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Numeric_Fractions/40484: Can someone help me?
I need to write the proportion that is equivalent to the given statement:
If Maria hit 8 home runs in 15 softball games, then she should hit 24 home runs in 45 games.
Thank you!
Lyn
1 solutions
Answer 25874 by Nate(3500) About Me  on 2006-06-02 19:45:03 (Show Source):

Numeric_Fractions/40483: I need some help on this problem.
Which is the better buy: 5 lb. of sugar for $4.75 or 20 lb. of sugar for $19.92?
Thanks,
Lyn
1 solutions
Answer 25873 by Nate(3500) About Me  on 2006-06-02 19:43:45 (Show Source):
You can put this solution on YOUR website!
$4.75/5 = cost per pound of sugar = $0.95
$19.92/20 = cost per pound of sugar = $0.996
The smaller sugar bag is the best buy.

Equations/40471: please help me solve this equation: 2x^2+4x=-2
1 solutions
Answer 25872 by Nate(3500) About Me  on 2006-06-02 19:40:10 (Show Source):
You can put this solution on YOUR website!
2x%5E2+%2B+4x+=+-2
2x%5E2+%2B+4x+%2B+2+=+0
2x%5E2+%2B+2x+%2B+2x+%2B+2+=+0
2x%28x+%2B+1%29+%2B+2%28x+%2B+1%29+=+0
%282x+%2B+2%29%28x+%2B+1%29+=+0
2x+%2B+2+=+0 or x+%2B+1+=+0
2x+=+-2 or x+=+-1
x+=+-1 or x+=+-1
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%2B2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A2%2A2=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%284%29%29%2F2%5C2.
Expression can be factored: 2x%5E2%2B4x%2B2+=+2%28x--1%29%2A%28x--1%29

Again, the answer is: -1, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B2+%29

Functions/40472: Could someone please help me understand how to solve this question? I really need help.
Velocity. If a ball is dropped from a height of 256 ft, then the formula
v(t) = -32t
expresses it’s velocity v(t) in feet per second as a function of time t in seconds.
a) Find v(0), the velocity of the ball at the time t = 0.
b) Find v(4).


1 solutions
Answer 25871 by Nate(3500) About Me  on 2006-06-02 19:36:12 (Show Source):
You can put this solution on YOUR website!
a) Find v(0), the velocity of the ball at the time t = 0.
v(t) = -32t
v(t) = -32(0)
v(t) = 0
b) Find v(4).
v(t) = -32t
v(t) = -32(4)
v(t) = -128

Inverses/40476: I tried finding a solver on the site to find the reciprocal for this question.
y^2+5y-9 / y^2-9y+3
This is a bit tricky.
I simply dont understand it.
1 solutions
Answer 25870 by Nate(3500) About Me  on 2006-06-02 19:33:08 (Show Source):
You can put this solution on YOUR website!
The recipricol of 4 is (1/4), so the recipricol of this is:
%28y%5E2-9y%2B3%29%2F%28y%5E2%2B5y-9%29

Inverses/40473: I am attemping to solve this rational expression problem.
The problem consist of adding and simplifying .
6w/w^2-64 + w/w-8
i think the answer is w^2+8 / (w-4)(w+4)
However I am unsure ..
If I performed this problem incorrectly
Please show me the correct format.
1 solutions
Answer 25869 by Nate(3500) About Me  on 2006-06-02 19:31:00 (Show Source):

test/40464: how can I find the equations if its a word problem???can somebody give me some ideas on how??pleaseeeeeeeeeeeeeeee...........
1 solutions
Answer 25864 by Nate(3500) About Me  on 2006-06-02 17:09:42 (Show Source):
You can put this solution on YOUR website!
You read and focus on the main points. You should type it out for us to solve.

Rate-of-work-word-problems/40454: This question is from textbook
There are 2 overflow pipes at a dam. The larger overflow pipe can lower the level of the water in the reservoir by 1 foot in 45 minutes. The smaller one lowers the level of water by 1 foot in 2 hours 15 minutes. If both overflow pipes are open at the same time, how long will it take them to lower the level of water by 1 foot? Thenk you in advance.
1 solutions
Answer 25863 by Nate(3500) About Me  on 2006-06-02 17:08:17 (Show Source):
You can put this solution on YOUR website!
Rate of the first pipe is (1/45). The rate of the second pipe is (1/135).
Rate times time yields work, so the you have: (t/45) and (t/135).
%28t%2F45%29+%2B+%28t%2F135%29+=+1 one job is being done
135%28t%2F45%29+%2B+135%28t%2F135%29+=+135
3t+%2B+t+=+135
4t+=+135
t+=+33.75
(0.75)(60) = 45
33 minutes and 45 seconds

Polynomials-and-rational-expressions/40463: 36a^2b^3-45ab^4
1 solutions
Answer 25862 by Nate(3500) About Me  on 2006-06-02 16:59:36 (Show Source):

Polynomials-and-rational-expressions/40459: This question is from textbook
1-9/x^2
________
1- 1/x - 6/x^2
Simplify the complex fraction
1 solutions
Answer 25861 by Nate(3500) About Me  on 2006-06-02 16:56:50 (Show Source):

Polynomials-and-rational-expressions/40458: This question is from textbook
_4a___
2a^3+2
_________
___8a____
4a+4
Simplify the complex fraction.
1 solutions
Answer 25860 by Nate(3500) About Me  on 2006-06-02 16:53:06 (Show Source):

Polynomials-and-rational-expressions/40461: This question is from textbook
x+6/x+3 - 2 = 3/x+3
1 solutions
Answer 25856 by Nate(3500) About Me  on 2006-06-02 16:47:47 (Show Source):
You can put this solution on YOUR website!
%28x+%2B+6%29%2F%28x+%2B+3%29+-+2+=+3%2F%28x%2B3%29

x+%2B+6+-+2x+-+6+=+3
-x+=+3
x+=+-3
Negative three can not be an answer due to anything divided by zero is undefined, so there are no real solutions.

Inequalities/40457: please help!!
If 100C^2 has a value of 4,950, what is the value of 100C^98?
I thought it would be that 2475*98 would give me the answer but that wasnt an option
1 solutions
Answer 25855 by Nate(3500) About Me  on 2006-06-02 16:44:52 (Show Source):

Permutations/40456: please help... I tried the 10*9*8*7*6*5*4*3*2*1 and that was not an option
a teacher has a set of 12 problems to use on a math exam. The teacher makes different versions of the exam by putting 10 questions on each exam. How many differsnt exams can the teacher make?
1 solutions
Answer 25853 by Nate(3500) About Me  on 2006-06-02 16:39:05 (Show Source):
You can put this solution on YOUR website!
You would use permutations:
P(12,10) = 12!/(2!) = 239,500,800
This is if she cares how the test questions are ordered.

Polynomials-and-rational-expressions/37515: _/245 integers is? 4&5 or 17&18 15 &16 49&50
1 solutions
Answer 25852 by Nate(3500) About Me  on 2006-06-02 16:34:01 (Show Source):
You can put this solution on YOUR website!
(x)(x + 1) = 245
x^2 + x - 245 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B245+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%281%29%5E2-4%2A1%2A245=-979.

The discriminant -979 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -979 is + or - sqrt%28+979%29+=+31.288975694324.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B245+%29

No such integers exists!

Polynomials-and-rational-expressions/40435: Solve for X
X^2(2x-5)^2+x(5-2x)^3
Possible answers:
a. -13
b. -13/2
c. 13/2
d. 13
1 solutions
Answer 25851 by Nate(3500) About Me  on 2006-06-02 16:30:05 (Show Source):
You can put this solution on YOUR website!
x%5E2%282x-5%29%5E2+%2B+x%285-2x%29%5E3=0
x%5E2%284x%5E2+-+20x+%2B+25%29+%2B+x%28-8x%5E3+%2B+60x%5E2+-+150x+%2B+125%29+=+0
4x%5E4+-+20x%5E3+%2B+25x%5E2+%2B+-8x%5E4+%2B+60x%5E3+-+150x%5E2+%2B+125x+=+0
-4x%5E4+%2B+40x%5E3+-+125x%5E2+%2B+125x+=+0
Plug in your available answers, and none work.

Polynomials-and-rational-expressions/40385: Simply.
x^4 * x^-6
1 solutions
Answer 25850 by Nate(3500) About Me  on 2006-06-02 16:14:00 (Show Source):

Quadratic_Equations/40361: The hypotinuse of a right triangle is 8cm long. One leg is 2 cm longer than the other. find the length of the longer leg to the nearest tenth.
Thank you

1 solutions
Answer 25848 by Nate(3500) About Me  on 2006-06-02 16:08:00 (Show Source):
You can put this solution on YOUR website!
One leg = z
Other leg = x
Equation:
z+%2B+2+=+x
Use pythagorus formula:
a%5E2+%2B+b%5E2+=+c%5E2
z%5E2+%2B+x%5E2+=+8%5E2
z%5E2+%2B+%28z+%2B+2%29%5E2+=+64
z%5E2+%2B+z%5E2+%2B+4z+%2B+4+=+64
2z%5E2+%2B+4z+-+60+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%2B-60+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A2%2A-60=496.

Discriminant d=496 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+496+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+496+%29%29%2F2%5C2+=+4.56776436283002
x%5B2%5D+=+%28-%284%29-sqrt%28+496+%29%29%2F2%5C2+=+-6.56776436283002

Quadratic expression 2x%5E2%2B4x%2B-60 can be factored:
2x%5E2%2B4x%2B-60+=+2%28x-4.56776436283002%29%2A%28x--6.56776436283002%29
Again, the answer is: 4.56776436283002, -6.56776436283002. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-60+%29

z is about 4.6
x is about 6.6

Polynomials-and-rational-expressions/40362: This question is from textbook
3 + ___4____
5x - 2
1 solutions
Answer 25847 by Nate(3500) About Me  on 2006-06-02 16:02:11 (Show Source):

Polynomials-and-rational-expressions/40382: Simplify.
(x^-2)^-3 / x^-4
1 solutions
Answer 25845 by Nate(3500) About Me  on 2006-06-02 15:58:11 (Show Source):

Probability-and-statistics/40453: please help me with this
in how many ways can you arrange eight books on a shelf?
and for my knowledge how would you figure out a question like this?
1 solutions
Answer 25844 by Nate(3500) About Me  on 2006-06-02 15:52:26 (Show Source):
You can put this solution on YOUR website!
P(8,8) = 8!/0! = 40,320
You would use permutations because your arrangement does matter.
Also, look at this:
How many books can be first? .... answer: 8
How many books can be second? .... answer: 7
How many books can be third? .... answer: 6
How many books can be fourth? .... answer: 5
How many books can be fifth? .... answer: 4
How many books can be sixth? .... answer: 3
How many books can be seventh? .... answer: 2
How many books can be eigth? .... answer: 1
Find the product of the whole row .... 8*7*6*5*4*3*2*1 = 40,320

Money_Word_Problems/40347: How long will it take a $9000 investment to earn $180 interest at an annual interest rate of 8%?
Thanks you very much

1 solutions
Answer 25842 by Nate(3500) About Me  on 2006-06-02 15:46:36 (Show Source):
You can put this solution on YOUR website!
I = PRT
180 = 9000*0.08*T
(1/4) = T
3 Months

expressions/40369: Simplify (be sure to rationalize all denominators)
11. 3/[SQRT(5) - 2]
I tried and got this for my answer, 1/-2/3+5/9. This isn't right and I dont know exactly how to go about finding the correct answer. Thank you!
1 solutions
Answer 25841 by Nate(3500) About Me  on 2006-06-02 15:41:33 (Show Source):

Polynomials-and-rational-expressions/40452: I would like to know how to simplify this problem
2 9
_____ + ____
x + 4 5x + 20

the 2 is over the x + 4, and the 9 is over the 5x + 20
1 solutions
Answer 25840 by Nate(3500) About Me  on 2006-06-02 15:37:09 (Show Source):

Money_Word_Problems/40342: $700 simple interest was earned over 4 years on an investment of $2500. What was the annual rate?
1 solutions
Answer 25838 by Nate(3500) About Me  on 2006-06-02 15:29:57 (Show Source):
You can put this solution on YOUR website!
I = PRT
700 = 2500*R*4
7/100 = 0.07 = R
The rate was 7%

Money_Word_Problems/40348: one thousand dollars in a savings account pays 7% interest per year. The interest earned after the first year is added to the account. How much interest is earned on the new principle the following year?
Thanks you very much

1 solutions
Answer 25836 by Nate(3500) About Me  on 2006-06-02 15:27:01 (Show Source):
You can put this solution on YOUR website!
I = PRT
I = 1000*0.07*1 = 70
now ...
I = PRT = 1070*0.07*1 = 74.9
or
P(a) = a(1 + r)^t = 1000(1.07)^2 = 1144.9
Throughout the time, the total interest is $144.9

Linear-systems/40341: CAN SOMEONE TEACH ME HOW TO DO LINEAR INEQUALITIES?
like - how do i find a boundry of a line?
ex. y>x y=____

1 solutions
Answer 25835 by Nate(3500) About Me  on 2006-06-02 15:21:53 (Show Source):
You can put this solution on YOUR website!
y doesn't equal x and no values under that line are not equal to y
Asymptote: y = x

Polynomials-and-rational-expressions/40363: The hypotenuse of a right triangle is 6m long. One leg is 1m longer than the other find the length of the shorter leg.
Thank you
1 solutions
Answer 25834 by Nate(3500) About Me  on 2006-06-02 15:18:17 (Show Source):
You can put this solution on YOUR website!
One leg's size = z
Other leg's size = x
Equation:
z+%2B+1+=+x
Use pythagorus's theorm:
a%5E2+%2B+b%5E2+=+c%5E2
%28z%29%5E2+%2B+%28x%29%5E2+=+%286%29%5E2
%28z%29%5E2+%2B+%28z+%2B+1%29%5E2+=+%286%29%5E2
z%5E2+%2B+z%5E2+%2B+2z+%2B+1+=+36
2z%5E2+%2B+2z+-+35+=+0
z is about 3.71m
x is about 4.71m

Linear-equations/40451: The Question is Line 3 has a slope of 3/4 and passes through the point (-3,7).
So, I know the slope is 3/4 but my teacher wants us to solve this problem using the slope formula, point slope formula, slope intercept formula and the general form. I do not know how to start this because I wasn't given the x1,y1 points and the x2,y2 points. Help?!
1 solutions
Answer 25832 by Nate(3500) About Me  on 2006-06-02 15:07:49 (Show Source):
You can put this solution on YOUR website!
Use point-slope formula:
y+-+yp+=+m%28x+-+xp%29
y+-+7+=+%283%2F4%29%28x+%2B+3%29
y+-+7+=+%283%2F4%29x+%2B+2.25%29
y+=+%283%2F4%29x+%2B+9.25%29
Use slope-intercept formula:
y+=+mx+%2B+b
7+=+%283%2F4%29%28-3%29+%2B+b
7+=+%283%2F4%29%28-3%29+%2B+b
9.25+=+b
so ....
y+=+%283%2F4%29x+%2B+9.25
You do not need to use slope formula because you have the slope!
General form:
%28-3%2F4%29x+%2B+y+=+%2837%2F4%29
3x+-+4y+=+-37

Miscellaneous_Word_Problems/40351: DIRECT VARIATION
Find an equation of variation where y varies directly as x and y=2 when x=10 find y when x = -25.
y=____
Thanks you very much

1 solutions
Answer 25831 by Nate(3500) About Me  on 2006-06-02 15:02:24 (Show Source):
You can put this solution on YOUR website!
Find an equation of variation where y varies directly as x and y=2 when x=10 find y when x = -25.
(y)/(x)
(2)/(10) = (y)/(-25)
-5 = y

Polynomials-and-rational-expressions/40355: DIRECT VARIATION
the number of kg of water (W) in a human body varies directly as the total body weight(B). A person who weighs 72kg contains 54kg of water. How many kilograms of water are in a person weighing 180kg?
A person weighing 180kg has about ____kg of water in their body.
--is it 135???
thank you for your time

1 solutions
Answer 25829 by Nate(3500) About Me  on 2006-06-02 14:54:33 (Show Source):
You can put this solution on YOUR website!
the number of kg of water (W) in a human body varies directly as the total body weight(B).
This means: (W)/(B)
(54)/(72)=(W)/180
135 = W
Yes!