Let's analyze the given mathematical expression:
[tex]\[
|x^3| + 5
\][/tex]
We'll break it down into parts to understand it fully.
1. Understanding [tex]\(x^3\)[/tex]:
- [tex]\(x^3\)[/tex] refers to the cube of the number [tex]\(x\)[/tex]. This means multiplying [tex]\(x\)[/tex] by itself three times.
- Mathematically, it's written as [tex]\(x \times x \times x\)[/tex].
2. Absolute Value [tex]\(|x^3|\)[/tex]:
- The absolute value of [tex]\(x^3\)[/tex] is represented by [tex]\(|x^3|\)[/tex]. Absolute value makes any number non-negative (i.e., it converts negative numbers to positive).
- For example, if [tex]\(x = -2\)[/tex], [tex]\(x^3 = -8\)[/tex] but [tex]\(|x^3| = |-8| = 8\)[/tex].
3. Adding 5:
- Finally, the expression [tex]\(|x^3| + 5\)[/tex] simply adds 5 to the absolute value of the cube of [tex]\(x\)[/tex].
- This means no matter the value of [tex]\(x\)[/tex], after cubing it, taking the absolute value, we add 5 to the result.
Now, we need to match this detailed understanding with one of the given statements.
A. The sum of the absolute value of three times a number and 5:
- This would translate to [tex]\(|3x| + 5\)[/tex], which is not our given expression.
B. The absolute value of three limes a number added to 5:
- This is not a correct mathematical operation fitting our expression's description; it seems irrelevant.
C. 5 more than the absolute value of the cube of a number:
- This matches our understanding perfectly. We first take the cube of a number ([tex]\(x^3\)[/tex]), then the absolute value ([tex]\(|x^3|\)[/tex]), and finally add 5. So, it's 5 more than the absolute value of the cube.
D. The cube of the sum of a number and 5:
- This would translate to [tex]\((x + 5)^3\)[/tex], which again does not match our expression.
The correct statement that describes the expression [tex]\(|x^3| + 5\)[/tex] is:
[tex]\[
\text{C. 5 more than the absolute value of the cube of a number}
\][/tex]
