Determine if each statement is true or false. If the statement is false, explain why, or show work proving that it is false.a. If a = 5, then ac = 5c.b. If ac = 5c, then a = 5.

Accepted Solution

Answer:a). trueb). trueStep-by-step explanation:a).Given : If a = 5, then ac = 5c             Let c be any constant.             a = 5 (given)             Therefore, ac = 5cHere a  is given a constant value (5), also let assume c to be a constant. So when we multiply each term we will get a constant value of 5c. The ratio does not change.Hence proved.b).Given : If ac = 5c, then a = 5             Let c be any constant             It is given, a = 5Therefore, ac = 5cHere the product of two terms is given as 5c, where c is assume to be a constant. Then as a product rule, the value of a will be 5. The ratio will not change.Hence proved.