the readius of the outer circle is R. the radius of the inner circle is r. Write an expression for the area of the outer circle. write an expression for the area of the inner circle. write expression representing the area of the ring shaded region in the illustration. factor the representing expression

45% of the trees in a park are apple trees. there are 27 apple trees in the park. how many trees are in the park in all?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Segment an is an altitude of right δabc with a right angle at a. if ab = 2, squared 5 in and nc = 1 in, find bn, an, ac.