Question

which equations? select the three equations that represent the relationship between the length of the original rectangle, b, and the length of the new rectangle, c. (100 - 72)b = c; c = 0.28b; 0.72b = c; (1 - 0.72)b = c; c = b - 0.72; c = 1b - 0.72b

Explanation:

Step1: Analyze the relationship

The original length is \( b \), and the new length \( c \) is the part of \( b \) not in the 72% segment. So \( c = b - 0.72b \) (since 72% of \( b \) is \( 0.72b \), subtracting gives the remaining). Also, \( b - 0.72b=(1 - 0.72)b = 0.28b \), so \( c = 0.28b \) and \( (1 - 0.72)b = c \), and \( c = 1b - 0.72b \). Let's check each equation:

• \((100 - 72)b = c\): \(100 - 72 = 28\), but \(100 - 72\) is a percentage difference? Wait, no, \(100 - 72 = 28\), but as a decimal, 28% is 0.28, but \((100 - 72)b\) is \(28b\), which is wrong. So this is incorrect.
• \(c = 0.28b\): Correct, as \(1 - 0.72 = 0.28\), so \(c=(1 - 0.72)b = 0.28b\).
• \(0.72b = c\): This would mean \(c\) is 72% of \(b\), but the diagram shows \(c\) is the remaining part, so incorrect.
• \((1 - 0.72)b = c\): \(1 - 0.72 = 0.28\), so this is \(0.28b = c\), correct.
• \(c = b - 0.72\): This subtracts 0.72 (a number, not a percentage of \(b\)), so incorrect.
• \(c = 1b - 0.72b\): This simplifies to \(c=(1 - 0.72)b = 0.28b\), correct.

Step2: Identify correct equations

From the analysis, the correct equations are \(c = 0.28b\), \((1 - 0.72)b = c\), and \(c = 1b - 0.72b\).

Answer:

\(c = 0.28b\), \((1 - 0.72)b = c\), \(c = 1b - 0.72b\) (the checkboxes for these three equations should be selected)