Question

way to go! you got all the correct answers! durham is 11 miles from chapel hill. durham is also 24 miles from pittsboro. select each value that could be the distance from chapel hill to pittsboro. (select all that apply.) 5 11 13 18 24 30 35 36

Explanation:

Step1: Apply triangle - inequality theorem

Let the distance between Durham and Chapel Hill be $a = 11$ miles, the distance between Durham and Pittsboro be $b = 24$ miles, and the distance between Chapel Hill and Pittsboro be $c$. According to the triangle - inequality theorem, $|a - b|\leq c\leq a + b$.

Step2: Calculate the lower and upper bounds

Calculate $|a - b|=|11 - 24| = 13$ and $a + b=11 + 24 = 35$. So, $13\leq c\leq35$.

Answer:

18, 24, 30