Answer:
9
Step-by-step explanation:
Rotational symmetry is when a shape has the same orientation after being rotated.
For example, an equilateral triangle rotated 120° will line back up with itself. A square rotated 90° will also return to its original orientation. Same with a pentagon rotated 72°.
Basically, an n-gon rotated by a multiple of 360°/n will return to its original position.
θ = k 360°/n
For the first rotation:
160° = k 360°/n
160 / 360 = k / n
4/9 = k/n
For the second rotation:
120° = k 360°/n
120 / 360 = k / n
1/3 = k/n
For the third rotation:
80° = k 360°/n
80 / 360 = k / n
2/9 = k/n
For the fourth rotation:
280° = k 360°/n
280 / 360 = k / n
7/9 = k/n
The total rotation angle is -160°.
160 = k 360/n
160 / 360 = k / n
4/9 = k/n
Comparing the denominators, n must be the smallest multiple of 3 and 9. Therefore, n = 9.
I hope this helps I couldn’t explain it with words
remember that you can do anything to an equation as long as you do it to both sides
remember the distributive property: a(b+c)=ab+ac
also commutative property of addition: a+b=b+a
so
6(6x-2)+8(1-5x)=2x
distribute
6(6x-2)=6(6x)+6(-2)=36x-12
8(1-5x)=8(1)+8(-5x)=8-40x
36x-12+8-40x=2x
group like terms
36x-40x-12+8=2x
add like terms
-4x-4=2x
add 4x to both sides to get x by itself
4x-4x-4=2x+4x
0-4=6x
-4=6x
divide both sides by 6
-4/6=(6x)/6
-2/3=x(6/6)
-2/3=x(1)
-2/3=x
x=-2/3
the solution is x=-2/3
By adding, subtracting, multiplying or dividing numbers
