Translate into an equation and solve. the sum of two numbers is thirty-three. six times the smaller is equal to five times the larger. find the larger number.

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 is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4? 1 –1 i –i

In each diagram, line p is parallel to line f, and line t intersects lines p and f. based on the diagram, what is the value of x? ( provide explanation)