Question

kari and samantha have determined that their water - balloon launcher works best when they launch the balloon at an angle within 3 degrees of 45 degrees. which equation can be used to determine the minimum and maximum optimal angles of launch, and what is the minimum angle that is still optimal? |x - 3| = 45; minimum angle: 42 degrees |x - 3| = 45; minimum angle: 45 degrees |x - 45| = 3; minimum angle: 42 degrees |x - 45| = 3; minimum angle: 45 degrees

Explanation:

Step1: Understand absolute - value equation concept

The distance between a variable \(x\) and a fixed value \(a\) can be represented by \(|x - a|\). Here, the ideal angle is 45 degrees and the acceptable deviation is 3 degrees. So the equation representing the angles \(x\) within 3 degrees of 45 degrees is \(|x - 45|=3\).

Step2: Solve the absolute - value equation for the minimum value

If \(|x - 45| = 3\), then we have two cases: \(x-45 = 3\) or \(x - 45=-3\). Solving \(x-45=-3\) gives \(x = 42\) (which is the minimum angle), and solving \(x - 45=3\) gives \(x = 48\) (the maximum angle).

Answer:

C. \(|x - 45| = 3\); minimum angle: 42 degrees