Angles ∝ and β are the two acute angles in a right triangle. use the relationship between sine and cosine to find the value of β if β > ∝. sin( x 2 + 20x) = cos(2x + 15x 2 )

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?

If there is 20 dogs in the shelter and 5 dogs get homes, and then 43 more dogs come. how many dogs are there in the shelter?

What is the equation of a line passing through (-6,5) and having a slope of 1/3