Which best proves why the expressions 4(x+3)+2x and 6(x+2) must be equivalent expressions?
when x = 3, both expressions have a value of 30.
when x = 5, both expressions have a value of 42.
when x= 1, both expressions have a value of 18, and when x = 8, both expressions have a value of 60.
when x= 2, both expressions have a value of 15, and when x=6, both expressions have a value of 39.

What is the percentile for data value 6 in the following data set? 4 13 8 6 4 4 13 6 4 13 2 13 15 5 9 4 12 8 6 13 40 25 35 62

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?

Convert the mixed numbers into improper fractions. convert the improper fraction to mixed numbers.