Question

1. robin and trey love the cold weather. in fact, the colder the weather, the happier robin and trey are. both robin and trey have very precise thermometers that measure the temperature to the nearest tenth of a degree. the temperature in robin’s location is -6.8°c and the weather in trey’s location is -14.2°c. trey tells robin that his location is warmer than her location because 14.2 is greater than 6.8, but robin disagrees with trey. plot the two temperatures on a number line, then write two statements of inequality to represent the situation. is robin or trey colder? lynn and max are divers. lynn’s depth gauge says she is 43.6 feet deep. max’s depth gauge says that he is 54.2 feet deep. who is closer to the surface? write two statements of inequality to describe the situation.

Explanation:

Problem 1 (Robin and Trey's Temperature)

Step1: Recall Number Line for Negatives

On a number line, negative numbers with larger absolute values are farther left (colder, for temperature). Robin: \(-6.8^\circ\text{C}\), Trey: \(-14.2^\circ\text{C}\). Absolute values: \(|-6.8| = 6.8\), \(|-14.2| = 14.2\). Since \(14.2 > 6.8\), \(-14.2 < -6.8\).

Step2: Determine Colder Location

A lower (more negative) temperature means colder. Since \(-14.2 < -6.8\), Trey’s location is colder. Inequalities: \(-14.2 < -6.8\) (Trey’s temp < Robin’s temp) and \(|-14.2| > |-6.8|\) (absolute value of Trey’s temp > Robin’s).

Step1: Compare Distances to Surface

Depth is a positive measure (distance from surface). Closer to surface means smaller depth. Lynn: \(43.6\) ft, Max: \(54.2\) ft. Since \(43.6 < 54.2\), Lynn is closer.

Step2: Write Inequalities

Two inequalities: \(43.6 < 54.2\) (Lynn’s depth < Max’s depth) and \(54.2 > 43.6\) (Max’s depth > Lynn’s depth).

Answer:

Trey’s location is colder. Inequalities: \(-14.2 < -6.8\) and \(|-14.2| > |-6.8|\).

Problem 2 (Lynn and Max's Depth)