PLEASE I NEED HEP ASAP! USA TESTPREP

Suppose that the price p, in dollars, and the number of sales, x, of a certain item follow the equation 4 p plus 4 x plus 2 pxequals56. suppose also that p and x are both functions of time, measured in days. find the rate at which x is changing when xequals2, pequals6, and startfraction dp over dt endfraction equals1.5.

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. 1^2 + 4^2 + 7^2 + + (3n - 2)^2 = [n(6n^2-3n-1)/2]

1. judy took $30 with her to spend on popcorn and drinks for herself and her friends at the movie theater. the price for each bag of popcorn was $5. the price of each drink was half the price of a bag of popcorn. (a) sketch the graph that represents the situation and label the intercepts. use one axis to represent the number of bags of popcorn and the other axis to represent the number of drinks. (b) explain your graph.