Answer:
10.3
Step-by-step explanation:
As we move from (-3,-6) to (2,3), x increases by 5 (this is the horizontal distance between (2,3) and (-3,-6) ) and y decreases by 9 (vertical distance).
We apply the Pythagorean Theorem here:
d^2 = x^2 + y^2, or
d^2 = (5)^2 + (-9)^2 = 25 + 81 = 106
Thus, the distance between (2,3) and (-3,-6) is d = sqrt(106), or approx.
10.3.
14 I think.You would subtract 15-8 which is 7 and then add 7 which is 14
Answer:
![\boxed{-3xy^{2}\sqrt [3] {2x^{2}}}](https://tex.z-dn.net/?f=%5Cboxed%7B-3xy%5E%7B2%7D%5Csqrt%20%5B3%5D%20%7B2x%5E%7B2%7D%7D%7D)
Step-by-step explanation:
Your expression is
![\sqrt [3] {-54x^{5}y^{6}}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B-54x%5E%7B5%7Dy%5E%7B6%7D%7D)
Here's how I would simplify it.
![\begin{array}{rcll}\sqrt [3] {-54x^{5}y^{6}} & = & \sqrt [3] {(-1)^{3}\times 2 \times 27 \times x^{2} \times x^{3} \times y^{6}} & \text{Factored the cubes}\\& = & \sqrt [3] {(-1)^{3} \times 3^{3}\times x^{3} \times y^{6}\times 2 \times x^{2}} & \text{Grouped the cubes}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcll%7D%5Csqrt%20%5B3%5D%20%7B-54x%5E%7B5%7Dy%5E%7B6%7D%7D%20%26%20%3D%20%26%20%5Csqrt%20%5B3%5D%20%7B%28-1%29%5E%7B3%7D%5Ctimes%202%20%5Ctimes%2027%20%5Ctimes%20x%5E%7B2%7D%20%5Ctimes%20x%5E%7B3%7D%20%5Ctimes%20y%5E%7B6%7D%7D%20%26%20%5Ctext%7BFactored%20the%20cubes%7D%5C%5C%26%20%3D%20%26%20%5Csqrt%20%5B3%5D%20%7B%28-1%29%5E%7B3%7D%20%5Ctimes%203%5E%7B3%7D%5Ctimes%20x%5E%7B3%7D%20%5Ctimes%20y%5E%7B6%7D%5Ctimes%202%20%5Ctimes%20x%5E%7B2%7D%7D%20%26%20%5Ctext%7BGrouped%20the%20cubes%7D%5C%5C%5Cend%7Barray%7D)
![\begin{array}{rcll}& = & \sqrt [3] {(-1)^{3} \times {3^{3}\times x^{3} \times y^{6}}} \times\sqrt [3] { 2 \times x^{2}} & \text{Separated the cubes}\\&=& \mathbf{-3xy^{2}\sqrt [3] {2x^{2}}} & \text{Took cube roots}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcll%7D%26%20%3D%20%26%20%5Csqrt%20%5B3%5D%20%7B%28-1%29%5E%7B3%7D%20%5Ctimes%20%7B3%5E%7B3%7D%5Ctimes%20x%5E%7B3%7D%20%5Ctimes%20y%5E%7B6%7D%7D%7D%20%5Ctimes%5Csqrt%20%5B3%5D%20%7B%202%20%5Ctimes%20x%5E%7B2%7D%7D%20%26%20%5Ctext%7BSeparated%20the%20cubes%7D%5C%5C%26%3D%26%20%5Cmathbf%7B-3xy%5E%7B2%7D%5Csqrt%20%5B3%5D%20%7B2x%5E%7B2%7D%7D%7D%20%26%20%5Ctext%7BTook%20cube%20roots%7D%5C%5C%5Cend%7Barray%7D)
![\text{The simplified expression is $\boxed{\mathbf{-3xy^{2}\sqrt [3] {2x^{2}}}}$}](https://tex.z-dn.net/?f=%5Ctext%7BThe%20simplified%20expression%20is%20%24%5Cboxed%7B%5Cmathbf%7B-3xy%5E%7B2%7D%5Csqrt%20%5B3%5D%20%7B2x%5E%7B2%7D%7D%7D%7D%24%7D)
