Answer: see proof below
<u>Step-by-step explanation:</u>
Given: cos 330 = 
Use the Double-Angle Identity: cos 2A = 2 cos² A - 1

Proof LHS → RHS:
LHS cos 165
Double-Angle: cos (2 · 165) = 2 cos² 165 - 1
⇒ cos 330 = 2 cos² 165 - 1
⇒ 2 cos² 165 = cos 330 + 1
Given: 

Divide by 2: 

Square root: 
Scratchwork: 

Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

LHS = RHS 
Answer:
$63
Step-by-step explanation:
let x represent Charity B then Charity A = 5x
Sum the two and equate to 378, that is
x + 5x = 378
6x = 378 ( divide both sides by 6 )
x = 63
Thus Charity B received $63
1 a 2c 3b 4a 5d hoooooooooppppppppeeeee thiiss hellps
Answer:
smaller number = 17, larger number = 34
Step-by-step explanation:
Let x be the smaller number and y be the larger nuber
x + y = 51 --(1)
y - 17 = x --(2)
Sub (2) into (1)
y - 17 + y = 51
y = 34
Put y = 34 into (2)
34 - 17 = x
x = 17
Ans: smaller number = 17, larger number = 34
Answer:
C = 2d + 15
Step-by-step explanation:
$2 per km, so $40 for 20km.
55-40 is 15 so $15 is a fixed price.
Hence, C = 2d + 15