Use mathematical induction to prove that the statement is true for every positive integer n. 8 + 16 + 24 + . . + 8n = 4n(n + 1)

You are looking at two area rugs for your bedroom. one is a square with side lengths of 6.3 feet. the other is a rectangle that is 4.8 feet by 8.2 feet. which rug will cover the greatest area? how much more area will it cover? with work plzz and u so much

Players on the school soccer team are selling candles to raise money for an upcoming trip. each player has 24 candles to sell. if a player sells 4 candles a profit of$30 is made. if he sells 12 candles a profit of $70 is made. determine an equation to model his situation?

Kayla wants to find the width, ab, of a river. she walks along the edge of the river 65 ft and marks point c. then she walks 25 ft further and marks point d. she turns 90° and walks until her location, point a, and point c are collinear. she marks point e at this location, as shown. (a) can kayla conclude that δ and δ are similar? why or why not? (b) suppose de = 15 ft. what can kayla conclude about the width of the river?