![\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\ \rule{31em}{0.25pt}\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7Bratio%20relations%7D%20%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bccccllll%7D%20%26%5Cstackrel%7Bratio~of~the%7D%7BSides%7D%26%5Cstackrel%7Bratio~of~the%7D%7BAreas%7D%26%5Cstackrel%7Bratio~of~the%7D%7BVolumes%7D%5C%5C%20%26-----%26-----%26-----%5C%5C%20%5Ccfrac%7B%5Ctextit%7Bsimilar%20shape%7D%7D%7B%5Ctextit%7Bsimilar%20shape%7D%7D%26%5Ccfrac%7Bs%7D%7Bs%7D%26%5Ccfrac%7Bs%5E2%7D%7Bs%5E2%7D%26%5Ccfrac%7Bs%5E3%7D%7Bs%5E3%7D%20%5Cend%7Barray%7D%5C%5C%5C%5C%20%5Crule%7B31em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Ccfrac%7B%5Ctextit%7Bsimilar%20shape%7D%7D%7B%5Ctextit%7Bsimilar%20shape%7D%7D%5Cqquad%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%7Bs%5E2%7D%7D%7B%5Csqrt%7Bs%5E2%7D%7D%3D%5Ccfrac%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%20)
![\bf \rule{31em}{0.25pt}\\\\ \cfrac{smaller}{larger}\qquad \cfrac{s}{s}=\cfrac{\sqrt{98}}{\sqrt{162}}~~ \begin{cases} 98=2\cdot 7\cdot 7\\ \qquad 2\cdot 7^2\\ 162=2\cdot 9\cdot 9\\ \qquad 2\cdot 9^2 \end{cases}\implies \cfrac{s}{s}=\cfrac{\sqrt{2\cdot 7^2}}{\sqrt{2\cdot 9^2}} \\[2em] \cfrac{s}{s}=\cfrac{7\sqrt{2}}{9\sqrt{2}}\implies \cfrac{s}{s}=\cfrac{7}{9}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Crule%7B31em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Ccfrac%7Bsmaller%7D%7Blarger%7D%5Cqquad%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%7B98%7D%7D%7B%5Csqrt%7B162%7D%7D~~%20%5Cbegin%7Bcases%7D%2098%3D2%5Ccdot%207%5Ccdot%207%5C%5C%20%5Cqquad%202%5Ccdot%207%5E2%5C%5C%20162%3D2%5Ccdot%209%5Ccdot%209%5C%5C%20%5Cqquad%202%5Ccdot%209%5E2%20%5Cend%7Bcases%7D%5Cimplies%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%7B2%5Ccdot%207%5E2%7D%7D%7B%5Csqrt%7B2%5Ccdot%209%5E2%7D%7D%20%5C%5C%5B2em%5D%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B7%5Csqrt%7B2%7D%7D%7B9%5Csqrt%7B2%7D%7D%5Cimplies%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B7%7D%7B9%7D%20)
bearing in mind that the ratio of the sides, is the same as the ratio of the perimeters.
3x - 3y + 2z = 7
3x + 1y - 3z = -5 ⇒ 6x - 2y - 1z = 2 ⇒ 42x - 14y - 7z = 14
7x - 1y - 2z = 0 ⇒ 7x - 1y - 2z = 0 ⇒ <u>42x - 6y - 12z = 0 </u>
-20y - 19z = 14
-20y + 20y - 19z = 14 + 20y
<u /> <u>-19z</u> = <u>14 + 20y</u>
-19 -19
z = -14/19 - 1 1/19y
3x - 3y + 2(-14/19 - 1 1/19y) = 7
3x - 3y - 1 9/19 - 2 2/19y = 7
3x - 5 2/19y - 1 9/19 = 7
<u> +1 9/19 +1 9/19 </u>
3x - 5 2/19y = 8 9/19
3x - 3x - 5 2/19y = 8 9/19 - 3x
<u /> <u>-5 2/19y</u> = <u>8 9/19 - 3x</u>
-5 2/19 -5 2/19
y = -1 64/97 + 57/97x
3x - 3(-1 64/97 + 57/97x) + 2(-14/19 - 1 1/19y) = 7
3x + 4 95/97 + 1 74/97x - 1 9/19 - 2 2/19y = 7
4 74/97x - 2 2/19y + 3.5056972328 = 7
<u> -3.5056972328 -3.5056972328</u>
4 74/97x - 2 2/19y = 3.494302767
4 74/97x + 2 2/19y - 2 2/19y = 3.494302767 + 22/19y
<u>4 74/97x</u> = <u>3.494302767 + 2 2/19</u>
4 74/97 4 74/97
x = 0.7336523126 + 0.4420141262y
3(0.733652316 + 0.4420141262y) - 3(-1 64/97 + 57/97x) + 2(-14/19 - 1 1/19y)=7
2.200956948 + 1.326042379y + 4 95/97 - 1 74/97x - 1 9/19 - 2 2/19y = 7 -1 74/97x - 0.7792207789y + 5.706654181 = 7
<u> -5.706654181 -5.70665418</u>
-1 74/97x - 0.7792207789y = 1.293345820
(x, y, z) = (0.733652316 + 0.4420141262, -1 64/97 + 57/97x, -14/19 - 1 1/19y)
The answer to that is 20x^4
Answer:
about =502.65
Step-by-step explanation:
