Answer:
m∠1 = 92°
Step-by-step explanation:
∠2 corresponds to the supplement of ∠3 if (and only if) lines a and b are parallel. We find that
m∠2 + m∠3 = 73° +107° = 180°
so, the angles are supplementary and lines a and b are parallel.
Angles 4 and 1 are corresponding angles where the line d crosses the parallel lines a and b, so are congruent.
m∠1 = m∠4 = 92°
Answer:
![4x^{3} y^{2} (\sqrt[3]{4 x y})](https://tex.z-dn.net/?f=4x%5E%7B3%7D%20y%5E%7B2%7D%20%28%5Csqrt%5B3%5D%7B4%20x%20y%7D%29)
Step-by-step explanation:
Another complex expression, let's simplify it step by step...
We'll start by re-writing 256 as 4^4
![\sqrt[3]{256 x^{10} y^{7} } = \sqrt[3]{4^{4} x^{10} y^{7} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B256%20x%5E%7B10%7D%20y%5E%7B7%7D%20%7D%20%3D%20%5Csqrt%5B3%5D%7B4%5E%7B4%7D%20x%5E%7B10%7D%20y%5E%7B7%7D%20%7D)
Then we'll extract the 4 from the cubic root. We will then subtract 3 from the exponent (4) to get to a simple 4 inside, and a 4 outside.
![\sqrt[3]{4^{4} x^{10} y^{7} } = 4 \sqrt[3]{4 x^{10} y^{7} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B4%5E%7B4%7D%20x%5E%7B10%7D%20y%5E%7B7%7D%20%7D%20%3D%204%20%5Csqrt%5B3%5D%7B4%20x%5E%7B10%7D%20y%5E%7B7%7D%20%7D)
Now, we have x^10, so if we divide the exponent by the root factor, we get 10/3 = 3 1/3, which means we will extract x^9 that will become x^3 outside and x will remain inside.
![4 \sqrt[3]{4 x^{10} y^{7} } = 4x^{3} \sqrt[3]{4 x y^{7} }](https://tex.z-dn.net/?f=4%20%5Csqrt%5B3%5D%7B4%20x%5E%7B10%7D%20y%5E%7B7%7D%20%7D%20%3D%204x%5E%7B3%7D%20%5Csqrt%5B3%5D%7B4%20x%20y%5E%7B7%7D%20%7D)
For the y's we have y^7 inside the cubic root, that means the true exponent is y^(7/3)... so we can extract y^2 and 1 y will remain inside.
![4x^{3} \sqrt[3]{4 x y^{7} } = 4x^{3} y^{2} \sqrt[3]{4 x y}](https://tex.z-dn.net/?f=4x%5E%7B3%7D%20%5Csqrt%5B3%5D%7B4%20x%20y%5E%7B7%7D%20%7D%20%3D%204x%5E%7B3%7D%20y%5E%7B2%7D%20%5Csqrt%5B3%5D%7B4%20x%20y%7D)
The answer is then:
![4x^{3} y^{2} \sqrt[3]{4 x y} = 4x^{3} y^{2} (\sqrt[3]{4 x y})](https://tex.z-dn.net/?f=4x%5E%7B3%7D%20y%5E%7B2%7D%20%5Csqrt%5B3%5D%7B4%20x%20y%7D%20%3D%204x%5E%7B3%7D%20y%5E%7B2%7D%20%28%5Csqrt%5B3%5D%7B4%20x%20y%7D%29)
Answer:
42.84
Step-by-step explanation:
3.57*12=42.84
Answer:
28.9
Step-by-step explanation:
2782 divied by 96 gives you 28.9.