![\frac{a - c}{x - a}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%20-%20c%7D%7Bx%20-%20a%7D)
= m Multiply both sides by (x - a)
a - c = m (x - a) Use the Distributive Property
a - c = mx - ma Add ma to both sides
a - c + ma = mx Divide both sides by m
![\frac{a - c + ma}{m}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%20-%20c%20%2B%20ma%7D%7Bm%7D%20)
= x Switch the sides to make it easier to read
x = <span>
![\frac{a - c + ma}{m}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%20-%20c%20%2B%20ma%7D%7Bm%7D%20)
</span>
let's use some amount.... hmmm say "b", to get its percentage.
![\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{140\% of b}}{\left( \cfrac{140}{100} \right)b}\implies \cfrac{14}{10}b\implies \cfrac{7}{5}b\implies 1\frac{2}{5}b](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20%5Ctextit%7Ba%5C%25%20of%20b%7D%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20%5Cleft%28%20%5Ccfrac%7Ba%7D%7B100%7D%20%5Cright%29%5Ccdot%20b%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D~%5Chspace%7B5em%7D%5Cstackrel%7B%5Ctextit%7B140%5C%25%20of%20b%7D%7D%7B%5Cleft%28%20%5Ccfrac%7B140%7D%7B100%7D%20%5Cright%29b%7D%5Cimplies%20%5Ccfrac%7B14%7D%7B10%7Db%5Cimplies%20%5Ccfrac%7B7%7D%7B5%7Db%5Cimplies%201%5Cfrac%7B2%7D%7B5%7Db)
Answer:
D.
![\frac{y^2}{12}-\frac{x^2}{6}=1](https://tex.z-dn.net/?f=%5Cfrac%7By%5E2%7D%7B12%7D-%5Cfrac%7Bx%5E2%7D%7B6%7D%3D1)
Step-by-step explanation:
we are given
we can use standard equation of hyperbola
![\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28y-k%29%5E2%7D%7Ba%5E2%7D-%5Cfrac%7B%28x-h%29%5E2%7D%7Bb%5E2%7D%3D1)
where
center=(h,k)
center at origin
so, h=0 and k=0
vertex is
![(0,\sqrt{12})](https://tex.z-dn.net/?f=%280%2C%5Csqrt%7B12%7D%29)
we can use formula
vertices: (h, k + a)
we get
![k+a=\sqrt{12}](https://tex.z-dn.net/?f=k%2Ba%3D%5Csqrt%7B12%7D)
we can plug k=0
![a=\sqrt{12}](https://tex.z-dn.net/?f=a%3D%5Csqrt%7B12%7D)
now, we can plug these values
![\frac{(y-0)^2}{(\sqrt{12})^2}-\frac{(x-0)^2}{b^2}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28y-0%29%5E2%7D%7B%28%5Csqrt%7B12%7D%29%5E2%7D-%5Cfrac%7B%28x-0%29%5E2%7D%7Bb%5E2%7D%3D1)
now, we are given it passes through ![(2\sqrt{3} ,6)](https://tex.z-dn.net/?f=%282%5Csqrt%7B3%7D%20%2C6%29)
so, we have
![x=2\sqrt{3},y=6](https://tex.z-dn.net/?f=x%3D2%5Csqrt%7B3%7D%2Cy%3D6)
we can plug these values and then we can solve for b
![\frac{(6-0)^2}{(\sqrt{12})^2}-\frac{(2\sqrt{3}-0)^2}{b^2}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%286-0%29%5E2%7D%7B%28%5Csqrt%7B12%7D%29%5E2%7D-%5Cfrac%7B%282%5Csqrt%7B3%7D-0%29%5E2%7D%7Bb%5E2%7D%3D1)
and we get
![36b^2-144=12b^2](https://tex.z-dn.net/?f=36b%5E2-144%3D12b%5E2)
we can solve for b
and we get
![b=\sqrt{6}](https://tex.z-dn.net/?f=b%3D%5Csqrt%7B6%7D)
now, we can plug these values
![\frac{(y-0)^2}{(\sqrt{12})^2}-\frac{(x-0)^2}{(\sqrt{6})^2}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28y-0%29%5E2%7D%7B%28%5Csqrt%7B12%7D%29%5E2%7D-%5Cfrac%7B%28x-0%29%5E2%7D%7B%28%5Csqrt%7B6%7D%29%5E2%7D%3D1)
we can simplify it
and we get
![\frac{y^2}{12}-\frac{x^2}{6}=1](https://tex.z-dn.net/?f=%5Cfrac%7By%5E2%7D%7B12%7D-%5Cfrac%7Bx%5E2%7D%7B6%7D%3D1)
Answer:
A
Step-by-step explanation:
The formula for the perimeter is 2l +2w. 4x^2+4x^2=8x^2. y^2+y^2=2y^2.
If we add them together the answer is 8x^2+2y^2.