Answer:
<h2>There are needed 3 burgers to reach the maximum measure of happiness of 25.</h2>
Step-by-step explanation:
The given function is

Where
is the number of burgers and
the measure of happiness.
To find the maximum burgers needed to reach the maximum happiness, we just need to find the vertex of this function, which is defined as
where
, and
,
, replacing these values, we have


Therefore, there are needed 3 burgers to reach the maximum measure of happiness of 25.
let's do so using substitution
![\bf \begin{cases} -3x-4y=-14\\ 9x+2y=22 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{solving for "y" in the 1st equation}~\hfill }{-3x-4y=-14\implies -3x+14-4y=0} \\\\\\ -3x+14=4y\implies \cfrac{14-3x}{4}=\boxed{y} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting "y" in the 2nd equation}}{9x+2\left( \boxed{\cfrac{14-3x}{4}} \right)=22}\implies 9x+\cfrac{14-3x}{2}=22](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20-3x-4y%3D-14%5C%5C%209x%2B2y%3D22%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bsolving%20for%20%22y%22%20in%20the%201st%20equation%7D~%5Chfill%20%7D%7B-3x-4y%3D-14%5Cimplies%20-3x%2B14-4y%3D0%7D%20%5C%5C%5C%5C%5C%5C%20-3x%2B14%3D4y%5Cimplies%20%5Ccfrac%7B14-3x%7D%7B4%7D%3D%5Cboxed%7By%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bsubstituting%20%22y%22%20in%20the%202nd%20equation%7D%7D%7B9x%2B2%5Cleft%28%20%5Cboxed%7B%5Ccfrac%7B14-3x%7D%7B4%7D%7D%20%5Cright%29%3D22%7D%5Cimplies%209x%2B%5Ccfrac%7B14-3x%7D%7B2%7D%3D22)
![\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( 9x+\cfrac{14-3x}{2}\right)=2(22)}\implies 18x+(14-3x)=44\implies 15x+14=44 \\\\\\ 15x = 30\implies x = \cfrac{30}{15}\implies \blacktriangleright x = 2\blacktriangleleft \\\\\\ \stackrel{\textit{since we know that }}{\cfrac{14-3x}{4}=y}\implies \cfrac{14-3(2)}{4}=y\implies \cfrac{14-6}{4}=y\implies \blacktriangleright 2 = y \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (2,2)~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B2%7D%7D%7B2%5Cleft%28%209x%2B%5Ccfrac%7B14-3x%7D%7B2%7D%5Cright%29%3D2%2822%29%7D%5Cimplies%2018x%2B%2814-3x%29%3D44%5Cimplies%2015x%2B14%3D44%20%5C%5C%5C%5C%5C%5C%2015x%20%3D%2030%5Cimplies%20x%20%3D%20%5Ccfrac%7B30%7D%7B15%7D%5Cimplies%20%5Cblacktriangleright%20x%20%3D%202%5Cblacktriangleleft%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bsince%20we%20know%20that%20%7D%7D%7B%5Ccfrac%7B14-3x%7D%7B4%7D%3Dy%7D%5Cimplies%20%5Ccfrac%7B14-3%282%29%7D%7B4%7D%3Dy%5Cimplies%20%5Ccfrac%7B14-6%7D%7B4%7D%3Dy%5Cimplies%20%5Cblacktriangleright%202%20%3D%20y%20%5Cblacktriangleleft%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%282%2C2%29~%5Chfill)
Answer:
4 x 6 = 24 feet squared
Step-by-step explanation:
Answer:
270 centimeters squared
Step-by-step explanation:
A = H x W / 2
A = 18 x 30
A = 270