The cost of movie tickets is $9.50 for adults and $5.50 for children: if
65.50 = 9.50a + 5.50c represents the total ticket cost for a family to go to the
movies, what do the terms represent? if 4 adults went to the movies, what is the
value for c?

Solve the system of equations y= 3/2 - 1, -x+ y =-3

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?

What happens to the area as the sliders are adjusted? what do you think the formula for the area of a triangle is divided by 2?