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log10^0.000001 = 6

I think you might mean:

log(10,.000001) = -6 ?????

This form looks like after being put through algebra.com formula generator.

This would only be if:

10^(-6) = .000001 which looks like after being put through algebra.com formula generator.

since 10^(-6) is the same as 1/(10^6) which equals 1/1000000 which equals .000001, then I suspect this is what you are looking for.

in general, x^y = z if and only if log(x,z) = y

algebra.com formula generated form of this would look like:

in general, if and only if

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n = 80% of p means that:

n = .8*p

take the square root of both sides of this equation and you get:

sqrt(n) = sqrt(.8*p) = sqrt(.8) * sqrt(p)

sqrt(.8) = .894427191 * 100% = 89.4427191%

your answer is:

sqrt(n) = 89.4427191% of sqrt(p)

to confirm, let n = 100

this makes p = 100/.8 = 125

equation of

n = .8*p becomes

100 = .8*125

take sqrt of both sides to get:

sqrt(100) = sqrt(.8*125) = sqrt(.8) * sqrt(125)

this becomes:

10 = .894427191 * 11.18033989

this becomes:

10 = 10

Answer is confirmed.

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It travels 20 feet in (1/5) of a second.

There are 15 * (1/5) of a second in 3 seconds.

It will travel 15 * 20 = 300 feet.

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2.) Determine the future values if $5,000 is invested in each of the following situations:
a.) 5 percent for ten years
Begin with $100 - - - > 5 percent for 1 year - - > 105
then with each $1 - - - > 105/100 = 1.05 after 1 year
Then for $5,000 it would be 5,000 * 1.05 after 1 year
and then 5,000 * 1.05 * 1.05 after 2 year
for 10 year investment
it would be 5,000 * (1.05)^10 = $8144.473 Ans

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Here are some good ones.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.htm

http://www.purplemath.com/lessons.htm

http://tutorial.math.lamar.edu/Classes/Alg/Alg.aspx

http://www.jamesbrennan.org/algebra/

There's tons of stuff on the internet. Just do a search on "algebra" or "algebra lessons" or "algebra tutorials".

Some are pay sites and some are free. The ones above are free.

Algebra.com also has lessons.

You can scan down their home page using the search word "lessons" and down at the bottom towards the right you should find a link.

Here's a link that will guide you if it works.

http://www.algebra.com/tutors/all-lessons.mpl

There are also video lessons.

If you're going to use algebra.com, then some of the terminology that would be helpful is:

x*y means x multiplied by y
x/y means x divided by y
x^y means x raised to the power of y
root(n,x) means the nth root of x
sqrt(x) means the square root of x
a*(b+d) means do the addition first, then multiply

A couple of rules for exponents might help.

x^y*x^z = x^(y+z) example 3^2*3^3 = 3^(2+3) = 3^5

x^y/x^z = x^(y-z) example 3^5/3^2 = 3^(5-2) = 3^3

(x^y)^z = x^(y*z) example (3^2)^3 = 3^(2*3) = 3^6

x^(n/z) = root(z,x)^n example 3^(6/3) = root(3,3)^6 = root(3,3^6) = 3^2 = 9

x^(1/y) = root(y,x) example 27^(1/3) = root(3,27) = 3

x^(-n) = 1/x^n example 3^(-3) = 1/3^3 = 1/27

x*y*z = x*(y*z) = (x*y)*z = z*(y*x) = y*(z*x) example 1*2*3 = 1*(6) = (2)*3 = 3*(2) = 2*(3) with the terms in parentheses being multiplied first.

Your problem is:

Simplify 4z to the eighth power z to the -6 power y to the -9 power times 5y to the -1 power w to the -7 power times 2w to the 7th power

I had a little trouble understanding it.

This is what I think it is and how to simplify it.

4*z^8*z^(-6)*y^(-9)*5*y^(-1)*w^(-7)*2*w^7

If you put it through the algebra.com formula generator, it will look like this:



4z^8*z^(-6) = 4*z(8-6) = 4*z^2

y^(-9) * 5 * y^(-1) = 5*y^(-9)*y^(-1) = 5*y^(-9-1) = 5*y^(-10)

w^(-7)*2*w^7 = 2*w^(-7)*w^7 = 2*w^(-7+7) = 2*w^0 = 2*1 = 2

Your whole equation should then become:

4z^2*5y^(-10)*2

This can be re-ordered to be:

4*5*2*z^2*y^(-10)

This becomes:

40*z^2*y^(-10)

This becomes:

40z^2/y^10

To prove this is correct, then pick some values for z, y, w, and solve the original equation and solve the final equation. If they match, then the simplification was good.

Let z = 2, y = 3, w = 4

Your final equation of 40z^2/y^10 becomes:

40*(2)^2/3^10 = 160/59049 (from final equation)

Your original equation of
4*z^8*z^(-6)*y^(-9)*5*y^(-1)*w^(-7)*2*w^7 becomes:

4*(2)^8*(2)^(-6)*(3)^(-9)*5*(3)^(-1)*(4)^(-7)*2*(4)^7

This becomes:

1024 * (1/64) * (1/19683) * (5/3) * (1/16384) * 32768

This becomes:

(1024 * 5 * 32768) / (64 * 19683 * 3 * 16384)

This becomes:

(1024 * 5 * 2) / (64 * 19683 * 3)

This becomes:

(16 * 5 * 2) / (19683 * 3)

This becomes:

160 / 59049 (from original equation)

The answers match so the simplification looks good.

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how to find the exact value of sin 225
.
Looking at the unit circle
sin(225)
is in the third quadrant
225 - 180 = 45
sin(45) mapped to the third quadrant is

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Radioactive strontium 90Sr has been deposited in a large field by acid rain. If sufficient amounts make their way through the food chain to humans, bone cancer can result. It has been determined that the radioactivity level in the field is 1.7 times the save level S. 90Sr decyas according to the formula
A(t)=Aoe^-0.0239t
I think they want to know when the fields will be safe.
.
A(t)=Aoe^-0.0239t
Let x = initial amount of strontium
then
x/1.7 = A(t)
.
x/1.7 = xe^-0.0239t
1/1.7 = e^-0.0239t
ln(1/1.7) = -0.0239t
ln(1/1.7) /-0.0239 = t
22.2 years = t (years before the strontium decays to safe levels)

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A car radiator has a capacity of 8 quarts of coolant which is 20% antifreeze. A mechanic needs to drain part of the radiator fluid and replace it with 100% antifreeze to bring the coolant in the system to 60% antifreeze. How much of the original coolant should be drained and replaced by 100% antifreeze to achieve the desired mix?
.
Let x = amount drained and replaced by 100% antifreeze
then
.20(8-x) + x = .60(8)
1.6 - .20x + x = 4.8
1.6 + .80x = 4.8
.80x = 3.2
x = 4 quarts

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We have a 10x10x10 large cube that we are going to cut into 1000 small
1x1x1 cubes.

Only the small cubes cut from the edges of the large cube will have
at least two faces painted red.  All the rest will have either 1 or
0 faces painted red.
 
There are 8 small cubes which have exactly three sides painted. 
These are the 8 small cubes located at the 8 vertices (corners) of 
the big cube.  

So let's say we have counted these 8 with three faces painted red.

There are 12 edges of the big cube.  Each of these 12 edges of
the big cube consists of the edges of 10 small cubes.  But 2 of
these are at a corner of the big cube, and we have already
conted these.  So we only need to count the other 8 cubes along
each of the 12 edges, which have exactly 2 faces painted red.    
  
So that's an additional 12x8 or 96.

So the total is 8 small cubes with exactly three faces painted red
plus 96 cubes with exactly two faces painted red. That's 8+96 = 104.

-------------------

Another way to count them is to start with the 1000 cubes and 
start subtracting.

There are the inner 8x8x8 or 512 small cubes cut from the inside
of the big cube which have no faces painted.

On each of the 6 faces of the big cube there are 8x8 or 64 faces
of small cubes which only have 1 face painted.  So that's
64x6 or 384 small cubes which have 1 face painted.  So subtracting

 1000 small cubes 
- 512 small cubes which have no faces painted red
-----
  488 small cubes which have at least one face painted red.
- 384 small cubes which have exactly one face painted red.  
-----
  104 small cubes with at least two faces painted red.

Edwin

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x>-1/2 or x>or equal to -3/4

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It is correct, but more simplified would be -a - b

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y=1/2x+2

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2 point shots: 7
3 point shots: 4

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Solve each equation
2(t-4)= 3-(3t+1)
2t-8 = 3 -3t - 1
5t = 2+8
5t = 10
t = 2
-----------------
Cheers,
Stan H.

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Solve the equation
9y+5-2y= 2y+5-y+3
---
7y + 5 = y + 8
6y = 3
y = 1/2
============
Cheers,
Stan H.

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t(3t-1)2nd power
---
t(9t^2 - 6t + 1)
---
9t^3 - 6t^2 + t
============================================
Cheers,
Stan H.

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a boat can travel 5 miles downstream in the same length of time it travels 3 miles upstream. if the rate of the current is 3mph, find the speed of the boat in still water.
-------
Downstream DATA:
distance = 5 miles ; rate = b+3 mph ; time = d/r = 5/(b+3) hrs
----------------
Upstream DATA:
distance = 3 miles ; rate = b-3 mph ; time = d/r = 3/(b-3)
=============================================================
Equations:
time up = time down
3/(b-3) = 5/(b+3)
---
3(b+3) = 5(b-3)
3b+9 = 5b-15
2b = 24
b = 12 mph (speed of the boat in still water)
===============================================
Cheers,
Stan H.

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I do not understand can you help?
Simplify the problem and write answers in exponential form.
3^4 + 2 * 3^4
---
(3^4) + 2(3^4)
---
= (3^4)(1 + 2)
---
= (3^4)*3
---
= 3^5
= 243
==========
Cheers,
Stan H.

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A CAR TRAVELS 540 MILES IN 10 HOURS . HOW FAR WILL IT TRAVEL IN 7 HOURS
----------
540/10 = 54 mph
54*7 = 378 miles

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the wavelength(W) of a radio wave varies inversely as its frequency(F). A wave with a frequency of 200kHz has a length of 252m. What is the length of a wave with a frequency of 900kHz?
------------------
200*252 = k (a constant)
L*900 = k = 50400
L = 50400/900 = 56 meters
-----------------
-----------------
That's the answer given the data, but it's not correct.
The wavelength in meters is 300/f, f = frequency in Megahertz.
200 KHz = 0.2 MHz
300/0.2 = 1500 meters,
not 252 meters

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a right triangle

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x+y=9, y=-x+9
-2x+y=-3
-2x-x+9=-3
-3x=-12
x=4
-----------------
4+y=9
y=5
---------------
-2*4+5=-3
-8+5=-3

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y=-3x+11

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y=2x+8
y int=(0,8)
x int=(-4,0)

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Try the elimination method
:
Write an equation for each statement:
:
"The sum of lisa's age and Ellen's age is 41."
E + L = 41
:
" five years from now, the sum of their ages will be three times lisa's present age."
(E+5) + (L+5) = 3L
E + L + 10 = 3L
E + L - 3L = -10
E - 2L = -10
Subtract this equation from the 1st equation
E + L = 41
E -2L = -10
--------------subtraction eliminates E, find L
3L = 51
L =
L = 17 yrs is Lisa's present age
:
:
Check solution, E = 41 - 17 = 24
"five years from now, the sum of their ages will be three times lisa's present age."
24 + 5 + 17 + 5 = 3(17)
29 + 22 = 51; confirms our solution

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2:3

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68=104 base 8

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did you read the example of a bad question?

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perpendicular to

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.11x-.04(10000-x)=650
.11x-400+.04x=650
.15x=1050
x=$7000 at 11%
$3000 at 4%

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5/4x+1/8x=3/8+x
10/8x+1/8x=3/8+8/8x
3/8x=3/8
x=(3/8)/(3/8)
x=3/8*8/3
x=24/24
x=1