geno3141

Use the distributive property by multiplying 2π times r and times x and times 4.

2π(r + x + 4)   =   2π·r  + 2π·x  +  2π·4   =   2πr + 2πx + 8π

Do you mean it as you typed it or is there a symbol between (5x+8) and x?

The rate is the distance divided by the time.

   60 feet in 10 seconds   =   60 ft / 10 sec   =  6 ft / sec

   42 feet in 6 seconds   =   42 ft / 6 sec   =   7 ft / sec    <--- We have a winner!

Since    |-4| = 4    and also    |4| = 4     there will be two answer

One:     6x + 3 = -4                            The other:    6x + 3 = 4

                   6x = -7                                                     6x = 1

                     x = -7/6                                                   x = 1/6

Cross multipy --

13 x 12 = 11 x y

156 = 11y                               Divide by 11.

y = 156 / 11

Was this problem originally:    g(x) = 7x+ 5       and you were supposed to find g(9/7) ?

If so:    replace 9/7 in for x throughout the original expression:

                                           g(9/7) = 7(9/7) + 5                    (multiply 7 times 9/7 to get 9)

                           --->          g(9/7) = 9 + 5

                           --->          g(9/7) = 14

-9 x 3/4

is the same as   -9/1  x  3/4

When multiplying common fractions, multiply the numerator times the numerator and the denominator times the denominator.

( -9 x 3 ) / ( 1 x 4 )      =     -27 / 4

This can be rewritten as a mixed fraction or as a decimal, if you wish. 

9 ( 4 ( 2n + r ) - 11r ) + 3 ( r - n )

Work from the innermost parentheses first: Solve 4 ( 2n + r ) by using the distributive property:

    4 ( 2n + r  ) =  4 x 2n + 4 x r   =   8n + 4r

This gives us:   9 ( 8n + 4r - 11r ) + 3 ( r - n )

Still working inside the first set of parentheses, combine   4r   with   - 11r   to give   - 7r.

We now have:   9 ( 8n - 7r ) + 3 ( r - n ).

Now use the distributive property on both sets of parentheses:

    9 ( 8n - 7r )   =  9 x 8n  -  9 x 7r   =   72n - 63r                         3 ( r - n )   =  3 x r  -  3 x n   =   3r - 3n

This becomes:   72n - 63r + 3r - 3n

Which is:   69n - 60r 

My calculator tells me that 1 + 1 = 2

Since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

The inverse (opposite operation) of "to the fourth power" is "to the fourth root".

   (x^4) ^ ¼  = 81 ^ ¼ 

   81 = 3^4    so (3 ^ 4) ^ ¼  =   3 ^ 1   = 3

By hand: (3 ^ 4) ^ ¼  =  3 ^ (4 x ¼) = 3 ^ 1  = 3   (When you take a power to a power, multiply the exponents.)

Or, do it by calculator. One way of finding the fourth root is to use ^ (1/4)