Answer:
(-2, -3)
Step-by-step explanation:
2x + 1 = 3x + 3
minus 3 from both sides
2x - 2 = 3x
minus 2x from both sides
-2 = x
then plug in -2 for x
y = 2(-2) + 1
y = -4 + 1
y = -3
(-2, -3).
Answer:
![f(n) =4 + f(n-1) \\for\ n>2](https://tex.z-dn.net/?f=f%28n%29%20%3D4%20%2B%20f%28n-1%29%20%5C%5Cfor%5C%20n%3E2)
Step-by-step explanation:
Given
![f(1)=2\\ f(2)= 6\\ f(3)= 10\\ f(4)= 14\\ f(5)= 18](https://tex.z-dn.net/?f=f%281%29%3D2%5C%5C%20f%282%29%3D%206%5C%5C%20f%283%29%3D%2010%5C%5C%20f%284%29%3D%2014%5C%5C%20f%285%29%3D%2018)
Required
Determine the formula
First, we need to solve common difference (d)
![d = f(n) - f(n-1)](https://tex.z-dn.net/?f=d%20%3D%20f%28n%29%20-%20f%28n-1%29)
Take n as 2
![d = f(2) - f(2-1)](https://tex.z-dn.net/?f=d%20%3D%20f%282%29%20-%20f%282-1%29)
![d = 6 - 2](https://tex.z-dn.net/?f=d%20%3D%206%20-%202)
![d = 4](https://tex.z-dn.net/?f=d%20%3D%204)
Represent each function as a sum of the previous
![f(1) = 2](https://tex.z-dn.net/?f=f%281%29%20%3D%202)
![f(2) = 2 + 4 = f(1) + 4](https://tex.z-dn.net/?f=f%282%29%20%3D%202%20%2B%204%20%3D%20f%281%29%20%2B%204)
![f(3) = 6 + 4 = f(2) + 4](https://tex.z-dn.net/?f=f%283%29%20%3D%206%20%2B%204%20%3D%20f%282%29%20%2B%204)
![f(4) = 10 + 4 = f(3) + 4](https://tex.z-dn.net/?f=f%284%29%20%3D%2010%20%2B%204%20%3D%20f%283%29%20%2B%204)
![f(5) = 14 + 4 = f(4) + 4](https://tex.z-dn.net/?f=f%285%29%20%3D%2014%20%2B%204%20%3D%20f%284%29%20%2B%204)
Represent the function as ![f(n)](https://tex.z-dn.net/?f=f%28n%29)
![f(n) =f(n-1) + 4](https://tex.z-dn.net/?f=f%28n%29%20%3Df%28n-1%29%20%2B%204)
Reorder
![f(n) =4 + f(n-1) \\for\ n>2](https://tex.z-dn.net/?f=f%28n%29%20%3D4%20%2B%20f%28n-1%29%20%5C%5Cfor%5C%20n%3E2)
Just multiply the numbers by 1.25
![6 \times 1.25 = 7.5 \\ 12 \times 1.25 = 15](https://tex.z-dn.net/?f=6%20%5Ctimes%201.25%20%3D%207.5%20%5C%5C%2012%20%5Ctimes%201.25%20%3D%2015)
so the height is 15 in
and base is 7.5 in
goodluck