We are to determine if the given are differences of perfect cubes and in order to do so, we simply have to calculate for the cube root of the terms in the given.
(a) 9a³ - 27 = ((∛9)a)³ - 3³ ; NO
(b) 125a¹² - 72 = (5a⁴)³ - (∛72)³ ; NO
(c) 216a⁶ - 27y³ = (6a²)³ - (3y)³ ; YES
(d) 8a¹⁵ - 27 = (2a⁵)³ - (3)³ ; YES
(e) 225a³ - 216 = (15a)³ - (6)³ ; YES
Therefore, the answers are the third, fourth, and fifth choices.
Answer:
elga is 32 and alvin is 49
Given:
Consider the given expression is
To find:
The radical form of given expression.
Solution:
We have,
![(4x^3y^2)^{\frac{3}{10}}=\sqrt[5]{2^3}\sqrt[10]{x^9}\sqrt[5]{y^3}](https://tex.z-dn.net/?f=%284x%5E3y%5E2%29%5E%7B%5Cfrac%7B3%7D%7B10%7D%7D%3D%5Csqrt%5B5%5D%7B2%5E3%7D%5Csqrt%5B10%5D%7Bx%5E9%7D%5Csqrt%5B5%5D%7By%5E3%7D)
![[\because x^{\frac{1}{n}}=\sqrt[n]{x}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20x%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D%3D%5Csqrt%5Bn%5D%7Bx%7D%5D)
![(4x^3y^2)^{\frac{3}{10}}=\sqrt[5]{8y^3}\sqrt[10]{x^9}](https://tex.z-dn.net/?f=%284x%5E3y%5E2%29%5E%7B%5Cfrac%7B3%7D%7B10%7D%7D%3D%5Csqrt%5B5%5D%7B8y%5E3%7D%5Csqrt%5B10%5D%7Bx%5E9%7D)
Therefore, the required radical form is ![\sqrt[5]{8y^3}\sqrt[10]{x^9}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B8y%5E3%7D%5Csqrt%5B10%5D%7Bx%5E9%7D)
.
Answer:
must be parallel
Step-by-step explanation:
They must be parallel.
Answer: B) y = -x^4
Work: I just plugged in the numbers into all the equations listed, and B worked correctly for them all, thus that's the correct answer.
<em>I hope this helps, and Happy Holidays. :)</em>
