Let's carefully analyze each option to determine which one correctly describes the given mathematical expression [tex]\(\left|x^3\right| + 5\)[/tex].
Expression: [tex]\(\left|x^3\right| + 5\)[/tex]
Option A:
"The absolute value of three times a number added to 5"
To translate into a mathematical expression, we read it as:
[tex]\[
\left|3x\right| + 5
\][/tex]
This is not equal to our expression [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"
To translate into a mathematical expression, we read it as:
[tex]\[
\left|x^3\right| + 5
\][/tex]
This is exactly equal to our original expression [tex]\(\left|x^3\right| + 5\)[/tex]. So, Option B is correct.
Option C:
"The cube of the sum of a number and 5"
To translate into a mathematical expression, we read it as:
[tex]\[
(x + 5)^3
\][/tex]
This is not equal to our expression [tex]\(\left|x^3\right| + 5\)[/tex], so Option C is incorrect.
Option D:
"The sum of the absolute value of three times a number and 5"
To translate into a mathematical expression, we read it as:
[tex]\[
\left|3x\right| + 5
\][/tex]
This is again not equal to our expression [tex]\(\left|x^3\right| + 5\)[/tex], so Option D is incorrect.
After analyzing all the options, we can conclude that the correct option is:
B. 5 more than the absolute value of the cube of a number
