2(2x-4) because when you multiply 2 x 2x it equals 4x. When you multiply 2 x 4 it equals 8. Leaving you with 4x-8
The p-axis is 10 and the e-axis is 150
The new mixture exists 56.5% peanuts.
<h3>How to estimate the total number of peanuts required for the mixture?</h3>
The first batch of 9 lb of mixed nuts possesses 40% peanuts.
This means the quantity of peanuts exists:
9
40/100 = 3.6 lb
The second batch of 9 lb of mixed nuts possesses 73% peanuts.
This means the quantity of peanuts exists:
9
73/100 = 6.57 lb
The total quantity of peanuts in the mix exists
3.6 lb + 6.57 lb = 10.17 lb
There exist 9 lb + 9 lb = 18 lb of mix.
Therefore, the percent of peanuts in the mix exists:
10.17 / 18
100 = 56.5%
The new mixture exists 56.5% peanuts.
To learn more about the total quantity refer to:
brainly.com/question/18919760
#SPJ4
Consider, please, the suggested solution.
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{Double Angle:}\qquad \dfrac{\cos 2A+1}{2}+\dfrac{\cos 2B+1}{2}+\cos^2 C\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg(2+\cos 2A+\cos 2B\bigg)+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\dfrac{1}{2}\bigg(\cos 2A+\cos 2B\bigg)+\cos^2 C](https://tex.z-dn.net/?f=%5Ctext%7BDouble%20Angle%3A%7D%5Cqquad%20%5Cdfrac%7B%5Ccos%202A%2B1%7D%7B2%7D%2B%5Cdfrac%7B%5Ccos%202B%2B1%7D%7B2%7D%2B%5Ccos%5E2%20C%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%282%2B%5Ccos%202A%2B%5Ccos%202B%5Cbigg%29%2B%5Ccos%5E2%20C%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D1%2B%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%28%5Ccos%202A%2B%5Ccos%202B%5Cbigg%29%2B%5Ccos%5E2%20C)
![\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{Given:}\qquad \qquad 1+\cos C\cdot \cos (A-B)+\cos^2C](https://tex.z-dn.net/?f=%5Ctext%7BGiven%3A%7D%5Cqquad%20%5Cqquad%201%2B%5Ccos%20C%5Ccdot%20%5Ccos%20%28A-B%29%2B%5Ccos%5E2C)
![\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)
![\text{Given:}\qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+A}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-B}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1+2\cos C \cdot \cos A\cdot \cos (-B)](https://tex.z-dn.net/?f=%5Ctext%7BGiven%3A%7D%5Cqquad%20%5Cqquad%20%3D1%2B2%5Ccos%20C%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7BA%2BA%7D%7B2%7D%5Cbigg%29%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7B-B-B%7D%7B2%7D%5Cbigg%29%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D1%2B2%5Ccos%20C%20%5Ccdot%20%5Ccos%20A%5Ccdot%20%5Ccos%20%28-B%29)
![\text{Even/Odd:}\qquad \qquad 1+2\cos C \cdot \cos A\cdot \cos B\\\\\\.\qquad \qquad \qquad \quad =1+2\cos A \cdot \cos B\cdot \cos C](https://tex.z-dn.net/?f=%5Ctext%7BEven%2FOdd%3A%7D%5Cqquad%20%5Cqquad%201%2B2%5Ccos%20C%20%5Ccdot%20%5Ccos%20A%5Ccdot%20%5Ccos%20B%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cquad%20%3D1%2B2%5Ccos%20A%20%5Ccdot%20%5Ccos%20B%5Ccdot%20%5Ccos%20C)
LHS = RHS: 1 + 2 cos A · cos B · cos C = 1 + 2 cos A · cos B · cos C ![\checkmark](https://tex.z-dn.net/?f=%5Ccheckmark)