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109... You could have just used the calculator for a more accurate response

The answer is 21

My suggestion is to use a calculator to solve this; the one at this site will give you a good approximation.

7(x-3)+2x=150

7x-21+2x=150

9x=129

x=129/9 = 43/3 

the answer is very simple , 2r+3r=5r

an "anti log" refers to using whatever the base of the log was (ie. natural logs base is "e") and taking that base raised to whatever the number you are applying the anti log to.

example: the anti log of ln(16) is e^ln(16) = 16

g(x)=2^-x find x

$$\begin{array}{rcl}
g(x) &=& 2^{-x} \quad | \quad \ln() \\\\
\ln{(g(x))} &=& -x\ln{(2)} \\\\
\boxed{x = - \frac{ \ln{(g(x))} } {\ln{(2)} }}
\end{array}$$

3/11 = 12/33    ????     cross-multiplying, we have

3 * 33 = 11 * 12

99 = 132   

So these two things are not proportional, because cross-products of equal proportions themselves are equal.

To test whether or not it is a true proportion, cross multiply:

3/11  =  12/33                 -->  Is 3 x 33 equal to 11 x 12? If so, it is a true statement, if not, it is incorrect.

Find 10% of 2008  by turning 10% into a decimal and multiplying times 2008:  0.10 x 2008  =  the answer

arg  refers to the size of the angle of a complex number placed in polar coordinates. I believe that this is a mistype in this question.

arc cos  is the size of the angle whose cos is .47.

If you want to find arc cos(θ) = .47, then use a calculator to find the invCos(.47); usually done by pressing (2nd) (cos) and entering .47. If you wish your answer to be in degrees, it is approximately 62 degrees.

A number to a negative exponent can be written as the same number to a positive exponent if you place it in the denominator:

10^-2  =  1 / 10^2  =  1 / 100

9850  =  8060(1 + x)^4

Remove the multiplier of 8060 by dividing both sides by 8060:

     9850 / 8060  =  (1 + x)^4

Remove the exponent of 4 by finding the 4th root of both sides:

    (9850 / 8060) ^ (1/4)  =  1 + x

Now, subtract the 1:

    (9850 / 8060) ^ (1/4)  -1  =  x

To turn x into a percentage, multiply by 100.

If you can't use the calculator:

If you use Pascal's triangle to get the coefficients:

Row 0:                                1

Row 1:                             1     1

Row 2:                         1      2       1

Row 3:                     1      3      3       1

Row 4:                  1     4       6      4      1                      

(a + b) ^ 4  =  1a^4  +  4a^3b  +  6a^2b^2  +  4ab^3  + 1b^4

In (x² + 2/x)^4,  a = x²   and   b = 2/x

                       1(x²)^4  +  4(x²)^3(2/x)  +  6(x²)^2(2/x)^2  +  4(x²)(2/x)^3  +  1(2/x)^4

                            x^8  +  4(x^6)(2/x)  +  6(x^4)(4/x²)  +  4(x²)(8/x^3)  + 16/x^4

                            x^8  +  8/x^5  +  24x^2  +  32/x  +  16/x^4

A procedure that isn't as easy as doing it by calculator, and a way in which more mistakes can be made!

If you must do it by hand and if you know combinations (nCr) you don't need to use Pascal's triangle to find the coefficients: the coefficients of row 4 are:   4C0,  4C1,   4C2,   4C3,   4C4

tan A = 0.58384

$$A = 30.2780919731\ensurement{^{\circ}}$$

I (i) ate (8) some (Sumation) Pie (Pi)

This is one of the better ones I've seen!

Thank you CPhill

Expand this binomial power (x^2+2/x)^4

a/b  =  5/7

a/9  =  5/7

cross multiply:               7·a  =  9·5

                                      7a  =  45

divide both sides by 7:       a  =  45 / 7

8/30 = about .266

And .266%  = .00266 in decimal form

Thanks, heureka....that's pretty neat.....!!!  I'm going to recommend this one for Melody's "Daily Wrap."

-5 × 9 -21 + 6   perform the multiplication first

-45 - 21 + 6     now, just add/subtract

-66 + 6   =

-60

What is the formula of this sequence?

1, 8, 27, 256, 3125, 46656, 823543

$$a_n=n^{
\left[
n+integerPart\left(\dfrac{2}{n}\right)
\right]}
\quad \text{ and } \quad n > 0$$

Let x be the complement

Then the measure of the other angle is just 2x - 12

And they sum to 90 degrees....so we have

x + 2x - 12 = 90

3x - 12 = 90     add 12 to both sides

3x = 102          divide by 3 on both sides

x = 34 degrees    and that's the measure of the complement

Then ...2*34 - 12  =  68  - 12  =  56 degrees...... is the measure of our angle