If x = 6 tan θ, write the expression θ 2 − sin 2θ 4 in terms of just x. (simplify the double angle using a double-angle identity.)

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:

Luke wants to reduce the area of his rectangular garden by 1/4 the expression 14/w can be used to represent this change. what is another way to write this expression?

Julie was able to walk 16 km through the zoo in 6 hours. how long will it take her to walk 24 km through the zoo?