Given the vertices of a rhombus, A(0, 0) , B(b, c) , C(b+b2+c2−−−−−−√, c) , and D(b2+c2−−−−−−√, 0) , prove that the diagonals form four right angles. (Hint: Think about the products of the slopes of perpendicular lines.

Awasher and a dryer cost $701 combined. the washer costs $51 more than the dryer. what is the cost of the dryer?

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.

Luke started a weight-loss program. the first week, he lost x pounds. the second week, he lost pounds less than times the pounds he lost the first week. the third week, he lost 1 pound more than of the pounds he lost the first week. liam started a weight-loss program when luke did. the first week, he lost 1 pound less than times the pounds luke lost the first week. the second week, he lost 4 pounds less than times the pounds luke lost the first week. the third week, he lost pound more than times the pounds luke lost the first week.