To solve this problem, let's carefully analyze the given expression:
[tex]\[ \left|x^3\right|+5. \][/tex]
We will break down the components of this expression to determine which statement best describes it.
1. Absolute Value: The expression [tex]\(\left|x^3\right|\)[/tex] refers to the absolute value of [tex]\(x^3\)[/tex]. The absolute value is a function that takes any real number and makes it non-negative. Therefore, it ensures that any negative values of [tex]\(x^3\)[/tex] become positive, while positive values remain unchanged.
2. Cube of a Number: The term [tex]\(x^3\)[/tex] refers to [tex]\(x\)[/tex] raised to the power of 3. This means that we are multiplying [tex]\(x\)[/tex] by itself twice (i.e., [tex]\(x \cdot x \cdot x\)[/tex]).
3. Sum with 5: After computing the absolute value of [tex]\(x^3\)[/tex], we then add 5 to the result. This indicates that 5 is added to the absolute value of [tex]\(x^3\)[/tex].
With these points in mind, let's evaluate the given choices one by one:
A. The cube of the sum of a number and 5: This description refers to the expression [tex]\((x + 5)^3\)[/tex], which is not equivalent to [tex]\(\left|x^3\right|+5\)[/tex].
B. The absolute value of three times a number added to 5: This description refers to [tex]\(\left|3x\right|+5\)[/tex], which is not the same as [tex]\(\left|x^3\right|+5\)[/tex].
C. The sum of the absolute value of three times a number and 5: This description refers to [tex]\(\left|3x\right|+5\)[/tex], which, again, is not the same as [tex]\(\left|x^3\right|+5\)[/tex].
D. 5 more than the absolute value of the cube of a number: This restates [tex]\(\left|x^3\right|+5\)[/tex] exactly. The expression [tex]\(\left|x^3\right|\)[/tex] is the absolute value of the cube of a number, and adding 5 to it confirms that this description is correct.
Thus, the correct answer is:
[tex]\[ 5 \text{ more than the absolute value of the cube of a number} \][/tex]
The correct statement that describes the expression [tex]\(\left|x^3\right|+5\)[/tex] is:
[tex]\[ D \][/tex]
