<u>ANSWER: </u>
The equation is y = 1.06x, so option D is correct.
<u>EXPLANATION:</u>
Given:
Amount Catherine is paid for an MP3 player=$159.00
The price paid includes a sales tax= 6%
To find:
Equations that can be used to determine the price of the MP3 player before tax?
Solution:
Now, we know that, total cost = selling price of item + sales tax on item
y = x + 6% of x
y = x + 
y = x + 0.06x
y = 1.06x
Hence, the equation is y = 1.06x, so option D is correct.
It looks like the given equation is
sin(2x) - sin(2x) cos(2x) = sin(4x)
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
sin(2x) - sin(2x) cos(2x) = 2 sin(2x) cos(2x)
Move everything over to one side and factorize:
sin(2x) - sin(2x) cos(2x) - 2 sin(2x) cos(2x) = 0
sin(2x) - 3 sin(2x) cos(2x) = 0
sin(2x) (1 - 3 cos(2x)) = 0
Then we have two families of solutions,
sin(2x) = 0 or 1 - 3 cos(2x) = 0
sin(2x) = 0 or cos(2x) = 1/3
[2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
(where n is any integer)
[2x = 2nπ or 2x = π + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
[x = nπ or x = π/2 + nπ]
… … … or [x = 1/2 arccos(1/3) + nπ or x = -1/2 arccos(1/3) + nπ]
Answer:
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
hope this helps
A 180 degree clockwise rotation is the same thing as two 90 degree clockwise rotation.
