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f( f(x) )  =  x

So...

f( f(0) )  =  0               And  f(0)  =  2003 .

f( 2003 )  =  0

I think this answer is 4  for question B, because we could have 0 candies in the boxes.

Yes, 6x7 = 42

f(x)  =  $\frac95$x - 4

                                    Instead of  " f(x) " , let's say  " y ".

y  =  $\frac95$x - 4

                                    Add  4  to both sides of the equation.

y + 4  =  $\frac95$x

                                    Multiply both sides of the equation by  $\frac59$ .

$\frac59$(y + 4)  =  $\frac59$ * $\frac95$x

$\frac59$y + $\frac{20}9$  =  x

x  =  $\frac59$y + $\frac{20}9$

Now, to get the inverse function, swap  x  and  y .

y  =  $\frac59$x + $\frac{20}9$          This is the inverse function.

f^-1(x)  =  $\frac59$x + $\frac{20}9$          To find f^-1(20) , plug in  20  for  x .

f^-1(20)  =  $\frac59$(20) + $\frac{20}9$   =   $\frac{100}9$ + $\frac{20}9$   =   $\frac{120}9$   =   $\frac{40}3$

Dude, u must be legend... it worked.

Yes you are right Helper 

It is much nicer dealing with people who have given themselves an identity. 

There are benefits to being a member to and people never get any email spam from this site so it is really nice for everyone when guests become members.   

I have been trying and trying and trying, and I am counting 96. 

A "C" in the corner has 3 ways to make the word "cool." 

Since there are 4 of them, 3*4=12

A "C" adjacent to a C in the corner has 13 ways to make the word "cool."

Since there are 4 of them, 4*13=52

A "C" in the center column has 16 ways to make the word "cool."

Since there are 2 of them, 16*2=32

Now, add these combinations together. 12+52+32 = 96 ways to make the word "cool."

Please try this answer. If this is wrong, please let me know.

You are very welcome, and keep those questions rolling!

Good idea, though this 'question' may disappear soon in the archive...

Thanks, Mr. Owl, for the help. Thank you for making the problem sound so much less complicated. It makes a little more sense to me now.

Thank You!

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No problem, just let me know if you need help with anything else!

Here is the problem worded differently.

19 centimeters + how many = 30? 

Remember, one night = 1 centimeter 

Now we just count how many nights it will take to get from 19 to 30 centimeters.

SOLUTION = 11 nights

Hope that helps!

 <---- You

Thanks, supermanaccz! Thanks for replying so quickly and helping me! It means so much to me that people are able to reply quickly to really urgent homework help!

Thanks!

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I think it is a great idea!

19 + 1 * x = 30

x = 11

That is quite a bold statement to make. Can you provide an example of where the calculator made an error?

That's very rude, and, as a matter of fact, it does work. All you have to do is put parenthesis around the number with the - inside.

Doing this problem requires one to consider a few cases. 

Firstly, I will solve for x in the first given equation.

Now, let's solve for z in the second equation in the exact same fashion. 

In order to solve this problem, one must consider all 4 cases. I have created them all in a table for you! Then, simplify as much as possible.
 

Therefore, $|x-z|=37\hspace{1mm}\text{or}\hspace{1mm}|x-z|=1937$

x - y  =   950                         

y - z =    987    add these

x - z  =  1937      so  l  x - z l =  1937

x - y  =  -950

y - z =    987   add these

x - z  =  37       so   l x - z l  =   37

The only two other possibilites   are x - y  = -1937    and x - y  = -37......but the absolute values of these are already accounted for by the above answers....

| x - y |  =  950

x - y  =  ± 950

x  = ± 950 + y

|y - z|  =  987

y - z  =  ± 987

z  =  ±987 + y

x - z  =  (± 950 + y) - (± 987 + y )  =  ± 950 + y ± 987 - y

x - z  =  ± 950 ± 987

x - z = 950 + 987     or     x - z = 950 - 987     or     x - z = -950 + 987     or     x - z = -950 - 987

So

x - z  =  1937     or     x - z  =  -37     or     x - z  =  37     or     x - z  =  -1937

So the possible values for

|x - z|   are    1937   and     37     

lol wow it was supposed to be a joke.

you are the worst joker ever