Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = π → C = π - (A + B)
→ sin C = sin(π - (A + B)) cos C = sin(π - (A + B))
→ sin C = sin (A + B) cos C = - cos(A + B)
Use the following Sum to Product Identity:
sin A + sin B = 2 cos[(A + B)/2] · sin [(A - B)/2]
cos A + cos B = 2 cos[(A + B)/2] · cos [(A - B)/2]
Use the following Double Angle Identity:
sin 2A = 2 sin A · cos A
<u>Proof LHS → RHS</u>
LHS: (sin 2A + sin 2B) + sin 2C
![\text{Factor:}\qquad \qquad \qquad 2\sin C\cdot [\cos (A-B)+\cos (A+B)]](https://tex.z-dn.net/?f=%5Ctext%7BFactor%3A%7D%5Cqquad%20%5Cqquad%20%5Cqquad%202%5Csin%20C%5Ccdot%20%5B%5Ccos%20%28A-B%29%2B%5Ccos%20%28A%2BB%29%5D)
LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C 
Answer:
B
Step-by-step explanation:
f(x) - g(x)
= 2x² - 4x - 3 - (x - 4)(x + 4) ← expand using FOIL
= 2x² - 4x - 3 - (x² - 16) ← distribute by - 1
= 2x² - 4x - 3 - x² + 16 ← collect like terms
= x² - 4x + 13 → B
Answer:
18.44%
Step-by-step explanation:
Let :
Percentage who rode bus to work last year = x
Percentage who ride bus to work this year = 27.1%
Percentage who ride bus to work this year = [percentage who rode bus to work last year + 47% of percentage who rode bus to work last year]
Mathematically ;
27.1% = x + 47% of x
0.271 = x + (0.47x)
0.271 = x + 0.47x
0.271 = 1.47x
x = 0.271 / 1.47
x = 0.1843537
x = 0.1843537 * 100%
x = 18.435%
x = 18.44%
