10 to the fourth power times equals 70,000 what is in that blank what number

Jamie went to home depot.she bought 25 bags of soil that cost $9 per bag.she bought 15 pots at $8 each, and she bought 23 bags of pebbles at $15 each.she used a coupon that gave her $5 off for every 100 dollars she spent. how much did jamie pay at the end?

1- 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.2- 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 the first question?

Find the maximum value of p= 4x + 5y subject to the following constraints :