After getting new carpet installed, Antonio noticed that the door would not close. He trimmed to of an inch off of the bottom of the door to see if it would help. After doing this three more times, the door finally closed. If the door was originally 84 inches tall, how tall was it after he trimmed it? (PLEASE HELP THIS IS 90℅ IN MY GRADE) ​

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?

If chord ab is congruent to chord cd, then what must be true about ef and eg?

Mat bought a phone for $100. he has to pay $30 per mouth. if he has paid $640 in total, how many mouth has he had the phone?