<span>5y-{11y+[-(-7y-15)]}
</span>= 5y-(11y+7y+15)
= 5y-(18y+15)
= -13y+15
Answer:
(-1,-6)
Step-by-step explanation:
We have the following function:
![f(x) = x^{2} + 6x + 3](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E%7B2%7D%20%2B%206x%20%2B%203)
The following transformation is applied
![g(x) = f(x - 2)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20f%28x%20-%202%29)
So
![g(x) = f(x - 2) = (x - 2)^{2} + 6(x - 2) + 3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20f%28x%20-%202%29%20%3D%20%28x%20-%202%29%5E%7B2%7D%20%2B%206%28x%20-%202%29%20%2B%203)
![g(x) = x^{2} - 4x + 4 + 6x - 12 + 3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E%7B2%7D%20-%204x%20%2B%204%20%2B%206x%20-%2012%20%2B%203)
![g(x) = x^{2} + 2x - 5](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E%7B2%7D%20%2B%202x%20-%205)
For a second order function in the format:
![g(x) = ax^{2} + bx + c](https://tex.z-dn.net/?f=g%28x%29%20%3D%20ax%5E%7B2%7D%20%2B%20bx%20%2B%20c)
The vertex is:
![V = (x_{v}, g(x_{v})](https://tex.z-dn.net/?f=V%20%3D%20%28x_%7Bv%7D%2C%20g%28x_%7Bv%7D%29)
In which
![x_{v} = -\frac{b}{2a}](https://tex.z-dn.net/?f=x_%7Bv%7D%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
In this problem
![a = 1, b = 2](https://tex.z-dn.net/?f=a%20%3D%201%2C%20b%20%3D%202)
So
![x_{v} = -\frac{2}{2*1} = -1](https://tex.z-dn.net/?f=x_%7Bv%7D%20%3D%20-%5Cfrac%7B2%7D%7B2%2A1%7D%20%3D%20-1)
Then
![g(x_{v}}) = g(-1) = (-1)^{2} +2(-1) - 5 = -6](https://tex.z-dn.net/?f=g%28x_%7Bv%7D%7D%29%20%3D%20g%28-1%29%20%3D%20%28-1%29%5E%7B2%7D%20%2B2%28-1%29%20-%205%20%3D%20%20-6)
So the correct answer is:
(-1,-6)
Answer:
4th term = 29
to generate the terms, substitute n = 2, 3, 4 into the rule
noting that b(1) = - 7
b(2) = b(2 - 1) + 12 = b(1) + 12 = -7 + 12 = 5
b(3) = b(3 - 1) + 12 = b(2) + 12 = 5 + 12 = 17
b(4) = b(4 - 1) + 12 = b(3) + 12 = 17 + 12 = 29
Answer:
156
Step-by-step explanation:
f(x)= 4^(2x) -100
Let x =2
f(2)= 4^(2*2) -100
= 4^4 - 100
= 256 -100
= 156