Select the correct answer.
Which statement correctly describes this expression?
$\left|x^3\right|+5$
A. the absolute value of three times a number added to 5
B. 5 more than the absolute value of the cube of a number
C. the sum of the absolute value of three times a number and 5
D. the cube of the sum of a number and 5
Answer (1)
The expression is the absolute value of x cubed, plus 5.
Option A translates to ∣3 x ∣ + 5 .
Option B translates to ∣ x 3 ∣ + 5 .
Option C translates to ∣3 x ∣ + 5 or ∣3 x + 5∣ .
Option D translates to ( x + 5 ) 3 .
Therefore, the correct answer is B .
Explanation
Analyzing the Expression We need to identify the statement that accurately describes the expression x 3 + 5 . Let's break down the expression and each of the options.
Understanding the Expression The expression x 3 + 5 means we first cube a number x , then take the absolute value of the result, and finally add 5.
Analyzing the Statements Now, let's analyze the given statements:
A. the absolute value of three times a number added to 5: This can be written as ∣3 x ∣ + 5 .
B. 5 more than the absolute value of the cube of a number: This can be written as ∣ x 3 ∣ + 5 .
C. the sum of the absolute value of three times a number and 5: This is ambiguous and could be interpreted as either ∣3 x ∣ + 5 or ∣3 x + 5∣ .
D. the cube of the sum of a number and 5: This can be written as ( x + 5 ) 3 .
Identifying the Correct Statement Comparing the statements with the expression x 3 + 5 , we can see that statement B, which is '5 more than the absolute value of the cube of a number', correctly describes the expression.
Examples
Imagine you're designing a sound system where the volume is determined by the cube of a control signal. The absolute value ensures the volume is always positive, and adding 5 provides a base level of sound even when the control signal is zero. This expression helps model systems where a base value is added to a scaled, non-negative quantity.
