PLEASE HELP! I WILL MARK BRAINLEST! HELP! Please show step by step work! The complex numbers $z$ and $w$ satisfy $|z| = |w| = 1$ and $zw \ne -1.$

(a) Prove that $\overline{z} = \frac{1}{z}$ and $\overline{w} = \frac{1}{w}.$

(b) Prove that $\frac{z + w}{zw + 1}$ is a real number.

Sherina wrote and solved the equation. x-56=230 x-56-56=230-56 x=174 what was sherina’s error? sherina’s work is correct. sherina only needed to subtract 56 from 230. sherina made a subtraction error when subtracting 56 from 230. sherina should have added 56 to both sides of the equation.

You drop a rubber ball off the roof of a 50 meter high building onto a paved parking lot. it bounces back up with every bounce, but not quite all the way back up to you. after the first bounce it bounces back only 80 percent of the distance it was dropped from. the pattern continues, meaning after every bounce it comes up to just 80 percent of the previous maximum height. so if before the first bounce the height is 50 meters, what height does the ball reach after the fifth bounce? round your answer to one decimal place and chose the correct response from the choices below:

Amanager recorded the number of bicycles sold by his company each quarter. his projected sales after t years is given by the expression below. which of the following statements best describes the expression? a. the initial sales of 575 bicycles increases at the rate of 4% over 4 quarters. b. the initial sales of 575 bicycles increases at the rate of 18% over 4 years. c. the initial sales of 575 bicycles increases at the rate of 4% over t quarters. d. the initial sales of 575 bicycles increases at the rate of 18% over t years.