Final answer:
The correct equations to model the intersection of the arrow and target are y = -0.002x² + 0.25x + 6 for the arrow's trajectory and y = 0.15x for the target line, which corresponds to Option B.
Step-by-step explanation:
The student has provided multiple equations that could model the scenario where an arrow intersects a target. The correct option must represent a point of intersection between the trajectory of the arrow (modeled by a quadratic equation) and the target (modeled by a linear equation).
To find the correct equations, we have to consider the properties of the trajectory and the target line. A trajectory is generally represented by a parabolic equation of the form y = ax² + bx + c, and the target line is a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.
Given the scenario, the trajectory would have a negative a value because the arrow is moving downwards after reaching its peak, and the target line would typically have a positive slope as it moves upwards from the starting point.
Therefore, based on the understanding that the trajectory's coefficient 'a' should be negative to represent the downward motion after the peak, and the target line's slope should be positive, we can eliminate options where the quadratic equation has a positive 'a' (Option A) or where the linear equation has a non-positive slope (Options C and D).
Option B is the only set that meets these requirements, with the quadratic coefficient 'a' being negative (downward trajectory after the peak) and the linear slope being positive (upward line representing the target).
So Option B is the correct answer.