Answer:
D
Step-by-step explanation:
Any other product in Quadrant IV will be negative also, so Quadrant IV is part of my answer. The points (x, y), with xy < 0, lie in Quadrants II and IV.
Hello from MrBillDoesMath!
Answer: (4b-6) log(a) = log (3c + d)
Discussion:
Take the log of both sides of the equation:
log ( a ^(4b-6)) = log (3c + d)
As the log functions causes exponents to become multiplexers, this equation is the same as
(4b-6) log(a) = log (3c + d)
Thank you,
MrB
The equation of the line that passes through the points is y=3/5x+3
For this case we must simplify the following expression:
![\frac {6-3 \sqrt [3] {6}} {\sqrt [3] {9}}](https://tex.z-dn.net/?f=%5Cfrac%20%7B6-3%20%5Csqrt%20%5B3%5D%20%7B6%7D%7D%20%7B%5Csqrt%20%5B3%5D%20%7B9%7D%7D)
Multiplying the numerator and denominator by![(\sqrt [3] {9}) ^ 2](https://tex.z-dn.net/?f=%28%5Csqrt%20%5B3%5D%20%7B9%7D%29%20%5E%202)
![\frac {6-3 \sqrt [3] {6}} {\sqrt [3] {9}} * \frac {(\sqrt [3] {9}) ^ 2} {(\sqrt [3] { 9}) ^ 2} =](https://tex.z-dn.net/?f=%5Cfrac%20%7B6-3%20%5Csqrt%20%5B3%5D%20%7B6%7D%7D%20%7B%5Csqrt%20%5B3%5D%20%7B9%7D%7D%20%2A%20%5Cfrac%20%7B%28%5Csqrt%20%5B3%5D%20%7B9%7D%29%20%5E%202%7D%20%7B%28%5Csqrt%20%5B3%5D%20%7B%209%7D%29%20%5E%202%7D%20%3D)
We rewrite:
![\frac {\frac {6-3 \sqrt [3] {6}} * (\sqrt [3] {9}) ^ 2} {\sqrt [3] {9} * (\sqrt [3] {9 }) ^ 2} =](https://tex.z-dn.net/?f=%5Cfrac%20%7B%5Cfrac%20%7B6-3%20%5Csqrt%20%5B3%5D%20%7B6%7D%7D%20%2A%20%28%5Csqrt%20%5B3%5D%20%7B9%7D%29%20%5E%202%7D%20%7B%5Csqrt%20%5B3%5D%20%7B9%7D%20%2A%20%28%5Csqrt%20%5B3%5D%20%7B9%20%7D%29%20%5E%202%7D%20%3D)
By properties of powers we have that:
![a ^ m * a ^ n = a ^ {m + n}\\\frac {(6-3 \sqrt [3] {6}) * (\sqrt [3] {9}) ^ 2} {(\sqrt [3] {9}) ^ 3} =\\\frac {(6-3 \sqrt [3] {6}) * (\sqrt [3] {9}) ^ 2} {9} =](https://tex.z-dn.net/?f=a%20%5E%20m%20%2A%20a%20%5E%20n%20%3D%20a%20%5E%20%7Bm%20%2B%20n%7D%5C%5C%5Cfrac%20%7B%286-3%20%5Csqrt%20%5B3%5D%20%7B6%7D%29%20%2A%20%28%5Csqrt%20%5B3%5D%20%7B9%7D%29%20%5E%202%7D%20%7B%28%5Csqrt%20%5B3%5D%20%7B9%7D%29%20%5E%203%7D%20%3D%5C%5C%5Cfrac%20%7B%286-3%20%5Csqrt%20%5B3%5D%20%7B6%7D%29%20%2A%20%28%5Csqrt%20%5B3%5D%20%7B9%7D%29%20%5E%202%7D%20%7B9%7D%20%3D)
We rewrite, moving the exponent within the radical:
![\frac {(6-3 \sqrt [3] {6}) * \sqrt [3] {9 ^ 2}} {9} =\\\frac {(6-3 \sqrt [3] {6}) * \sqrt [3] {81}} {9} =](https://tex.z-dn.net/?f=%5Cfrac%20%7B%286-3%20%5Csqrt%20%5B3%5D%20%7B6%7D%29%20%2A%20%5Csqrt%20%5B3%5D%20%7B9%20%5E%202%7D%7D%20%7B9%7D%20%3D%5C%5C%5Cfrac%20%7B%286-3%20%5Csqrt%20%5B3%5D%20%7B6%7D%29%20%2A%20%5Csqrt%20%5B3%5D%20%7B81%7D%7D%20%7B9%7D%20%3D)
We can rewrite
![\frac {(6-3 \sqrt [3] {6}) * \sqrt [3] {3 * 3 ^ 3}} {9} =](https://tex.z-dn.net/?f=%5Cfrac%20%7B%286-3%20%5Csqrt%20%5B3%5D%20%7B6%7D%29%20%2A%20%5Csqrt%20%5B3%5D%20%7B3%20%2A%203%20%5E%203%7D%7D%20%7B9%7D%20%3D)
We simplify:
![\frac {(6-3 \sqrt [3] {6}) * 3 \sqrt [3] {3}} {9} =](https://tex.z-dn.net/?f=%5Cfrac%20%7B%286-3%20%5Csqrt%20%5B3%5D%20%7B6%7D%29%20%2A%203%20%5Csqrt%20%5B3%5D%20%7B3%7D%7D%20%7B9%7D%20%3D)
We apply distributive property:
![\frac {18 \sqrt [3] {3} -9 \sqrt [3] {18}} {9} =](https://tex.z-dn.net/?f=%5Cfrac%20%7B18%20%5Csqrt%20%5B3%5D%20%7B3%7D%20-9%20%5Csqrt%20%5B3%5D%20%7B18%7D%7D%20%7B9%7D%20%3D)
Simplifying we finally have:
![2 \sqrt [3] {3} - \sqrt [3] {18}](https://tex.z-dn.net/?f=2%20%5Csqrt%20%5B3%5D%20%7B3%7D%20-%20%5Csqrt%20%5B3%5D%20%7B18%7D)
Answer:
![2 \sqrt [3] {3} - \sqrt [3] {18}](https://tex.z-dn.net/?f=2%20%5Csqrt%20%5B3%5D%20%7B3%7D%20-%20%5Csqrt%20%5B3%5D%20%7B18%7D)
Answer:
The x-intercepts are - (-1, 0) and (-11,0)
The y-intercept is - (0,11)
Step-by-step explanation: I just did it ..