cos (2x) = cos x
2 cos^2 x -1 = cos x using the double angle formula
2 cos ^2 x -cos x -1 =0
factor
(2 cos x+1) ( cos x -1) = 0
using the zero product property
2 cos x+1 =0 cos x -1 =0
2 cos x = -1 cos x =1
cos x = -1/2 cos x=1
taking the arccos of each side
arccos cos x = arccos (-1/2) arccos cos x = arccos 1
x = 120 degrees x=-120 degrees x=0
remember you get 2 values ( 2nd and 3rd quadrant)
these are the principal values
now we need to add 360
x = 120+ 360n x=-120+ 360n x = 0 + 360n where n is an integer
money going out (20.38+11.48+19.50) =51.36
balance - out = new balance
65.40-51.36 =
14.04
new balance = 14.04
Answer:
16, 8, 23
Step-by-step explanation:
2x+x+x+15=47
4x+15=47
4x=32
x=8
2x=16
x+15=23
<h3>
Answer:</h3>
x=30
<h3>
Solution:</h3>
- First, use the distributive property:
- 8x-3(2x-4)=3(x-6)
- 8x-6x+12=3x-18
- Simplify:
- 2x+12=3x-18
- 2x-3x=-12-18
- -x=-30
- x=30
Hope it helps.
Do comment if you have any query.
