I believe it is D also and my reason is cause i have the same problem and i got the answer D<span />
I can’t see the whole problem but The triangle is SAS and it it is translated
Answer: 12/5 or 2 2/5
2 divide 5=2/5
2/5 times 6 = 12/5
or 2 2/5
Answer:
see below
Step-by-step explanation:
f(x) = −16x^2 + 24x + 16
Set equal to zero to find the x intercepts
0 = −16x^2 + 24x + 16
Factor out -8
0 = -8(2x^2 -3x-2)
Factor
0 = -8(2x +1) (x-2)
Using the zero product property
2x+1 =0 x-2 =0
x = -1/2 x=2
The x intercepts are -1/2 ,2
Since the coefficient of x^2 is negative the graph will open down and the vertex will be a maximum
The x value of the maximum is 1/2 way between the zeros
(-1/2+2) /2 = 1.5/2 =.75
To find the y value substitute into the function
f(.75) = -8(2x +1) (x-2)
=-8(2*.75+1) (.75-2)
= -8(2.5)(-1.25)
=25
The vertex is at (.75, 25)
We have the zeros, and the vertex. We know the graph is symmetrical about the vertex
rationalizing the numerator, or namely, "getting rid of that pesky radical at the top".
we simply multiply top and bottom by a value that will take out the radicand in the numerator.
![\bf \cfrac{\sqrt[3]{144x}}{\sqrt[3]{y}}~~ \begin{cases} 144=2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3\\ \qquad 2^3\cdot 18 \end{cases}\implies \cfrac{\sqrt[3]{2^3\cdot 18x}}{\sqrt[3]{y}}\implies \cfrac{2\sqrt[3]{ 18x}}{\sqrt[3]{y}} \\\\\\ \cfrac{2\sqrt[3]{ 18x}}{\sqrt[3]{y}}\cdot \cfrac{\sqrt[3]{(18x)^2}}{\sqrt[3]{(18x)^2}}\implies \cfrac{2\sqrt[3]{(18x)(18x)^2}}{\sqrt[3]{(y)(18x)^2}}\implies \cfrac{2\sqrt[3]{(18x)^3}}{\sqrt[3]{18^2x^2y}}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B%5Csqrt%5B3%5D%7B144x%7D%7D%7B%5Csqrt%5B3%5D%7By%7D%7D~~%0A%5Cbegin%7Bcases%7D%0A144%3D2%5Ccdot%202%5Ccdot%202%5Ccdot%202%5Ccdot%203%5Ccdot%203%5C%5C%0A%5Cqquad%202%5E3%5Ccdot%2018%0A%5Cend%7Bcases%7D%5Cimplies%20%5Ccfrac%7B%5Csqrt%5B3%5D%7B2%5E3%5Ccdot%20%2018x%7D%7D%7B%5Csqrt%5B3%5D%7By%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Csqrt%5B3%5D%7B%20%2018x%7D%7D%7B%5Csqrt%5B3%5D%7By%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B2%5Csqrt%5B3%5D%7B%20%2018x%7D%7D%7B%5Csqrt%5B3%5D%7By%7D%7D%5Ccdot%20%5Ccfrac%7B%5Csqrt%5B3%5D%7B%2818x%29%5E2%7D%7D%7B%5Csqrt%5B3%5D%7B%2818x%29%5E2%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Csqrt%5B3%5D%7B%2818x%29%2818x%29%5E2%7D%7D%7B%5Csqrt%5B3%5D%7B%28y%29%2818x%29%5E2%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Csqrt%5B3%5D%7B%2818x%29%5E3%7D%7D%7B%5Csqrt%5B3%5D%7B18%5E2x%5E2y%7D%7D)
![\bf \cfrac{2(18x)}{\sqrt[3]{324x^2y}}~~ \begin{cases} 324=2\cdot 2\cdot 3\cdot 3\cdot 3\cdot 3\\ \qquad 12\cdot 3^3 \end{cases}\implies \cfrac{36x}{\sqrt[3]{12\cdot 3^3x^2y}} \\\\\\ \cfrac{36x}{3\sqrt[3]{12x^2y}}\implies \cfrac{12x}{\sqrt[3]{12x^2y}}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B2%2818x%29%7D%7B%5Csqrt%5B3%5D%7B324x%5E2y%7D%7D~~%0A%5Cbegin%7Bcases%7D%0A324%3D2%5Ccdot%202%5Ccdot%203%5Ccdot%203%5Ccdot%203%5Ccdot%203%5C%5C%0A%5Cqquad%2012%5Ccdot%203%5E3%0A%5Cend%7Bcases%7D%5Cimplies%20%5Ccfrac%7B36x%7D%7B%5Csqrt%5B3%5D%7B12%5Ccdot%203%5E3x%5E2y%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B36x%7D%7B3%5Csqrt%5B3%5D%7B12x%5E2y%7D%7D%5Cimplies%20%5Ccfrac%7B12x%7D%7B%5Csqrt%5B3%5D%7B12x%5E2y%7D%7D)