Answer :
To determine which pair of numbers are not opposites, let's first understand what it means for numbers to be opposites. Two numbers are considered opposites if one is the negative of the other. For example, the opposite of 7 is -7 because their sum is zero.
Now, let's evaluate each pair:
1. Pair 1: [tex]\(|7|\)[/tex] and -7
- [tex]\(|7|\)[/tex] means the absolute value of 7, which is 7.
- The numbers are 7 and -7.
- Since 7 is the opposite of -7, this pair is made up of opposites.
2. Pair 2: 71 and -71
- The numbers are 71 and -71.
- 71 is the opposite of -71 because their sum is zero.
- Thus, this pair is made up of opposites.
3. Pair 3: 17 and -17
- The numbers are 17 and -17.
- Similarly, 17 is the opposite of -17 because their sum is zero.
- So, this pair is made up of opposites.
4. Pair 4: 17 and [tex]\(|-17|\)[/tex]
- [tex]\(|-17|\)[/tex] is the absolute value of -17, which is 17.
- The numbers are 17 and 17.
- These two numbers are not opposites since they are the same number, not negatives of each other.
Thus, the pair that is not made up of opposites is the fourth one: 17 and [tex]\(|-17|\)[/tex].
Now, let's evaluate each pair:
1. Pair 1: [tex]\(|7|\)[/tex] and -7
- [tex]\(|7|\)[/tex] means the absolute value of 7, which is 7.
- The numbers are 7 and -7.
- Since 7 is the opposite of -7, this pair is made up of opposites.
2. Pair 2: 71 and -71
- The numbers are 71 and -71.
- 71 is the opposite of -71 because their sum is zero.
- Thus, this pair is made up of opposites.
3. Pair 3: 17 and -17
- The numbers are 17 and -17.
- Similarly, 17 is the opposite of -17 because their sum is zero.
- So, this pair is made up of opposites.
4. Pair 4: 17 and [tex]\(|-17|\)[/tex]
- [tex]\(|-17|\)[/tex] is the absolute value of -17, which is 17.
- The numbers are 17 and 17.
- These two numbers are not opposites since they are the same number, not negatives of each other.
Thus, the pair that is not made up of opposites is the fourth one: 17 and [tex]\(|-17|\)[/tex].
