The graph of the function P(x) = −0.52x2 + 23x + 92 is shown. The function models the profits, P, in thousands of dollars for a candle company to manufacture a candle, where x is the number of candles produced, in thousands: graph of a parabola opening down passing through points negative 3 and 69 hundredths comma zero, zero comma 92, 6 and 84 hundredths comma 225, 22 and 11 hundredths comma 346 and 33 hundredths, 37 and 39 hundredths comma 225, and 47 and 92 hundredths comma zero If the company wants to keep its profits at or above $225,000, then which constraint is reasonable for the model? 0 ≤ x < 6.84 and 37.39 < x ≤ 47.92 −3.69 ≤ x ≤ 6.84 and 37.39 < x ≤ 47.92 6.84 ≤ x ≤ 37.39 −3.69 ≤ x ≤ 47.92

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?

25) 56(1) = 5b a. identity property of addition b. identity property of multiplication c. commutative property of multiplication d. commutative property of addition

Factor the polynomial. b^2 + 4b + 4