DAY 1
You start with 4
You triple it to get 12
You subtract 2 to get 10
DAY 2
You start with 10
You triple it to get 20
You subtract 2 to get 18
DAY 3
You start with 18
You triple it to get 54
You subtract 2 to get 52...
This isn't going anywhere, now is it? You're never going to reach zero, it must be a trick question.
Step-by-step explanation:
![\frac{ {r}^{2} - 4r + 5}{r - 4} - \frac{ {r}^{2} + 2r - 8}{r - 4} \\ = \frac{ ({r}^{2} - 4r + 5) - ( {r}^{2} + 2r - 8) }{r + 4} \\ = \frac{ {r}^{2} - {r}^{2} - 4r - 2r + 5 - 8 }{r - 4} \\ = \frac{ - 6r - 3}{r - 4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7Br%7D%5E%7B2%7D%20%20-%204r%20%2B%205%7D%7Br%20-%204%7D%20%20-%20%20%5Cfrac%7B%20%7Br%7D%5E%7B2%7D%20%20%2B%202r%20-%208%7D%7Br%20-%204%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B%20%28%7Br%7D%5E%7B2%7D%20-%204r%20%2B%205%29%20-%20%28%20%7Br%7D%5E%7B2%7D%20%20%2B%202r%20-%208%29%20%7D%7Br%20%2B%204%7D%20%20%5C%5C%20%20%3D%20%20%20%5Cfrac%7B%20%7Br%7D%5E%7B2%7D%20-%20%20%7Br%7D%5E%7B2%7D%20%20-%204r%20-%202r%20%2B%205%20-%208%20%7D%7Br%20-%204%7D%20%20%5C%5C%20%20%3D%20%20%20%5Cfrac%7B%20-%206r%20-%203%7D%7Br%20-%204%7D%20)
Complete the table of values for the function f(x) = (1/3)x for a, b, and c. x : -2, -1, 0, 1, 2. f(x) : a, b, c, 1/3, 1/9
balu736 [363]
Given:
The function is
![f(x)=\left(\dfrac{1}{3}\right)^x](https://tex.z-dn.net/?f=f%28x%29%3D%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5Ex)
To find:
The missing values for a, b, and c in the given table.
Solution:
We have,
![f(x)=\left(\dfrac{1}{3}\right)^x](https://tex.z-dn.net/?f=f%28x%29%3D%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5Ex)
At x=-2,
![f(-2)=\left(\dfrac{1}{3}\right)^{-2}](https://tex.z-dn.net/?f=f%28-2%29%3D%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5E%7B-2%7D)
![\left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbecause%20%5Cleft%28%5Cdfrac%7Ba%7D%7Bb%7D%5Cright%29%5E%7B-n%7D%3D%5Cleft%28%5Cdfrac%7Bb%7D%7Ba%7D%5Cright%29%5E%7Bn%7D%5Cright%5D)
![a=9](https://tex.z-dn.net/?f=a%3D9)
At x=-1,
![f(-1)=\left(\dfrac{1}{3}\right)^{-1}](https://tex.z-dn.net/?f=f%28-1%29%3D%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5E%7B-1%7D)
![\left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbecause%20%5Cleft%28%5Cdfrac%7Ba%7D%7Bb%7D%5Cright%29%5E%7B-n%7D%3D%5Cleft%28%5Cdfrac%7Bb%7D%7Ba%7D%5Cright%29%5E%7Bn%7D%5Cright%5D)
![b=3](https://tex.z-dn.net/?f=b%3D3)
At x=0,
![f(0)=\left(\dfrac{1}{3}\right)^{0}](https://tex.z-dn.net/?f=f%280%29%3D%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5E%7B0%7D)
![\left[\because a^0=1, a\neq 0\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbecause%20a%5E0%3D1%2C%20a%5Cneq%200%5Cright%5D)
Therefore, the missing values of a,b and c are 9, 3, and 1 respectively.
Answer:
5 times 5 is 25 25 +12= 37
Step-by-step explanation:
I believe the variable d equals 13. Since the rule is x-6=y. So you just incorporate 7, since 7=y the equation now will look like x-6=7. Now you just solve it. X=13 other known as d=13.