Answer:
-5^x + 3x + 2
Step-by-step explanation:
(f - g)(x) = ƒ(x) -g(x) = -5^x -(-3x -2) = -5^x + 3x + 2
Answer:
![\sin\theta=\dfrac{15}{17}](https://tex.z-dn.net/?f=%5Csin%5Ctheta%3D%5Cdfrac%7B15%7D%7B17%7D)
![?=15](https://tex.z-dn.net/?f=%3F%3D15)
Step-by-step explanation:
Use the trigonometry formula
![\cos^2\theta+\sin^2\theta=1](https://tex.z-dn.net/?f=%5Ccos%5E2%5Ctheta%2B%5Csin%5E2%5Ctheta%3D1)
You are given that
![\cos \theta=\dfrac{8}{17}](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%3D%5Cdfrac%7B8%7D%7B17%7D)
Substitute into the first formula
![\left(\dfrac{8}{17}\right)^2+\sin^2\theta=1\\ \\\dfrac{64}{289}+\sin^2\theta=1\\ \\\sin^2\theta=1-\dfrac{64}{289}=\dfrac{289-64}{289}=\dfrac{225}{289}\\ \\\sin \theta=\pm \dfrac{15}{17}](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B8%7D%7B17%7D%5Cright%29%5E2%2B%5Csin%5E2%5Ctheta%3D1%5C%5C%20%5C%5C%5Cdfrac%7B64%7D%7B289%7D%2B%5Csin%5E2%5Ctheta%3D1%5C%5C%20%5C%5C%5Csin%5E2%5Ctheta%3D1-%5Cdfrac%7B64%7D%7B289%7D%3D%5Cdfrac%7B289-64%7D%7B289%7D%3D%5Cdfrac%7B225%7D%7B289%7D%5C%5C%20%5C%5C%5Csin%20%5Ctheta%3D%5Cpm%20%5Cdfrac%7B15%7D%7B17%7D)
Angle
is acute angle, then the sine of this angle is positive and
![\sin\theta=\dfrac{15}{17}](https://tex.z-dn.net/?f=%5Csin%5Ctheta%3D%5Cdfrac%7B15%7D%7B17%7D)
Given:
The equation of a function is
![y=(x-4)^2+1](https://tex.z-dn.net/?f=y%3D%28x-4%29%5E2%2B1)
To find:
The graph of the given function.
Solution:
The vertex form of a parabola is
...(i)
Where, (h,k) is vertex of the parabola.
We have,
...(ii)
From (i) and (ii), we get
![h=4, k=1](https://tex.z-dn.net/?f=h%3D4%2C%20k%3D1)
The vertex of the parabola is (4,1).
Now, the table of values is
x y
2 5
3 2
4 1
5 2
6 5
Plot these points on a coordinate plane and connect them by a free hand curve.
The graph of given function is shown below.
27/6 can be written as 27 divided by 6 to make it easier for you to understand the answer would be 4.5