6. At the beginning of this month, the balance of Esmeralda's checking account was $1023.49. So far this month, she has received a paycheck via direct deposit of $778.98, been charged a monthly

service fee from her bank of $18, used a debit card linked to her account to make a purchase of

$51.27, written a check for $388.63 that has already been deposited, and deposited a check written

to her for $102.76, all in that order. Esmeralda wants to know the current balance of her account. (5

points: Part 1 - 1 point; Part II - 1 point; Part III - 1 point; Part IV - 1 point; Part V- 1 point)

Part 1: What was the balance of Esmeralda's checking account after she received her paycheck via

direct deposit?

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?