One fruit punch has 45% fruit juice and another is 90% fruit juice. How much of the 45% punch should be mixed with 10 gal of the 90% punch to create a fruit punch that is 50% fruit juice?

What is 100,000 times 1/100,000, using the standard method of multiplication? write the answer as 10 to a power.

Two poles, ab and ed, are fixed to the ground with the of ropes ac and ec, as shown: what is the approximate distance, in feet, between the two poles? 6.93 feet 8.66 feet 12.32 feet 15.59 feet

Prove the converse of the pythagorean theorem using similar triangles. the converse of the pythagorean theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squares length of the hypotenuse, the triangle is a right triangle. be sure to create and name the appropriate geometric figures.