Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B = C → A = C - B
→ B = C - A
Use the Double Angle Identity: cos 2A = 2 cos² A - 1
→ (cos 2A + 1)/2 = cos² A
Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · 2 cos [(A - B)/2]
Use Even/Odd Identity: cos (-A) = cos (A)
<u>Proof LHS → RHS:</u>
LHS: cos² A + cos² B + cos² C
![\text{Sum to Product:}\quad 1+\dfrac{1}{2}\bigg[2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A-2B}{2}\bigg)\bigg]+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\cos (A+B)\cdot \cos (A-B)+\cos^2 C](https://tex.z-dn.net/?f=%5Ctext%7BSum%20to%20Product%3A%7D%5Cquad%201%2B%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%5B2%5Ccos%20%5Cbigg%28%5Cdfrac%7B2A%2B2B%7D%7B2%7D%5Cbigg%29%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7B2A-2B%7D%7B2%7D%5Cbigg%29%5Cbigg%5D%2B%5Ccos%5E2%20C%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D1%2B%5Ccos%20%28A%2BB%29%5Ccdot%20%5Ccos%20%28A-B%29%2B%5Ccos%5E2%20C)
![\text{Factor:}\qquad \qquad 1+\cos C[\cos (A-B)+\cos C]](https://tex.z-dn.net/?f=%5Ctext%7BFactor%3A%7D%5Cqquad%20%5Cqquad%201%2B%5Ccos%20C%5B%5Ccos%20%28A-B%29%2B%5Ccos%20C%5D)
![\text{Sum to Product:}\quad 1+\cos C\bigg[2\cos \bigg(\dfrac{A-B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{A-B-C}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+(C-B)}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-(C-A)}{2}\bigg)](https://tex.z-dn.net/?f=%5Ctext%7BSum%20to%20Product%3A%7D%5Cquad%201%2B%5Ccos%20C%5Cbigg%5B2%5Ccos%20%5Cbigg%28%5Cdfrac%7BA-B%2BC%7D%7B2%7D%5Cbigg%29%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7BA-B-C%7D%7B2%7D%5Cbigg%29%5Cbigg%5D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D1%2B2%5Ccos%20C%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7BA%2B%28C-B%29%7D%7B2%7D%5Cbigg%29%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7B-B-%28C-A%29%7D%7B2%7D%5Cbigg%29)
LHS = RHS: 1 + 2 cos A · cos B · cos C = 1 + 2 cos A · cos B · cos C 
Answer:
I think its 18
Step-by-step explanation:
Hi there!
The slope of this line is 5*. Therefore, the slope of any line that is parallel to y = 5x + 3 is 5 as well (since parallel lines have the same slope).
* In a linear formula in standard form y = ax + b the a represents the slope of the line. In other words: in a linear formula in above form, the slope is the number in front of x.
Answer:
B) 5 gallons
Step-by-step explanation:
4 quarts = 1 gallon
multiply each number by 5
20 quarters = 5 gallons
For 11, we can subtract x from both sides for the first equation to get y=8-x, making the slope -1 for both equations and therefore making it parallel.
For 13, we can solve for y in the first equation by subtracting 14 from both sides and therefore getting 2x-14=y. For the next one, we can subtract 4x from both sides to get 10-4x=2y. Dividing both sides by 2, we get 10-2x=y. Since for the equations to be parallel they must be the same and for perpendicular they must be -1/(slope), this fits neither.
Using those two explanations, I implore you to solve the other two on your own!
