Answer:
C) They are perpendicular lines.
Step-by-step explanation:
We first need to find the slope of the graph of the lines passing through these points using:
![m = \frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20)
The slope of the line that passes through (−12, 15) and (4, −5) is
![m_{1} = \frac{ - 5 - 15}{4 - - 12}](https://tex.z-dn.net/?f=%20m_%7B1%7D%20%3D%20%20%5Cfrac%7B%20-%205%20-%2015%7D%7B4%20-%20%20-%2012%7D%20)
![m_{1} = \frac{ - 20}{16} = - \frac{5}{4}](https://tex.z-dn.net/?f=m_%7B1%7D%20%3D%20%20%5Cfrac%7B%20-%2020%7D%7B16%7D%20%20%3D%20%20-%20%20%5Cfrac%7B5%7D%7B4%7D%20)
The slope of the line going through (−8, −9) and (16, 21) is
![m_{2} = \frac{21 - - 9}{16 - - 8}](https://tex.z-dn.net/?f=%20m_%7B2%7D%20%3D%20%20%5Cfrac%7B21%20-%20%20-%209%7D%7B16%20-%20%20-%208%7D%20)
![m_{2} = \frac{21 + 9}{16 + 8}](https://tex.z-dn.net/?f=%20m_%7B2%7D%20%3D%20%20%5Cfrac%7B21%20%20%2B%209%7D%7B16%20%20%2B%208%7D%20)
![m_{2} = \frac{30}{24} = \frac{5}{4}](https://tex.z-dn.net/?f=m_%7B2%7D%20%3D%20%20%5Cfrac%7B30%7D%7B24%7D%20%20%3D%20%20%5Cfrac%7B5%7D%7B4%7D%20)
The product of the two slopes is
![m_{1} \times m_{2} = - \frac{4}{5} \times \frac{5}{4} = - 1](https://tex.z-dn.net/?f=m_%7B1%7D%20%5Ctimes%20m_%7B2%7D%20%3D%20%20-%20%20%5Cfrac%7B4%7D%7B5%7D%20%20%5Ctimes%20%20%5Cfrac%7B5%7D%7B4%7D%20%20%3D%20%20-%201)
Since
![m_{1} \times m_{2} = - 1](https://tex.z-dn.net/?f=m_%7B1%7D%20%5Ctimes%20m_%7B2%7D%20%3D%20%20-%201)
the two lines are perpendicular.
Transformations of logarithmic graphs behave similarly to those of other parent functions. We can shift, stretch,compress, and reflect the parent function y=log b (x) without loss of shape.
Answer: A
Step-by-step explanation: You have so much tabs open
Answer:
y + 13 = 5(x + 2)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
given y = 5x - 3 with m = 5 and (a, b) = (- 2, - 13), then
y +13 = 5(x + 2) ← in point- slope form
The inverse function of
is![f^{-1}(x) = 4x^2- 3](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%204x%5E2-%203)
<h3>How to determine the inverse function?</h3>
The function is given as:
![f(x) = -\frac 12\sqrt{x + 3}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-%5Cfrac%2012%5Csqrt%7Bx%20%2B%203%7D)
Rewrite as;
![y = -\frac 12\sqrt{x + 3}](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%2012%5Csqrt%7Bx%20%2B%203%7D)
Swap the positions of x and y
![x = -\frac 12\sqrt{y + 3}](https://tex.z-dn.net/?f=x%20%3D%20-%5Cfrac%2012%5Csqrt%7By%20%2B%203%7D)
Multiply through by -2
![-2x = \sqrt{y + 3}](https://tex.z-dn.net/?f=-2x%20%3D%20%5Csqrt%7By%20%2B%203%7D)
Square both sides
4x^2 = y + 3
Subtract 3 from both sides
y = 4x^2 - 3
Express as an inverse function
![f^{-1}(x) = 4x^2- 3](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%204x%5E2-%203)
Hence, the inverse function of
is![f^{-1}(x) = 4x^2- 3](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%204x%5E2-%203)
Read more about inverse function at:
brainly.com/question/2541698
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