Question

c is between a and e. for each problem, draw a picture representing the three points and the information given. solve for indicated. 5. if ac = 24 in. and ce = 13 in., ae = ____ 6. if ce = 7 in. and ae = 23 in., ac = ____.

Explanation:

Problem 5

Step1: Recall segment addition postulate

Since \( C \) is between \( A \) and \( E \), by the segment addition postulate, \( AE = AC + CE \).

Step2: Substitute given values

We know \( AC = 24 \) in. and \( CE = 13 \) in. So, \( AE = 24 + 13 \).

Step3: Calculate the sum

\( 24 + 13 = 37 \).

Step1: Recall segment addition postulate

Since \( C \) is between \( A \) and \( E \), \( AE = AC + CE \). We can rearrange this formula to solve for \( AC \): \( AC = AE - CE \).

Step2: Substitute given values

We know \( CE = 7 \) in. and \( AE = 23 \) in. So, \( AC = 23 - 7 \).

Step3: Calculate the difference

\( 23 - 7 = 16 \).

Answer:

\( 37 \) in.

Problem 6