The answer is D because you can multiply the second equation by -4
Answer:
11 cups of dough
Step-by-step explanation:
1 cup x 11 dumplings = 11 cups of dough needed
This would be ( using the Pythagoras theorem) = sqrt (3^2 + 4^2) = sqrt 25
= 5 units (answer).
Answer:
8 possible outcomes
Step-by-step explanation:
I'm going to list all the possibilities and then count them up.
First Word is the wallpaper color, Second is the carpet color.
Red + Purple, Red + Yellow, Blue + Purple, Blue + Yellow, Yellow + Purple, Yellow + Yellow, Green + Purple, Green + Yellow
After counting them up, we get 8. Therefore there are 8 possible outcomes.
<u>Another way is to multiply the possible outcomes for each event together, and you can get the total number of outcomes. For example, in this problem there is 4 wallpaper colors and 2 carpet colors, so when u multiply them u get 8 total outcomes. Hope this helped!</u>
![\bf f(x)=\cfrac{2x-3}{x+1}~\hspace{10em}g(x)=\cfrac{x+3}{2-x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(~~g(x)~~)\implies \cfrac{2[g(x)]-3}{[g(x)]+1}\implies \cfrac{2\left( \frac{x+3}{2-x} \right)-3}{\left( \frac{x+3}{2-x} \right)+1}\implies \cfrac{\frac{2x+6}{2-x}-3}{\frac{x+3}{2-x}+1} \\\\\\ \cfrac{\frac{2x+6-6+3x}{2-x}}{\frac{x+3+2-x}{2-x}}\implies \cfrac{2x+6-6+3x}{2-x}\cdot \cfrac{2-x}{x+3+2-x}\implies \cfrac{5x}{5}\implies x](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29%3D%5Ccfrac%7B2x-3%7D%7Bx%2B1%7D~%5Chspace%7B10em%7Dg%28x%29%3D%5Ccfrac%7Bx%2B3%7D%7B2-x%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0Af%28~~g%28x%29~~%29%5Cimplies%20%5Ccfrac%7B2%5Bg%28x%29%5D-3%7D%7B%5Bg%28x%29%5D%2B1%7D%5Cimplies%20%5Ccfrac%7B2%5Cleft%28%20%5Cfrac%7Bx%2B3%7D%7B2-x%7D%20%5Cright%29-3%7D%7B%5Cleft%28%20%5Cfrac%7Bx%2B3%7D%7B2-x%7D%20%5Cright%29%2B1%7D%5Cimplies%0A%5Ccfrac%7B%5Cfrac%7B2x%2B6%7D%7B2-x%7D-3%7D%7B%5Cfrac%7Bx%2B3%7D%7B2-x%7D%2B1%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B%5Cfrac%7B2x%2B6-6%2B3x%7D%7B2-x%7D%7D%7B%5Cfrac%7Bx%2B3%2B2-x%7D%7B2-x%7D%7D%5Cimplies%20%5Ccfrac%7B2x%2B6-6%2B3x%7D%7B2-x%7D%5Ccdot%20%5Ccfrac%7B2-x%7D%7Bx%2B3%2B2-x%7D%5Cimplies%20%5Ccfrac%7B5x%7D%7B5%7D%5Cimplies%20x)
![\bf \rule{34em}{0.25pt}\\\\ g(~~f(x)~~)\implies \cfrac{[f(x)]+3}{2-[f(x)]}\implies \cfrac{\frac{2x-3}{x+1}+3}{2-\frac{2x-3}{x+1}}\implies \cfrac{\frac{2x-3+3x+3}{x+1}}{\frac{2x+2-(2x-3)}{x+1}} \\\\\\ \cfrac{2x-3+3x+3}{x+1}\cdot \cfrac{x+1}{2x+2-(2x-3)}\implies \cfrac{2x-3+3x+3}{x+1}\cdot \cfrac{x+1}{2x+2-2x+3} \\\\\\ \cfrac{5x}{5}\implies x](https://tex.z-dn.net/?f=%5Cbf%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0Ag%28~~f%28x%29~~%29%5Cimplies%20%5Ccfrac%7B%5Bf%28x%29%5D%2B3%7D%7B2-%5Bf%28x%29%5D%7D%5Cimplies%20%5Ccfrac%7B%5Cfrac%7B2x-3%7D%7Bx%2B1%7D%2B3%7D%7B2-%5Cfrac%7B2x-3%7D%7Bx%2B1%7D%7D%5Cimplies%20%5Ccfrac%7B%5Cfrac%7B2x-3%2B3x%2B3%7D%7Bx%2B1%7D%7D%7B%5Cfrac%7B2x%2B2-%282x-3%29%7D%7Bx%2B1%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B2x-3%2B3x%2B3%7D%7Bx%2B1%7D%5Ccdot%20%5Ccfrac%7Bx%2B1%7D%7B2x%2B2-%282x-3%29%7D%5Cimplies%20%5Ccfrac%7B2x-3%2B3x%2B3%7D%7Bx%2B1%7D%5Ccdot%20%5Ccfrac%7Bx%2B1%7D%7B2x%2B2-2x%2B3%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B5x%7D%7B5%7D%5Cimplies%20x)
and in case you recall your inverses, when f( g(x) ) = x, or g( f(x) ) = x, simply means, they're inverse of each other.
