreasing to increasing or vise versa after hitting a peak or a valley (a minima or maxima).
Approx. at -3 and 1 the function changes signs.
Exact:
f(x) = x^3 + 3x^2 - 7x - 1
f'(x) = 3x^2 + 6x - 7
0 = 3x^2 + 6x - 7
7 = 3x^2 + 6x
7/3 = x^2 + 2x
10/3 = (x + 1)^2
-1 +- sqrt(10/3) = x
When: x < -1 - sqrt(10/3) .. the function is increasing
When: -1 - sqrt(10/3) < x < -1 + sqrt(10/3) .. the function is decreasing
When: -1 + sqrt(10/3) < x .. the function is increasing again
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Rational-functions/87218: For the function f(x)= -3x^2 + x- 11, determine the difference quotient
f(a+h) - f(a)/h where h is not equal to 0. Simplify your result as much as possible.
1 solutions
Answer 63163 by Nate(3500) on 2007-07-03 23:45:28 (Show Source):
You can put this solution on YOUR website!lim( h -> 0 ) ( f(a + h) - f(a) ) / h
lim( h -> 0 ) ( -3(a + h)^2 + (a + h) - 11 + 3a^2 - a + 11 ) / h
lim( h -> 0 ) ( -3(a^2 + 2ah + h^2) + a + h - 11 + 3a^2 - a + 11 ) / h
lim( h -> 0 ) ( -3a^2 - 6ah - 3h^2 + h + 3a^2 ) / h
lim( h -> 0 ) ( -6ah - 3h^2 + h ) / h
lim( h -> 0 ) -6a - 3h + 1
~Derive~
lim( h -> 0 ) -6a - 3(0) + 1 = -6a + 1
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Rational-functions/87219: Determine any (global) maxima or minima of the function g(x)=x^2-x-20.
1 solutions
Answer 63162 by Nate(3500) on 2007-07-03 23:37:38 (Show Source):
You can put this solution on YOUR website!g(x) = x^2 - x - 20
This is a vertical parabola with the leading coefficient being positive.
The vertex will be a minimum.
(0.5,f(0.5))
(0.5,-20.25)
Minima of -20.25
~Calc~
g(x) = x^2 - x - 20
g'(x) = 2x - 1
g''(x) = 2
g''(0.5) > 0 ... this indicates a minima
g'(x) = 2x - 1
0 = 2x - 1
1 = 2x
0.5 = x
g(0.5) = 0.25 - 0.5 - 20 = -20.25
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Quadratic_Equations/87213: Would someone please help me with this one:
Solve the following quadratic equations by factoring or by any of the quadratic equations available such as square root, completing the square, etc.
4x^2-8x+3=5
1 solutions
Answer 63161 by Nate(3500) on 2007-07-03 23:17:36 (Show Source):
You can put this solution on YOUR website!Firstly, it is best to try and factor it:
4x^2 - 8x + 3 = 5
4x^2 - 8x - 2 = 0
It can't be factored, so the next simple thing would be to complete the square.
4x^2 - 8x = 2
x^2 - 2x = 1/2
(x - 1)^2 = 3/2
x - 1 = +- sqrt(1.5)
x = 1 +- sqrt(1.5)
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Graphs/87127: What are the slope and y-intercepts of x=-9?
1 solutions
Answer 63085 by Nate(3500) on 2007-07-03 00:04:19 (Show Source):
You can put this solution on YOUR website!x = -9 ...
Simplify the meaning by picking multiple coordinates.
( x , -2 ), ( x , -1 ), ( x , 0 ), ( x , 1 ), ( x , 2 )
There is  to plug in these values: x = 0y - 9
( -9 , -2 ), ( -9 , -1 ), ( -9 , 0 ), ( -9 , 1 ), ( -9 , 2 )
This is a vertical line, so the line doesn't intersect with the y-axis ... no y-intercepts.
slope = (y2 - y1) / (x2 - x1) = (2 - 1) / (-9 + 9) = 1 / 0
The slope is undefined.
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logarithm/87053: The size P of a small herbivore population at time t, in years obeys the function P(t)=500e^0.22t, if they have enough food and the predator population stays the same.
A) After how many years will the population reach 2500? Round to the nearest tenth.
B)What is the population after 2 and a half years. Round to the nearest whole number.
* I came up with putting 2500 in for "P" for part A, then I can't solve it right! The second part I thought put 2.5 years in for "t"...is that even right? I am SOOOOO lost! Sorry! Thanks! :)
1 solutions
Answer 63026 by Nate(3500) on 2007-07-02 00:26:46 (Show Source):
You can put this solution on YOUR website!A) After how many years will the population reach 2500? Round to the nearest tenth.
P(t) = 500e^0.22t
2500 = 500e^0.22t
5 = e^0.22t
ln( 5 ) = ln( e^0.22t )
ln( 5 ) = 0.22t
ln( 5 )/0.22 = t
log( 5 ) / ( 0.22*log( e ) ) = t
About 7.3 years
B)What is the population after 2 and a half years. Round to the nearest whole number.
t = 2.5 would be true
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Polynomials-and-rational-expressions/87054: Please help me to solve the following problem:
Factor each polynomial completely, given that the binomial following it is a factor of the polynomial:
x^3+4x^2-3x+10, x+5
Thank you
1 solutions
Answer 63022 by Nate(3500) on 2007-07-01 23:55:48 (Show Source):
You can put this solution on YOUR website!x^3 + 4x^2 - 3x + 10, x + 5
Synthetic Division (do long division if you do not know how to solve this way):
-5 | .... 1 ...... 4 ...... -3 ...... 10
..............1.......-1........2.........0
(x + 5)(x^2 - x + 2)
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Polynomials-and-rational-expressions/87060: Please help me to solve this word problem:
Decreasing cube: 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?
Thank you
1 solutions
Answer 63021 by Nate(3500) on 2007-07-01 23:52:09 (Show Source):
You can put this solution on YOUR website!If the original cube had a height, width, and length of units and a the width decreased by 6 to make a new cube, wouldn't each side be  units? ... This must be a rectanguler prism. ...
y^3 - 13y^2 + 54y - 72 = height * width * length
y^3 - 13y^2 + 54y - 72 = height * (y - 6) * length
(y^3 - 13y^2 + 54y - 72) / (y - 6) = height * length
Synthetic Division being the fastest (if you do not know how to do this procedure, do the long division):
6 | ..... 1 ...... -13 ...... 54 ...... -72
............1...........-7.........12..........0
y^2 - 7y + 12 = height * length
(y - 4)(y - 3) = height * length
y - 4 is either a height or a length
y - 3 is either a length or a height
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Polynomials-and-rational-expressions/86422: I need help with this question: use Descartes's Rule of Signs to determine the possible number of positive and negative zeros of the function: f(x)=x^6+4x^5-4x^4+5x^3-5x^2+x-5
1 solutions
Answer 62925 by Nate(3500) on 2007-06-30 13:19:30 (Show Source):
You can put this solution on YOUR website!f(x) = x^6 + 4x^5 - 4x^4 + 5x^3 - 5x^2 + x - 5
f(+x) ~> (+) (+) (-) (+) (-) (+) (-)
Positive Roots: 5
f(-x) ~> (+) (-) (-) (-) (-) (-) (-)
Negative Roots: 1
~~~
Pos: 5 . 3 . 1
Neg: 1 . 1 . 1
Img: 0 . 2 . 4
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Money_Word_Problems/86892: The odds against a horse winning a race are 6 to 5. What is the probability of the horse winning the race?
1 solutions
Answer 62852 by Nate(3500) on 2007-06-29 15:31:37 (Show Source):
You can put this solution on YOUR website!The odds against a horse winning a race are 6 to 5.
Odds are taken as: chances of winning: chances of losing
Probability: chances of winning / total chances
Prob: 6 / (6 + 5) = 6 / 11 = about 54.5%
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Square-cubic-other-roots/86904: Good day to everyone,I need some help with some square root problems,sorry but I don't have the square root symbol on my computer,but the problems I'm sending have the square roots over them,the first one is,If x=(square root symbol over)0.04,what is the value of x?The next one is,Estimate the value of the square root:(square root symbol over)0.85.And that's about it,thanks for anyone that can help.
1 solutions
Answer 62851 by Nate(3500) on 2007-06-29 15:27:40 (Show Source):
You can put this solution on YOUR website!x = sqrt(0.04)
x = sqrt(4*10^-2)
x = 2*sqrt(1/100)
x = 2(1/10) = 1/5
~
sqrt(0.85)
sqrt(85*10^-2)
sqrt(5*17/100)
sqrt(85)/10
sqrt(85) is between 9 and 10 ... closer to 9
~> 9.2/10 = about 0.92
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Miscellaneous_Word_Problems/86905: I need some help oh this word problem:
In order to pass a college class it is necessary to obtain an average of 70% correct on three tests of 100 points each and on one final exam of 200 points. If a students scores 81, 62, 63 on the tests, what is the minimum score on the final exam that the student can receive and still pass the course?
1 solutions
Answer 62850 by Nate(3500) on 2007-06-29 15:24:17 (Show Source):
You can put this solution on YOUR website!81/100, 62/100, 63/100, x
81%, 62%, 63%, x
(81% + 62% + 63% + x) / 4 >= 70%
(0.81 + 0.62 + 0.63 + x) / 4 >= 0.7
0.81 + 0.62 + 0.63 + x >= 2.8
x >= 0.74
x >= 74%
74% of 200 = 148
x >= 148 points
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Linear-systems/86906: Yuk! I hate applications. I always get mixed up picking picking what goes where in the equations. I had one person show me how to solve it using just equations, another showed me how by using a table. I'm confused with both of them.
Here it is.
A truck rental agency charges a daily fee plus a milage fee. Mel was charged $85 for 2 days plus 100 miles, and Sarah was charged $165 for 3 days and 400 miles. What is the agency's daily fee and their milage fee?
a) Write the system of equations for this problem.
b) Find the solution.
1 solutions
Answer 62849 by Nate(3500) on 2007-06-29 15:19:04 (Show Source):
You can put this solution on YOUR website!x will be the cost per mile
y will be the cost per day
.
Mel was charged $85 for 2 days plus 100 miles.
85 bucks for the sum of the costs
2 days would cost 2y
100 miles would cost 100x
2y + 100x = 85
.
Sarah was charged $165 for 3 days and 400 miles.
165 bucks for the sum of the costs
400 miles would cost 400x
3 days would cost 3y
3y + 400x = 165
.
a) Write the system of equations for this problem.
2y + 100x = 85
3y + 400x = 165
.
b) Find the solution.
-4(2y + 100x = 85)
3y + 400x = 165
.
-8y - 400x = -340
3y + 400x = 165
.
-5y = -175
y = 35
.
Pick one of the initial equations:
2y + 100x = 85
2(35) + 100x = 85
70 + 100x = 85
100x = 15
x = 0.15
.
$35 per day and $0.15 per mile
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logarithm/86866: Most calculators have 2 different logs on them: log, which is base 10, and ln, which is base e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he needs a log to base 2 which is not on any calculator. To find the log of a number to any base, we can use a conversion formula as shown here:
Using the formula, find log2 1000. Round your answer to the hundredths place.
1 solutions
Answer 62825 by Nate(3500) on 2007-06-29 00:38:08 (Show Source):
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Linear_Algebra/86861: f(x) = xsquared - x - 2 if f = 0,-2,1 I think i have to put the o and -2 and 1 where the x is and then do the equation but when I have a -2 and i subsitute it where their is a minus x then do I add the 2
1 solutions
Answer 62821 by Nate(3500) on 2007-06-28 23:41:15 (Show Source):
You can put this solution on YOUR website!If you get caught up in all the sign changes, I advise to use paranthesis.
f(x) = x^2 - x - 2
f(x) = (x)^2 - (x) - 2
~
If: f(x) = 0,-2,1
0 = (x)^2 - (x) - 2
-2 = (x)^2 - (x) - 2
1 = (x)^2 - (x) - 2
~
If: x = 0,-2,1
f(0) = (0)^2 - (0) - 2 = -2
f(-2) = (-2)^2 - (-2) - 2 = 4 + 4 - 2 = 6
f(1) = (1)^2 - (1) - 2 = 1 - 1 - 2 = -2
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Expressions-with-variables/86858: The height of a hot-air balloon was measured at different times as the balloon descended. A record of the heights and times is shown in the table below.
time(t) in minutes 1 2 3 4
Height (h) in meters 76 64 44 16
Based on the table, which of the following equations expresses the relationship between h and t?
(1) h = 60 + 16t
(2) h = 70 + 6t
(3) h = 80 - 4t
(4) h = 80 - 4t squared
(5) h = 90 - 14t squared
I don't understand this problem at all? Could you please solve?
1 solutions
Answer 62820 by Nate(3500) on 2007-06-28 23:15:56 (Show Source):
You can put this solution on YOUR website!You have coordinates: (t,h)
time(t) in minutes 1 2 3 4
Height (h) in meters 76 64 44 16
So:
(1,76), (2,64), (3,44), (4,16)
Obviously, the equation would not be linear due to the fact that after each minute the height doesn't change by a constant number.
(4) h = 80 - 4t squared
(5) h = 90 - 14t squared
Are the only two choices....
Now, we should plug in a value:
(4) h = 80 - 4(1) squared = 80 - 4 = 76
(5) h = 90 - 14(1) squared = 90 - 14 = 76
So, for each we have: (1,76) ... which applies to the value above
Now, we should plug in a different value:
(4) h = 80 - 4(2) squared = 80 - 16 = 64
(5) h = 90 - 14(2) squared = 90 - 56 = 34
(4) is the only equation that suits our two values ...
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Functions/86853: Find the value(s) of x for which f(x)=g(x)
f(x)=x"squared"+10x-14, g(x)=9x-8
so far i have:
x"squared"+10x-14=9x-8
1 solutions
Answer 62818 by Nate(3500) on 2007-06-28 22:35:54 (Show Source):
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