Exercise 2.4.3: Proving algebraic statements with direct proofs. About Prove each of the following statements using a direct proof. (a) For any positive real numbers, and , . Solution (b) If is a real number and , then . (c) If is a real number and , then . Solution (d) If is a real number such that , then .

Going from point a to point b, the cheetah traveled at an average rate of 70 mph. returning to point a, the cheetah traveled at an average rate of 40 mph. can we say that this cheetah’s average rate was 55 mph? uchet write an equation for the average rate for the trip. remember, the cheetah runs from point a to point b and back to point a. first leg of trip: second leg of trip: ⦁ the following equation represents the average rate for the trip. is this equation equivalent to the one you wrote above? explain why or why not.