x y
------ -----
-9 -2
-5 -7
-1 -12
3 -17
ur x's all have a difference of 4, and ur y's all have a difference of -5...so yes, this is linear with a slope of (-7+2) / (-5 + 9) = -5/4
Answer:
1) Pre-image.
Step-by-step explanation:
2) Translation.
The expression that is not a variation of the Pythagorean identity is the third option.
<h3>
What is the Pythagorean identity?</h3>
The Pythagorean identity can be written as:
![sin^2(x) + cos^2(x) = 1](https://tex.z-dn.net/?f=sin%5E2%28x%29%20%2B%20cos%5E2%28x%29%20%3D%201)
For example, if we subtract cos^2(x) on both sides we get the second option:
![sin^2(x) = 1 - cos^2(x)](https://tex.z-dn.net/?f=sin%5E2%28x%29%20%3D%201%20-%20cos%5E2%28x%29)
Which is a variation.
Now, let's divide both sides by cos^2(x).
![sin^2(x)/cos^2(x) + cos^2(x)/cos^2(x) = 1/cos^2(x)\\\\tan^2(x) + 1 = sec^2(x)\\\\tan^2(x) - sec^2(x) = -1](https://tex.z-dn.net/?f=sin%5E2%28x%29%2Fcos%5E2%28x%29%20%2B%20cos%5E2%28x%29%2Fcos%5E2%28x%29%20%3D%201%2Fcos%5E2%28x%29%5C%5C%5C%5Ctan%5E2%28x%29%20%2B%201%20%3D%20sec%5E2%28x%29%5C%5C%5C%5Ctan%5E2%28x%29%20-%20sec%5E2%28x%29%20%3D%20-1)
Notice that the third expression in the options looks like this one, but the one on the right side is positive. The above expression is in did a variation of the Pythagorean identity, then the one written in the options (with the 1 instead of the -1) is incorrect, meaning that it is not a variation of the Pythagorean identity.
Concluding, the correct option is the third one.
If you want to learn more about the Pythagorean identity, you can read:
brainly.com/question/24287773
Answer:
The coordinates of D is (-4,-9)
Step-by-step explanation:
Given
C = (2,7)
<em>M=(-1,-1) ----- Missing part of question</em>
Required
Determine the coordinates of D
<em>Let the coordinates of D be (x₂,y₂)</em>
<em>We'll solve this question using mid point formula;</em>
<em></em>
<em></em>
<em>Where</em>
and ![M(x,y) = (-1,-1)](https://tex.z-dn.net/?f=M%28x%2Cy%29%20%3D%20%28-1%2C-1%29)
Put these values in the formula
![(-1,-1) = (\frac{2+x_2}{2},\frac{7+y_2}{2})](https://tex.z-dn.net/?f=%28-1%2C-1%29%20%3D%20%28%5Cfrac%7B2%2Bx_2%7D%7B2%7D%2C%5Cfrac%7B7%2By_2%7D%7B2%7D%29)
By comparison;
and ![-1 = \frac{7+y_2}{2}](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7B7%2By_2%7D%7B2%7D)
![-1 = \frac{2+x_2}{2}](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7B2%2Bx_2%7D%7B2%7D)
Multiply both sides by 2
![-2 = 2 + x_2](https://tex.z-dn.net/?f=-2%20%3D%202%20%2B%20x_2)
Subtract 2 from both sides
![-2 -2 = x_2](https://tex.z-dn.net/?f=-2%20-2%20%3D%20x_2)
![x_2 = -4](https://tex.z-dn.net/?f=x_2%20%3D%20-4)
![-1 = \frac{7+y_2}{2}](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7B7%2By_2%7D%7B2%7D)
Multiply both sides by 2
![-2 = 7 + y_2](https://tex.z-dn.net/?f=-2%20%3D%207%20%2B%20y_2)
Subtract 7 from both sides
![-2 - 7 = y_2](https://tex.z-dn.net/?f=-2%20-%207%20%3D%20y_2)
![y_2 = -9](https://tex.z-dn.net/?f=y_2%20%3D%20-9)
<em>Hence, the coordinates of D is (-4,-9)</em>
The square root of -5
2.23606798
or
-2.23606798