Riley fishes from a boat dock 12 feet above sea level. The bottom of her fishing line is lowered to 22 feet below sea level.
a. Interpret the meaning of 12 > -22 in this situation.
The correct answer and explanation is:
In this situation, the expression 12>−2212 > -22 compares the height of the boat dock (12 feet above sea level) with the depth of the fishing line (22 feet below sea level). The sign of the numbers reflects their position relative to sea level, where positive numbers indicate above sea level and negative numbers indicate below sea level.
Here, 12 represents the height of the boat dock above sea level. The number 12 is positive because the dock is located 12 feet above the reference point, which is sea level. On the other hand, -22 represents the depth of the fishing line below sea level. Since sea level is considered 0, the negative sign indicates that the fishing line is 22 feet beneath this reference point.
The inequality 12>−2212 > -22 means that 12 feet (the height of the dock) is greater than -22 feet (the depth of the fishing line). This statement is true because any positive number is greater than any negative number. Therefore, the boat dock is above sea level, and the fishing line is below sea level, but the dock’s position is higher (greater) than the fishing line’s depth.
In practical terms, the inequality helps us understand the relative positions of the dock and the fishing line with respect to sea level. While the dock is above sea level at 12 feet, the fishing line, being 22 feet below sea level, is in a position that is farther from sea level and lower in elevation. The comparison of these two values highlights the difference in height and depth, giving context to their respective positions relative to the sea level reference point.