The breakeven point is when revenue equals cost or when the profit is zero. P(x) = R(x) - C(x) = 0. If the profit is zero, then R(x) = C(x) . We will use this equation to find the breakeven point-R(x) = C(x) . 3 x = 50 + 2 x. x = 50. So, the hot dog vendor needs to sell at least 50 hot dogs on a given day to break even.
Justinian I, who took power in 527 and would rule until his death in 565, was the first great ruler of the Byzantine Empire.
A. the daughter of a nobleman who became Justinian's wife in an arranged marriage B. the empress who shared power with Justinian and worked on behalf of women and the poor C. the ruler who became empress after Justinian's death D. the first woman to serve on the committee that codified the laws of the Byzantine Empire.