Answer:
-3/2 < x < 5......................
Option C:
is equivalent to the given expression.
Solution:
Given expression:
![$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B-18%20a%5E%7B-2%7D%20b%5E%7B5%7D%7D%7B-12%20a%5E%7B-4%7D%20b%5E%7B-6%7D%7D)
To find which expression is equivalent to the given expression.
![$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B-18%20a%5E%7B-2%7D%20b%5E%7B5%7D%7D%7B-12%20a%5E%7B-4%7D%20b%5E%7B-6%7D%7D)
Using exponent rule: ![\frac{1}{a^m}=a^{-m}, \ \ \frac{1}{a^{-m}}=a^{m}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Ba%5Em%7D%3Da%5E%7B-m%7D%2C%20%5C%20%5C%20%20%5Cfrac%7B1%7D%7Ba%5E%7B-m%7D%7D%3Da%5E%7Bm%7D)
![$=\frac{-18 a^{-2} b^{5}a^{4} b^{6}}{-12 }](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B-18%20a%5E%7B-2%7D%20b%5E%7B5%7Da%5E%7B4%7D%20b%5E%7B6%7D%7D%7B-12%20%7D)
![$=\frac{-18 a^{-2} a^{4} b^{5} b^{6}}{-12 }](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B-18%20a%5E%7B-2%7D%20a%5E%7B4%7D%20b%5E%7B5%7D%20b%5E%7B6%7D%7D%7B-12%20%7D)
Using exponent rule: ![{a^m}\cdot{a^n}=a^{m+n}](https://tex.z-dn.net/?f=%7Ba%5Em%7D%5Ccdot%7Ba%5En%7D%3Da%5E%7Bm%2Bn%7D)
![$=\frac{-18 a^{(-2+4)} b^{(5+6)}}{-12 }](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B-18%20a%5E%7B%28-2%2B4%29%7D%20b%5E%7B%285%2B6%29%7D%7D%7B-12%20%7D)
![$=\frac{-18 a^{2} b^{11}}{-12 }](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B-18%20a%5E%7B2%7D%20b%5E%7B11%7D%7D%7B-12%20%7D)
Divide both numerator and denominator by the common factor –6.
![$=\frac{3 a^{2} b^{11}}{2 }](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B3%20a%5E%7B2%7D%20b%5E%7B11%7D%7D%7B2%20%7D)
![$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}=\frac{3 a^{2} b^{11}}{2 }](https://tex.z-dn.net/?f=%24%5Cfrac%7B-18%20a%5E%7B-2%7D%20b%5E%7B5%7D%7D%7B-12%20a%5E%7B-4%7D%20b%5E%7B-6%7D%7D%3D%5Cfrac%7B3%20a%5E%7B2%7D%20b%5E%7B11%7D%7D%7B2%20%7D)
Therefore,
is equivalent to the given expression.
Hence Option C is the correct answer.
Get it to equal 0
minus 17x from both sides
2x²-17x+35=0
tricky part
get something like
(2x-a)(x-b)
we know the signs are negative since the middle term is negative and last term is positive
so a and b are either 1 and 35 or 5 and 7
(2x-1)(x-35), nope
(2x-35)(x-1) nope
(2x-5)(x-7), nope
(2x-7)(x-5), yep
(2x-7)(x-5)=0
set to zero
2x-7=0
2x=7
x=7/2
x-5=0
x=5
x=7/2 and 5
B is the correct answer
hope it helps!