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Chapter 2: Problem 3

Which one of the following intervals is not symmetric about \(x=5 ?\) a. (1,9) b. (4,6) c. (3,8) d. (4.5,5.5)

Short Answer

Expert verified
a. (1, 9) b. (4, 6) c. (3, 8) d. (4.5, 5.5) Answer: c. (3, 8)

Step by step solution

01

Find Midpoints for Each Interval

To find the midpoint of an interval, we can use the formula: Midpoint = (Start + End) / 2. Let's calculate the midpoint for each of the given intervals: a. (1, 9) Midpoint = (1 + 9) / 2 = 10 / 2 = 5 b. (4, 6) Midpoint = (4 + 6) / 2 = 10 / 2 = 5 c. (3, 8) Midpoint = (3 + 8) / 2 = 11 / 2 = 5.5 d. (4.5, 5.5) Midpoint = (4.5 + 5.5) / 2 = 10 / 2 = 5 Now we have the midpoints for each interval.
02

Determine Which One Is Not Symmetric about x = 5

Now we will check which interval has a midpoint that is not equal to 5: a. (1, 9) - Midpoint: 5 b. (4, 6) - Midpoint: 5 c. (3, 8) - Midpoint: 5.5 d. (4.5, 5.5) - Midpoint: 5 We see that option c has a midpoint of 5.5, which is not equal to 5. Therefore, the interval (3,8) is not symmetric about x = 5. So, the correct answer is c. (3, 8).

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