Answer:
see below
Step-by-step explanation:
x ≤ 3
There is a closed circle at 3 because of the equals sign
the lines goes to the left since it is less than
x < 3
There is a open circle at 3 because there is no equals sign
the lines goes to the left since it is less than
Answer:
Equation to solve is x+x+120=180
Solution to equation: x=30
Step-by-step explanation:
The angles in a triangle have a sum 180 degrees.
You know one angle is 120 degrees.
If you assume another angle has a measurement of x degrees, then the remaining angle has a measurement of x degrees. We know this because congruent means they will have the same measurement.
So we have this equation to solve:
x+x+120=180
Combine like terms:
2x+120=180
Subtract 120 on both sides:
2x=180-120
Simplify:
2x=60
Divide both sides by 2:
x=60/2
Simplify:
x=30
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]
