arun ran a mile in 9.8 minutes. lucas ran a mile in 11.74 minutes. how much faster did arun run than lucas.

What is the area of the trapezoid shown ?

To which sets of numbers does -12 belong? choose all answers that are correct. a) natural numbers b) integers c) real numbers d) irrational numbers

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?