7.4: How Much Applesauce? It takes 4 pounds of apples to make 6 cups of applesauce. At this rate, how much applesauce can you make with: 7 pounds of apples? 10 pounds of apples? How many pounds of apples would you need to make: 9 cups of applesauce? 20 cups of applesauce?

Will give are given that xy is parallel to zw. if xz is a transversal that intercepts xy and zw, angle angle alternate interior angles. since xy is parallel to zw, we know that these angles are we also know that angle xvy and angle zvw are , and thus congruent. we can conclude that △xyv ~ △zwv using the similarity theorem.

Consider the proof. given: segment ab is parallel to line de. prove: what is the missing statement in step 5?

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .