Answer:
x = -4
Step-by-step explanation:
Simplifying
2[x + 4] = 2[-8 + -1x] + -2x
Reorder the terms:
2[4 + x] = 2[-8 + -1x] + -2x
[4 * 2 + x * 2] = 2[-8 + -1x] + -2x
[8 + 2x] = 2[-8 + -1x] + -2x
8 + 2x = [-8 * 2 + -1x * 2] + -2x
8 + 2x = [-16 + -2x] + -2x
Combine like terms: -2x + -2x = -4x
8 + 2x = -16 + -4x
Solving
8 + 2x = -16 + -4x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4x' to each side of the equation.
8 + 2x + 4x = -16 + -4x + 4x
Combine like terms: 2x + 4x = 6x
8 + 6x = -16 + -4x + 4x
Combine like terms: -4x + 4x = 0
8 + 6x = -16 + 0
8 + 6x = -16
Add '-8' to each side of the equation.
8 + -8 + 6x = -16 + -8
Combine like terms: 8 + -8 = 0
0 + 6x = -16 + -8
6x = -16 + -8
Combine like terms: -16 + -8 = -24
6x = -24
Divide each side by '6'.
x = -4
Simplifying
x = -4
Applying the trig formula: sin a = cos (90 - a)
cos (2x + 8) = sin (x + 37) = cos (90 - x - 37) = cos (53 - x)
Property of the cosine function -->
(
2
x
+
8
)
=
±
(
53
−
x
)
a. 2x + 8 = 53 - x
3x = 45
x
=
15
∘
b. 2x + 8 = - 53 + x
x
=
−
61
∘
For general answers, add
k
360
∘
Check by calculator.
x = 15 --> sin (x + 37) = sin 52 = 0.788
cos (2x + 8) = cos (38) = 0.788. Proved
x = - 61 --> sin (x + 37) = sin (- 24) = - sin 24 = - 0.407
cos (2x + 8) = cos (-122 + 8) = cos (- 114) = - 0.407. Proved
Step-by-step explanation:
first 12^ 12
second 7^11
It would be: 6/25 * 100 = 6 * 4 = 24%
In short, Your Answer would be Option C
Hope this helps!