Answer:
The first one is 14.5 and the second one is that the decimal moves to the left every time a zero is added to the first number
Step-by-step explanation:
I’m pretty sure C because C is always right
Answer:
3 or
C
Step-by-step explanation:
(45 - 3x)^1/2 = x - 9 Square both sides
45 - 3x = x^2 - 18x + 81 Switch sides
x^2 - 18x + 81 = 45 - 3x Add 3x to both sides
x^2 - 15x + 81 = 45 Subtract 45 from both sides
x^2 - 15x + 36 = 0 Factor
(x - 12)(x - 3) =0
The answers are
x = 12
x = 3
Now the question asks which is extraneous. The answer will be which ever number won't solve the original equation. Looking at it right now, both look OK.
(45 - 3*12)^1/2 = 12 - 9
(45 - 36)^1/2 = 3
(9)^1/2 = 3
So 12 is a proper solution.
What about 3?
(45 - 3*3)^1/2 = 12 - 3
(45 - 9)^1/2 = 9
36^1/2 = 9
6 does not = 9
The extraneous solution is x = 3
![2^{-5} = \dfrac{1}{2^5} = \dfrac{1}{32}](https://tex.z-dn.net/?f=2%5E%7B-5%7D%20%3D%20%5Cdfrac%7B1%7D%7B2%5E5%7D%20%3D%20%5Cdfrac%7B1%7D%7B32%7D)
![3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{9}](https://tex.z-dn.net/?f=3%5E%7B-2%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%5E2%7D%20%3D%20%5Cdfrac%7B1%7D%7B9%7D)
![5^{-4} = \dfrac{1}{5^4} = \dfrac{1}{25^2} = \dfrac{1}{625}](https://tex.z-dn.net/?f=5%5E%7B-4%7D%20%3D%20%5Cdfrac%7B1%7D%7B5%5E4%7D%20%3D%20%5Cdfrac%7B1%7D%7B25%5E2%7D%20%3D%20%5Cdfrac%7B1%7D%7B625%7D)
![(3^3)^{-2} = 3^{-6} = \dfrac{1}{3^6} = \dfrac{1}{9^3} = \dfrac{1}{729}](https://tex.z-dn.net/?f=%283%5E3%29%5E%7B-2%7D%20%3D%203%5E%7B-6%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%5E6%7D%20%3D%20%5Cdfrac%7B1%7D%7B9%5E3%7D%20%3D%20%5Cdfrac%7B1%7D%7B729%7D)
![\dfrac{1}{4^{-4}} = 4^4 = 16^2 = 256](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%5E%7B-4%7D%7D%20%3D%204%5E4%20%3D%2016%5E2%20%3D%20256)
![\dfrac{1}{2^{-5}} = 2^5 = 32](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%5E%7B-5%7D%7D%20%3D%202%5E5%20%3D%2032)
![(5^{-3})^{-2}=5^6 = 15625 \quad](https://tex.z-dn.net/?f=%285%5E%7B-3%7D%29%5E%7B-2%7D%3D5%5E6%20%3D%2015625%20%5Cquad)
needed the calculator for that one
![\dfrac{4}{5^{-2}} = 4 \cdot 5^{2} = 4 \cdot 25 =100](https://tex.z-dn.net/?f=%5Cdfrac%7B4%7D%7B5%5E%7B-2%7D%7D%20%3D%204%20%5Ccdot%205%5E%7B2%7D%20%3D%204%20%5Ccdot%2025%20%3D100)
![3^{6} \times 3^{-2} = 3^{6 - 2} = 3^4 = 9^2=81](https://tex.z-dn.net/?f=3%5E%7B6%7D%20%5Ctimes%203%5E%7B-2%7D%20%3D%203%5E%7B6%20-%202%7D%20%3D%203%5E4%20%3D%209%5E2%3D81)
![4^{-8} \times 4^5 = 4^{-3} = \dfrac{1}{4^3} = \dfrac{1}{64}](https://tex.z-dn.net/?f=4%5E%7B-8%7D%20%5Ctimes%204%5E5%20%3D%204%5E%7B-3%7D%20%3D%20%5Cdfrac%7B1%7D%7B4%5E3%7D%20%3D%20%5Cdfrac%7B1%7D%7B64%7D)
Substitute each variable for the coefficient. Remember PEMDAS.