Question

select the correct answer from each drop - down menu.
a machine cuts dry wall screws with specifications such that the length of each screw is 1.25 inches with an allowable margin of error of 0.02 inches.
use this information to complete each statement.
the equation that can be used to find x, the length of a new dry wall screw is | | = .
the minimum allowable length for a new dry wall screw is , and the maximum allowable length is .

Explanation:

Step1: Define the absolute value equation

The general form for a margin of error is \(|x - \text{target}| = \text{margin}\). Here, the target length is \(1.25\) inches and the margin of error is \(0.02\) inches. So the equation is \(|x - 1.25| = 0.02\).

Step2: Find the minimum length

To find the minimum length, we solve \(x - 1.25 = - 0.02\) (since the absolute value equation \(|A| = B\) implies \(A = B\) or \(A=-B\)). Adding \(1.25\) to both sides: \(x=1.25 - 0.02=1.23\) inches.

Step3: Find the maximum length

To find the maximum length, we solve \(x - 1.25 = 0.02\). Adding \(1.25\) to both sides: \(x = 1.25+0.02 = 1.27\) inches.

Answer:

The equation that can be used to find \(x\), the length of a new dry wall screw is \(|x - 1.25| = 0.02\). The minimum allowable length for a new dry wall screw is \(1.23\) inches, and the maximum allowable length is \(1.27\) inches.

So filling in the blanks:

• First drop - down: \(x - 1.25\)
• Second drop - down: \(0.02\)
• Third drop - down: \(1.23\)
• Fourth drop - down: \(1.27\)