Find the magnitude and the direction of AB⃗⃗⃗⃗⃗, BC⃗⃗⃗⃗⃗, and AC⃗⃗⃗⃗⃗, if
AB⃗⃗⃗⃗⃗ = 12î− 5ĵand BC⃗⃗⃗⃗⃗ = 3î− 4ĵ.

Adj has a total of 1075 dance and rock songs on her system. the dance selection is 4 times the size of the rock selection. write a system of equations to represent the situation.

If 25% of y is 30, what is 60% of y?

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?