According to the question, Reactant A does not react unless B gets to a certain concentration. Therefore, the correct answer will have an initial flat line for A while the line for B is rising. Only graph (B) shows this initial relationship. Therefore, the correct answer is (B).

All of the answers have the same lines graphed, so this question is really about the shading. Plugging In is probably the easiest way to approach this problem. Start with (0, 0) because this is an easy value to check. This works in all three equations since 0 ≤ 8, -3 ≤ 0, and 1 ≥ 0. Therefore, this value needs to be shaded as a possible answer. Eliminate (B), (C), and (D) because they do not include this point. The correct answer is (A).

Use Process of Elimination to answer this question. According to the question, P represents the population, so the outcome of the entire equation has something to do with the population. Therefore, eliminate both (A) and (B) because 1.0635 can’t represent the population if P does. In the equation given, the only operations are multiplication and addition, which means that over time the population would increase. Therefore, eliminate (D). The correct answer is (C).

To solve the quadratic equation, first set the equation equal to 0. The equation becomes x² + 12x – 64 = 0. Next, factor the equation to get (x + 16)(x – 4) = 0. Therefore, the two possible solutions for the quadratic equation are x + 16 = 0 and x – 4 = 0, so x = -16 or 4. Since the question states that x > 0, x = 4 is the only possible solution. Another way to approach this question is to plug in the answers. Start with (B), x = 4. Plug 4 into the equation to get 4² + 12(4) = 64. Solve the left side of the equation to get 16 + 48 = 64, or 64 = 64. Since this is a true statement, the correct answer is (B).