⦁The completed construction of a regular hexagon is shown below. Explain why ACF is a 30º-60º-90º triangle. (10 points)

Step-by-step explanation:

You can prove that angle C is 30°. This is because we know that angle B is 120° also, and co-interior angles add to 180°, which makes angle BCF 60°. Then we can divide this by 2 as angle BCF is bisected by AC, so therefore angle ACF is 30° as 60 ÷ 2 = 30.

You can then prove angle A is 90°. First we can find angle BAC because it is part of a triangle, and angles in a triangle add to 180°. This means we can do 30 + 120 = 150, and 180 - 150 = 30° which is angle BAC. Then we do 120 - 30 = 90, as the whole of angle BAF is 120°.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3