Answer:
the answer is a
Step-by-step explanation:
i took the test
2
Length x width= area
3/4 x blank= 3/2
So then you can divide area by the given length
3/2 divided by 3/4= 2
And to check your answer you would put 2 in as your width
3/4 x 2= 6/4. And 6/4 reduces to 3/2
We can apply the following properties of radicals:
![\begin{gathered} \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\Rightarrow\text{ Product property} \\ \sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}\Rightarrow\text{ Quotient property} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Csqrt%5Bn%5D%7Bab%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5Ccdot%5Csqrt%5Bn%5D%7Bb%7D%5CRightarrow%5Ctext%7B%20Product%20property%7D%20%5C%5C%20%5Csqrt%5Bn%5D%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%3D%5Cfrac%7B%5Csqrt%5Bn%5D%7Ba%7D%7D%7B%5Csqrt%5Bn%5D%7Bb%7D%7D%5CRightarrow%5Ctext%7B%20Quotient%20property%7D%20%5Cend%7Bgathered%7D)
Then, we have:
![\begin{gathered} \text{ Apply the product property} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\sqrt[]{\frac{7}{8}\cdot\frac{7}{18}} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\sqrt[]{\frac{7\cdot7}{8\cdot18}} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\sqrt[]{\frac{49}{144}} \\ \text{ Apply the quotient property} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\frac{\sqrt[]{49}}{\sqrt[]{144}} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\frac{7}{12} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7B%20Apply%20the%20product%20property%7D%20%5C%5C%20%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B8%7D%7D%5Ccdot%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B18%7D%7D%3D%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B8%7D%5Ccdot%5Cfrac%7B7%7D%7B18%7D%7D%20%5C%5C%20%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B8%7D%7D%5Ccdot%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B18%7D%7D%3D%5Csqrt%5B%5D%7B%5Cfrac%7B7%5Ccdot7%7D%7B8%5Ccdot18%7D%7D%20%5C%5C%20%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B8%7D%7D%5Ccdot%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B18%7D%7D%3D%5Csqrt%5B%5D%7B%5Cfrac%7B49%7D%7B144%7D%7D%20%5C%5C%20%5Ctext%7B%20Apply%20the%20quotient%20property%7D%20%5C%5C%20%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B8%7D%7D%5Ccdot%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B18%7D%7D%3D%5Cfrac%7B%5Csqrt%5B%5D%7B49%7D%7D%7B%5Csqrt%5B%5D%7B144%7D%7D%20%5C%5C%20%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B8%7D%7D%5Ccdot%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B18%7D%7D%3D%5Cfrac%7B7%7D%7B12%7D%20%5Cend%7Bgathered%7D)
Therefore, the choice that is equivalent to the given product is:
First get a common denominator. (3x*2)
x(x-8) -3(3x)
-------------------
3x^2
x^2 - 8x - 9x
------------------
3x^2
x^2 - 17x
--------------
3x^2
The first one is correct