Two arcades charge an entrance fee and a fee per game. at arcade a, the total cosi y (in dollars) of playing 2 games is represented by the linear function y=0.75.2 + 2. the table shows the total cost for playing i games at arcade b. determine which arcade is described by each phrase below. number of games, 0 4 8 12 total cost (dollars), y 8 10 12 14 arcade a arcade b higher fee per game higher entrance fee higher total cost for 12 games

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?