Given:
The functions are:
![f(x)=|3x-5|+7x](https://tex.z-dn.net/?f=f%28x%29%3D%7C3x-5%7C%2B7x)
![g(x)=-2x+9](https://tex.z-dn.net/?f=g%28x%29%3D-2x%2B9)
To find:
The function
.
Solution:
We have,
![f(x)=|3x-5|+7x](https://tex.z-dn.net/?f=f%28x%29%3D%7C3x-5%7C%2B7x)
![g(x)=-2x+9](https://tex.z-dn.net/?f=g%28x%29%3D-2x%2B9)
We know that,
![(f+g)(x)=f(x)+g(x)](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3Df%28x%29%2Bg%28x%29)
On substituting the values of given functions, we get
![(f+g)(x)=|3x-5|+7x+(-2x+9)](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3D%7C3x-5%7C%2B7x%2B%28-2x%2B9%29)
![(f+g)(x)=|3x-5|+7x-2x+9](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3D%7C3x-5%7C%2B7x-2x%2B9)
![(f+g)(x)=|3x-5|+5x+9](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3D%7C3x-5%7C%2B5x%2B9)
Therefore, the required function is
.
Answer:
The Answer is: y = -1/4x + 6
Step-by-step explanation:
Given point: (4, 5)
Given equation: y = -1/4x - 11
Slope: m = -1/4, a parallel line will have the same slope.
Start with the point slope form and solve for y:
y - y1 = m(x - x1)
y - 5 = -1/4(x - 4)
y - 5 = -1/4x + 1
y = -1/4x + 1 + 5
y = -1/4x + 6
Proof:
f(x) = -1/4x + 6
f(4) = -1/4(4) + 6
= -1 + 6 = 5, giving (4, 5)
Hope this helps!! Have an Awesome day!!! :-)
Answer:
D
Step-by-step explanation:
Its D because when you rotate 360 degrees you end up back where you were
Find the slope of the line first:
5x - 2y = -6,
y = (5/2)x + 3;
Since we need a line that's perpendicular, m = - (2/5).
The only equation that has the slope of this m is 2x + 5y = -10;