Zfarris96idn
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Which statement correctly describes this expression?
[tex]\[ \left|x^3\right| + 5 \][/tex]

A. The sum of the absolute value of three times a number and 5

B. 5 more than the absolute value of the cube of a number

C. The absolute value of three times a number added to 5

D. The cube of the sum of a number and 5

Sagot :

GinnyAnsweridn
To determine which statement correctly describes the expression [tex]\(\left|x^3\right| + 5\)[/tex], let's evaluate each option step by step:

Option A: The sum of the absolute value of three times a number and 5.
- This statement suggests the expression [tex]\(\left|3x\right| + 5\)[/tex].
- [tex]\(\left|3x\right|\)[/tex] means taking the absolute value after multiplying a number [tex]\(x\)[/tex] by 3.
- This is not the same as [tex]\(\left|x^3\right| + 5\)[/tex], so option A is incorrect.

Option B: 5 more than the absolute value of the cube of a number.
- This statement suggests the operation of cubing a number [tex]\(x\)[/tex], taking the absolute value of the result, and then adding 5.
- Mathematically, this is written as [tex]\(\left|x^3\right| + 5\)[/tex].
- This matches the given expression exactly, so option B is correct.

Option C: The absolute value of three times a number added to 5.
- This statement also suggests the expression [tex]\(\left|3x\right| + 5\)[/tex].
- Similar to Option A, this involves taking the absolute value after multiplying [tex]\(x\)[/tex] by 3 and then adding 5.
- This is not the same as [tex]\(\left|x^3\right| + 5\)[/tex], so option C is incorrect.

Option D: The cube of the sum of a number and 5.
- This statement suggests adding a number [tex]\(x\)[/tex] to 5 first and then cubing the result.
- Mathematically, this is written as [tex]\((x + 5)^3\)[/tex].
- This is not the same as [tex]\(\left|x^3\right| + 5\)[/tex], so option D is incorrect.

Therefore, the statement that correctly describes the expression [tex]\(\left|x^3\right| + 5\)[/tex] is option B: 5 more than the absolute value of the cube of a number.
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