This isnt something I can do... But draw and label a tape diagram that goes from 0 to 30.
Option C:
![$\frac{\sqrt[3]{100 x}}{5}=\sqrt[3]{\frac{4 x}{5}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B5%7D%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%20x%7D%7B5%7D%7D)
Solution:
Given expression is
![$\sqrt[3]{\frac{4 x}{5}}](https://tex.z-dn.net/?f=%24%5Csqrt%5B3%5D%7B%5Cfrac%7B4%20x%7D%7B5%7D%7D)
Note: ![\sqrt[3]{125}=\sqrt[3]{{5^3}} = 5](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B125%7D%3D%5Csqrt%5B3%5D%7B%7B5%5E3%7D%7D%20%20%3D%205)
To find the correct expression for the above simplified expression.
Option A: ![\frac{\sqrt[3]{4 x}}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B4%20x%7D%7D%7B5%7D)
5 can be written as
.
![$\frac{\sqrt[3]{4 x}}{5}=\frac{\sqrt[3]{4 x}}{\sqrt[3]{125} }](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csqrt%5B3%5D%7B4%20x%7D%7D%7B5%7D%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B4%20x%7D%7D%7B%5Csqrt%5B3%5D%7B125%7D%20%7D)
![$=\sqrt[3]{\frac{4x}{125} }](https://tex.z-dn.net/?f=%24%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4x%7D%7B125%7D%20%7D)
It is not the given simplified expression.
Option B: ![\frac{\sqrt[3]{20 x}}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B20%20x%7D%7D%7B5%7D)
![$\frac{\sqrt[3]{20 x}}{5}=\frac{\sqrt[3]{20 x}}{\sqrt[3]{125} }](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csqrt%5B3%5D%7B20%20x%7D%7D%7B5%7D%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B20%20x%7D%7D%7B%5Csqrt%5B3%5D%7B125%7D%20%7D)
![$=\sqrt[3]{\frac{20x}{125} }](https://tex.z-dn.net/?f=%24%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B20x%7D%7B125%7D%20%7D)
Cancel the common factor in both numerator and denominator.
![$=\sqrt[3]{\frac{4x}{25} }](https://tex.z-dn.net/?f=%24%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4x%7D%7B25%7D%20%7D)
It is not the given simplified expression.
Option C: ![\frac{\sqrt[3]{100 x}}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B5%7D)
![$\frac{\sqrt[3]{100 x}}{5}=\frac{\sqrt[3]{100 x}}{\sqrt[3]{125} }](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B5%7D%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B%5Csqrt%5B3%5D%7B125%7D%20%7D)
![$=\sqrt[3]{\frac{100x}{125} }](https://tex.z-dn.net/?f=%24%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B100x%7D%7B125%7D%20%7D)
Cancel the common factor in both numerator and denominator.
![$=\sqrt[3]{\frac{4 x}{5}}](https://tex.z-dn.net/?f=%24%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%20x%7D%7B5%7D%7D)
It is the given simplified expression.
Option D: ![\frac{\sqrt[3]{100 x}}{125}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B125%7D)
![$\frac{\sqrt[3]{100 x}}{125}=\frac{\sqrt[3]{100 x}}{5^3}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B125%7D%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B5%5E3%7D)
It is not the given simplified expression.
Hence Option C is the correct answer.
![$\frac{\sqrt[3]{100 x}}{5}=\sqrt[3]{\frac{4 x}{5}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B5%7D%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%20x%7D%7B5%7D%7D)
Answer:
x = 13
Step-by-step explanation:
1. 4x + 1 = 8x - 51
2. 4x = 8x - 52
3. -4x = -52
4. x = 13
see the attached figure to better understand the problem
we know that
The equilateral triangle has three equal sides
so
in the equilateral triangle ABC

the height of the triangle is the segment BD
in the right triangle BCD
Applying the Pythagorean Theorem

solve for BD

substitute the values



therefore
<u>the answer is</u>
the height of the triangle is 
Answer:
pls give me brainliest
Step-by-step explanation: