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? vert x-3vert =45 minimum angle: 42 degrees vert x-3vert =45 minimum angle: 45 degrees vert x-45vert =3 minimum angle: 42 degrees vert x-45vert =3 minimum angle: 45 degrees

## Step 1<br />The problem involves determining the optimal angles for launching a water balloon. The optimal angle is defined as the angle that is within 3 degrees of 45 degrees. This means that the angle can be either 3 degrees less than 45 degrees or 3 degrees more than 45 degrees.<br /><br />## Step 2<br />The absolute value equation \(|x - 45| = 3\) is used to represent this situation. The absolute value of a number is its distance from zero on the number line, regardless of direction. In this case, the absolute value of \(x - 45\) is 3, which means that \(x - 45\) is either 3 or -3.<br /><br />## Step 3<br />Solving the equation \(x - 45 = 3\) gives \(x = 48\), which is the maximum optimal angle.<br /><br />## Step 4<br />Solving the equation \(x - 45 = -3\) gives \(x = 42\), which is the minimum optimal angle.