Answer:
The equivalent expression for the given expression ![\sqrt[3]{256x^{10}y^{7} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D)
is
![4x^{3} y^{2}(\sqrt[3]{4xy} )](https://tex.z-dn.net/?f=4x%5E%7B3%7D%20y%5E%7B2%7D%28%5Csqrt%5B3%5D%7B4xy%7D%20%29)
Step-by-step explanation:
Given:
Solution:
We will see first what is Cube rooting.
![\sqrt[3]{x^{3}} = x](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E%7B3%7D%7D%20%3D%20x)
Law of Indices
Now, applying above property we get
![\sqrt[3]{256x^{10}y^{7} }=\sqrt[3]{(4^{3}\times 4\times (x^{3})^{3}\times x\times (y^{2})^{3}\times y )} \\\\\textrm{Cube Rooting we get}\\\sqrt[3]{256x^{10}y^{7} }= 4\times x^{3}\times y^{2}(\sqrt[3]{4xy}) \\\\\sqrt[3]{256x^{10}y^{7} }= 4x^{3}y^{2}(\sqrt[3]{4xy})](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D%3D%5Csqrt%5B3%5D%7B%284%5E%7B3%7D%5Ctimes%204%5Ctimes%20%28x%5E%7B3%7D%29%5E%7B3%7D%5Ctimes%20x%5Ctimes%20%28y%5E%7B2%7D%29%5E%7B3%7D%5Ctimes%20y%20%20%20%29%7D%20%5C%5C%5C%5C%5Ctextrm%7BCube%20Rooting%20we%20get%7D%5C%5C%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D%3D%204%5Ctimes%20x%5E%7B3%7D%5Ctimes%20y%5E%7B2%7D%28%5Csqrt%5B3%5D%7B4xy%7D%29%20%5C%5C%5C%5C%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D%3D%204x%5E%7B3%7Dy%5E%7B2%7D%28%5Csqrt%5B3%5D%7B4xy%7D%29)
∴ The equivalent expression for the given expression is
Step-by-step explanation:
81x⁴ - 16y⁴
(9x²)² - (4y²)²
(9x² + 4y²)(9x² - 4y²)
(9x² + 4y²)(3x + 2y)(3x - 2y)
Answer:
7.D) 107°
8. A) 123°
Step-by-step explanation:
To find the correct measurement of the angel the sum of the interior angels needs to equal 360°. Angels where the lines intersect with the circle would be both 90°. ( If that makes sense.)
90°+90°=180
180°+73°= 253°
360°-253°= 107°
The same for the second one. (those two angles would also be 90° each.)
90°+90°=180°
180°+57°=237°
360°-237°=123°
Answer:
Their y-intercepts are equal
Step-by-step explanation:
The y-intercept is the y-value where the function crosses the y-axis. In this problem, functions are presented in 2 ways: algebraically and in a table.
1) Fortunately, the algebraic equation is written in slope-intercept form; this means that intercept is easy to find. The slope-intercept form is y=mx+b, where b is the y-intercept. In function 1, the b value is 10.
2) Another way to describe the y-intercept is the y-value when x=0. So, the y-intercept on a table is wherever the x-value is 0. In this case, the first row represents when x=0. The table says that when x=0, y=10. This means that the y-intercept for function 2 is 10.
Since the y-intercept for both of the functions is 10, it can be said that the 2 functions have equivalent y-intercepts.
