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1/3. since they are never in the same same place, and can only be either inside or outside, then (1 - (2/3) ) = 1/3

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x=1/8y-1
y=1/4x+39





x = (40/8)-1 = 4
(4,40)
System is consistent since there is a solution

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Perimeter is the sum of all the sides.
Let w be the width.
L = 2w-4
P = w + l + w + l
28 = w + 2w -4 + w + 2w -4
28 = 6w - 8
36 = 6w
6 = w
l = 12 - 4
l = 8
Does that work?
28 = 12 + 16 check!

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See this --> http://en.wikipedia.org/wiki/Law_of_sines
Use the law of sines.
You are given 2 angles, so you can find the third angle (180 - (70+30) )
Now use law of sines to find the distance AB or AC
Once you have AB or AC, use sin and that length to find the width of the river.

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Take a look at this video. There is a problem just voer halfway through that is almost exactly this problem.
http://collabvsl.wetpaint.com/page/Basic+Probability

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Yes.
Thw angle where the ladder touches the ground is given as 75.5 degrees. sin is defined as opposite/hypotenuse.

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90.15
Let n be the number of nickels
Dimes = 2n - 6 --> d = 2n - 6
Quarters = 4n + 3 --> q = 4n +3

9015 = 5n + 10d + 25q = n + 10*(2n - 6) + 25*(4n +3)
9015 = 5n + 20n - 60 + 100n + 75
9015 = 125n - 15
9000 = 125n
72 = n
d = 144 -6 = 138
q = 291
Does that check?
0.25*291 + 0.1*138 + 0.05* 72 = 90.15

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Setup a ratio
52/13 = x/10
then cross multiply to find x

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Given

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Given
standard form is Ax + By = C (where A and B are integers, A is positive)

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see this --> http://collabvsl.wetpaint.com/page/Solving+Systems+of+Equations

4x - 2y = 8
2x + 4y =8
2x + 4y = 8
2x = 8 -4y
x = (8-4y)/2 use this and sub into the first equation
4x - 2y = 8
4((8-4y)/2) - 2y = 8
16 - 8y - 2y = 8
-10y = -8
y = 4/5
Use this value of y to sub back in and solve for x
x = 12/5
check your answers

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See this and let me know if you still cant solve the problem.
http://collabvsl.wetpaint.com/page/Solving+Systems+of+Equations

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Minor error is causing you grief
2(r+c)=30--->2r+2c=30-->6r+6c=90
3(r-c)=30---->3r-3c=30--> 6r+6c=60 <-- you changed - to + here
3(r-c)=30---->3r-3c=30--> 6r-6c=60 should be this
Now just use elimination to solve. See here for a video on solving systems of equations. http://collabvsl.wetpaint.com/page/Solving+Systems+of+Equations
6r + 6c = 90
6r - 6c = 60
------------
12r = 150
r = 12.5
r+c = 15
12.5 + c = 15
c = 2.5
Does that check out?

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There is really no simple way to do that beyond taking a few points and making a table.
I suggest plugging in x = -3, -2, -1, 0, 1, 2, 3 Solve for Y at each of those values of x. Then plot the points. The shape of the plot will be clear enough with that number of points.
X Y
-3 6*(-3)^3 = -162
-2 6*(-2)^3 = -48
-1 -6
0 0
1 6
2 48
3 162

Make sure your graph scale is large enough allow for the fact that the Y values are growing exponential.

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You have two right triangles.
Both have an adjacent leg of 50 ft.
Looking up at 20degrees. The opposite leg of the 'upper triangle' can be found by



Looking down at 35 degrees. The opposite leg of the lower triangle' can be found by



So the next building is = 53.21ft high

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You are given three pieces of information.
Label the axis on the box w, d and h (for width, depth and height).
Now setup equations for what you 'know'

-->
-->
Combining the previous two equations yeilds

Now plug in the values for d and h into the Volume equation.


Reduce to get


Substitute w=5 back into the earlier equations to get
= 6
= = 8
That's a pretty small box

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Let the width = w.
The length is given as "10 feet more than twice the width". So
The perimeter is givenb as 260 feet. You know the perimeter of a rectangle is






Check your answer.
If w = 40 , then length = 10+80 = 90.
Is 2*40 + 2+90 = 260??

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watch this - I bet you can do it yourself afterwards
http://collabvsl.wetpaint.com/page/Simplifying+rational+expressions+using+multiplication+or+division
Let me know if you can't get it after watching

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Can't do it. The best you can do is to get down to one varialbe in terms of the other two.

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Given :

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Let's do the first one. Then you can do then next 2

Using logs







2 and 3 are much the same
For the last problem, remember that anything raised to the 0 power is "1".
Given



Which looks like the same problems as above

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given r = 14 inches and pi is apporxiamted as 22/7

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logaX^4 = 4* logaX
ln(y^5) = 5 * ln(y)
See here --> Look at rule 3 http://www.purplemath.com/modules/logrules.htm

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Tangent = opposite/adjacent
See here for a good picture --> http://www.grc.nasa.gov/WWW/K-12/airplane/sincos.html
When thinking about sine, cosine and tangent, one has to think about which vertex of the triangle you are referencing. Assume you pick one vertex, then the adjacent leg is the one that 'touches' your vertex. The hypotenuse is always the 'long side'. make sense?
When you have an angle, and also one of the sides (but not a second side), you setup the ratios as you nothed above, and then use your calculator to find the sine or cosine ro tangent of the angle. The cross multiply to find the unknown side.

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All you need to do is prove the line segments that create one of the vertex are not at right angles.
Find the slope of one side segment, then find the slope of the segment that intersects at that vertex. Then show the products of those slopes is not equal to -1.
If you can show that, then the shape cannot be a rectangle.

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A' is everything in U that is not in A --> A'={r,s,t,u,v,w}
C' is everything in U not in C --> C' = {n,o,s,u,v,w}
Union of A' and C' is everything in either one A' U C' ={n,o,r,s,t,u,v,w}
Now you figure out B'
Then take the intersection og B' and A' U C' (get the elements that are common to both B' and A'U C')
Ping me if you dont understand

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Let sqrt(7) be x

Can you solve that one? i bet you can.

but x = sqrt(7)

The sqrt(7) adds and subtracts just like any other number ... just more difficult to get your mind around what the value is. For this problem, we don't care what the sqrt(7) is. We just let it ride !

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You gotta be kidding. Do you think we own your math book? If you want help, you need to assume what we 'know' is what you provide to us.

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let the total cost = C
The person cost is :
Let the cost per person with 40 = c
The cost per person at 36 = c+ 12
Total cost is the same:




Check yor answer. does 40*108 = 36(120)?? as they say in fargo 'you betcha'

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Use logs
Given:
Take the log of both sides

When using logs, if the term inside parens is raised to a power, then your can 'bring the power down' as a multiplier.

Now get out your handy calculator and find log(3) and log(40)

Now solve for x as a one step algebra simplification

Finally, check your answer using a calculator. Does 3^3.3576 = 40? Close enough!
For the second problem, use logs again. Except this time, use natural log (ln)
Given:
Take the ln of both sides

The ln of a power of e, it just the power.

Whip out your calculator and find ln(1500) (somebody help that man!)


Check your answer using the calculator. Does it check out? You bet it does,