Although sarah would like to visit all of these cities, because she only has a budget of €1,410, she recognizes that she will have to drop some of these cities from her plan. which of the following pairs of cities will not put sarah back under budget if she drops them? a. thessaloniki and serres b. volos and athens c. larissa and kavala d. heraklion and chania

2y= 3 2 x−2 y = − 1 3 x + 1 y=− 3 1 x+1

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?

A(1,1) b(-3,0) c(-4,-1) d(3,-2) drag it to correct position