concrete tiles are made using buckets of cement, sand and gravel mixed in the ratio 1:4:6. how many buckets of gravel are need for 4 buckets of cement?

The vet charges $45 for an office visit and $10 for each vaccination your dog needs. write an eaquation

Can someone me and do the problem plz so i can understand it more better

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?