If the two angles are supplementary, they must equal 180 degrees
Answer:
D
Step-by-step explanation:
Consider all options:
A. False, because
![(a^2+b^2)(c^2+d^2)=a^2c^2+a^2d^2+b^2c^2+b^2d^2\\ \\(ab-cd)^2+(ac+bd)^2=a^2b^2-2abcd+c^2d^2+a^2c^2+2abcd+b^2d^2=\\ =a^2b^2+c^2d^2+a^2c^2+b^2d^2\\ \\a^2c^2+a^2d^2+b^2c^2+b^2d^2\neq a^2b^2+c^2d^2+a^2c^2+b^2d^2](https://tex.z-dn.net/?f=%28a%5E2%2Bb%5E2%29%28c%5E2%2Bd%5E2%29%3Da%5E2c%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%2Bb%5E2d%5E2%5C%5C%20%5C%5C%28ab-cd%29%5E2%2B%28ac%2Bbd%29%5E2%3Da%5E2b%5E2-2abcd%2Bc%5E2d%5E2%2Ba%5E2c%5E2%2B2abcd%2Bb%5E2d%5E2%3D%5C%5C%20%3Da%5E2b%5E2%2Bc%5E2d%5E2%2Ba%5E2c%5E2%2Bb%5E2d%5E2%5C%5C%20%5C%5Ca%5E2c%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%2Bb%5E2d%5E2%5Cneq%20a%5E2b%5E2%2Bc%5E2d%5E2%2Ba%5E2c%5E2%2Bb%5E2d%5E2)
B. False, because
![(a^2-b^2)(c^2+d^2)=a^2c^2+a^2d^2-b^2c^2-b^2d^2\\ \\(ac-bd)^2-(ad+bc)^2=a^2c^2-2abcd+b^2d^2+a^2d^2+2abcd+b^2c^2=\\=a^2c^2+b^2d^2+a^2d^2+b^2c^2\\ \\a^2c^2+a^2d^2-b^2c^2-b^2d^2\neq a^2c^2+b^2d^2+a^2d^2+b^2c^2](https://tex.z-dn.net/?f=%28a%5E2-b%5E2%29%28c%5E2%2Bd%5E2%29%3Da%5E2c%5E2%2Ba%5E2d%5E2-b%5E2c%5E2-b%5E2d%5E2%5C%5C%20%5C%5C%28ac-bd%29%5E2-%28ad%2Bbc%29%5E2%3Da%5E2c%5E2-2abcd%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2B2abcd%2Bb%5E2c%5E2%3D%5C%5C%3Da%5E2c%5E2%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%5C%5C%20%5C%5Ca%5E2c%5E2%2Ba%5E2d%5E2-b%5E2c%5E2-b%5E2d%5E2%5Cneq%20a%5E2c%5E2%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2)
C. False, because
![(a^2+b^2)(c^2-d^2)=a^2c^2-a^2d^2+b^2c^2-b^2d^2\\ \\(ac+bd)^2-(ad+bc)^2=a^2c^2+2abcd+b^2d^2-a^2d^2-2abcd-b^2c^2=\\=a^2c^2+b^2d^2-a^2d^2-b^2c^2\\ \\a^2c^2-a^2d^2+b^2c^2-b^2d^2\neq a^2c^2+b^2d^2-a^2d^2-b^2c^2](https://tex.z-dn.net/?f=%28a%5E2%2Bb%5E2%29%28c%5E2-d%5E2%29%3Da%5E2c%5E2-a%5E2d%5E2%2Bb%5E2c%5E2-b%5E2d%5E2%5C%5C%20%5C%5C%28ac%2Bbd%29%5E2-%28ad%2Bbc%29%5E2%3Da%5E2c%5E2%2B2abcd%2Bb%5E2d%5E2-a%5E2d%5E2-2abcd-b%5E2c%5E2%3D%5C%5C%3Da%5E2c%5E2%2Bb%5E2d%5E2-a%5E2d%5E2-b%5E2c%5E2%5C%5C%20%5C%5Ca%5E2c%5E2-a%5E2d%5E2%2Bb%5E2c%5E2-b%5E2d%5E2%5Cneq%20a%5E2c%5E2%2Bb%5E2d%5E2-a%5E2d%5E2-b%5E2c%5E2)
D. True, because
![(a^2+b^2)(c^2+d^2)=a^2c^2+a^2d^2+b^2c^2+b^2d^2\\ \\(ac-bd)^2-(ad+bc)^2=a^2c^2-2abcd+b^2d^2+a^2d^2+2abcd+b^2c^2=\\=a^2c^2+b^2d^2+a^2d^2+b^2c^2\\ \\a^2c^2+a^2d^2+b^2c^2+b^2d^2= a^2c^2+b^2d^2+a^2d^2+b^2c^2](https://tex.z-dn.net/?f=%28a%5E2%2Bb%5E2%29%28c%5E2%2Bd%5E2%29%3Da%5E2c%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%2Bb%5E2d%5E2%5C%5C%20%5C%5C%28ac-bd%29%5E2-%28ad%2Bbc%29%5E2%3Da%5E2c%5E2-2abcd%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2B2abcd%2Bb%5E2c%5E2%3D%5C%5C%3Da%5E2c%5E2%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%5C%5C%20%5C%5Ca%5E2c%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%2Bb%5E2d%5E2%3D%20a%5E2c%5E2%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2)
Hey there!
So the original profit is y=22x; x=number of necklaces and y=profit
New:
y=29x; x=number of necklaces and y=profit
Xavier will earn $7 more if he switches to his new plan because a keyword in the question is "How many more" and that usually means to subtract, so take away 22 from 29 and you get 7
Hope this helps!
XY
01
11
21
31
41
This will simply be a horizontal line at y = 1
ANSWER
Brayden should have expanded the parenthesis first.
EXPLANATION
The expression Brayden is trying to simplify is
![4n - {( n - 2)}^{2}](https://tex.z-dn.net/?f=4n%20-%20%20%7B%28%20n%20-%202%29%7D%5E%7B2%7D%20)
To simplify this expression, the first thing to do is to expand the perfect square to obtain:
![4n - {( n}^{2} - 4n + 4)](https://tex.z-dn.net/?f=4n%20-%20%20%7B%28%20n%7D%5E%7B2%7D%20%20-%204n%20%2B%204%29)
We can now distribute the negative to the terms in the parenthesis.
![4n - { n}^{2} + 4n - 4](https://tex.z-dn.net/?f=4n%20-%20%20%7B%20n%7D%5E%7B2%7D%20%20%20%2B%204n%20%20-%204)