Answer :
To solve this problem, we need to determine both the opposite and the absolute value of the number 89. Let's go through the steps one by one:
1. Identify the opposite of 89:
- The opposite (or additive inverse) of a number [tex]\( x \)[/tex] is defined as [tex]\(-x\)[/tex]. So, the opposite of 89 is [tex]\(-89\)[/tex].
2. Identify the absolute value of 89:
- The absolute value of a number [tex]\( x \)[/tex] is defined as the distance of [tex]\( x \)[/tex] from zero on the number line, regardless of the direction. For positive numbers, the absolute value is the number itself. For negative numbers, the absolute value is the positive counterpart.
- Since 89 is already a positive number, its absolute value is [tex]\( 89 \)[/tex].
Thus, let's examine the multiple-choice answers:
1. The opposite is [tex]\(-89\)[/tex]. [tex]\( |89| = -89 \)[/tex]:
- This is incorrect because the absolute value of 89 should be 89, not -89.
2. The opposite is [tex]\(-89\)[/tex]. [tex]\( |89| = 89 \)[/tex]:
- This is correct. The opposite of 89 is indeed -89, and the absolute value of 89 is 89.
3. The opposite is [tex]\( 89 \)[/tex]. [tex]\( |89| = 89 \)[/tex]:
- This is incorrect because the opposite of 89 should be -89, not 89.
4. The opposite is [tex]\( 89 \)[/tex]. [tex]\( |89| = -89 \)[/tex]:
- This is incorrect because both the opposite and absolute value calculations are wrong.
Therefore, the correct answer is:
The opposite is [tex]\(-89\)[/tex]. [tex]\( |89| = 89 \)[/tex].
1. Identify the opposite of 89:
- The opposite (or additive inverse) of a number [tex]\( x \)[/tex] is defined as [tex]\(-x\)[/tex]. So, the opposite of 89 is [tex]\(-89\)[/tex].
2. Identify the absolute value of 89:
- The absolute value of a number [tex]\( x \)[/tex] is defined as the distance of [tex]\( x \)[/tex] from zero on the number line, regardless of the direction. For positive numbers, the absolute value is the number itself. For negative numbers, the absolute value is the positive counterpart.
- Since 89 is already a positive number, its absolute value is [tex]\( 89 \)[/tex].
Thus, let's examine the multiple-choice answers:
1. The opposite is [tex]\(-89\)[/tex]. [tex]\( |89| = -89 \)[/tex]:
- This is incorrect because the absolute value of 89 should be 89, not -89.
2. The opposite is [tex]\(-89\)[/tex]. [tex]\( |89| = 89 \)[/tex]:
- This is correct. The opposite of 89 is indeed -89, and the absolute value of 89 is 89.
3. The opposite is [tex]\( 89 \)[/tex]. [tex]\( |89| = 89 \)[/tex]:
- This is incorrect because the opposite of 89 should be -89, not 89.
4. The opposite is [tex]\( 89 \)[/tex]. [tex]\( |89| = -89 \)[/tex]:
- This is incorrect because both the opposite and absolute value calculations are wrong.
Therefore, the correct answer is:
The opposite is [tex]\(-89\)[/tex]. [tex]\( |89| = 89 \)[/tex].
