Arectangle is inscribed in a right isosceles triangle, such that two of its vertices lie on the hypotenuse, and two other on the legs. what are the lengths of the sides of the rectangle, if their ratio is 5: 2, and the length of the hypotenuse is 45 in? (two cases) picture:

Jessica and martha each have a bag of cookies with unequal quantities. they have 30 cookies total between the two of them. each of them ate 6 cookies from their bag. the product of the number of cookies left in each bag is not more than 80. how many more cookies will jessica have martha? if x represents the number of cookies jessica started with, complete the statements below.the inequality that describes the relationship between the number of cookies each one of them has is x^2 - x +224 > = 0.jessica has at least cookies more than martha.

Two cyclists 84 miles apart start riding toward each other at the same. one cycles 2 times as fast as the other. if they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?

In the diagram, gef and hef are congruent. what is the value of x