Answer:
4 cannot be the measure of the third side. This is because of the Triangle Inequality Theorem, which states that the sum of two sides of a triangle must be greater than the third side (A+B>C, A+C>B, B+C>A) In this example, if side C were 4, side C (4) plus side A (8) would be 12. Since side B is 12, and 12 cannot be greater than 12, 4 would not work.
Answer=8
Step-by-step explanation:
Since we have a cubic root, we're interested in factoring cubes inside the root, so that we can take them out. If we factor 648, we have

So, we have
![3x\sqrt[3]{648 x^4 y^8} = \sqrt[3]{3\times 6^3\cdot x^3\cdot x \cdot y^6\cdot y^2}=3x\cdot 6\cdot x\cdot y^2\sqrt[3]{3\cdot x\cdot y^2}](https://tex.z-dn.net/?f=3x%5Csqrt%5B3%5D%7B648%20x%5E4%20y%5E8%7D%20%3D%20%5Csqrt%5B3%5D%7B3%5Ctimes%206%5E3%5Ccdot%20x%5E3%5Ccdot%20x%20%5Ccdot%20y%5E6%5Ccdot%20y%5E2%7D%3D3x%5Ccdot%206%5Ccdot%20x%5Ccdot%20y%5E2%5Csqrt%5B3%5D%7B3%5Ccdot%20x%5Ccdot%20y%5E2%7D)
And the result simplifies to
![18x^2y^2\sqrt[3]{3xy^2}](https://tex.z-dn.net/?f=18x%5E2y%5E2%5Csqrt%5B3%5D%7B3xy%5E2%7D)
The answer to the question
Answer:
Step-by-step explanation:
Q1)
Use Phythogoras theorem:

Q2)
Apply phythogoras theorem:

Q3)
Apply phythogoras theorem again:

I have an attached an image for Question 2 for better understanding the length of DE in question equals 15 - 6 = 9
Answer:

Step-by-step explanation:
Slope Formula: 
Step 1: Find 2 points
(0, 2) y-int
(-4, 0) x-int
Step 2: Plug into slope formula to find slope <em>m</em>
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