A theatre contains 460 seats and the ticket prices for a recent play were $50 for adults and $28 for children. If the total proceeds were $16,972 for a sold-out matinee, how many of each type of ticket were sold?
The number of adult tickets was

How many triangles can be drawn with side lengths 4 centimeters, 4.5 centimeters, and 9 centimeters? explain

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?

Solve the following simultaneous equation by using an algebraic method (either substitution or elimination) 2x + 3y=-4 4x-y=11