Question

1. the area of the rectangle shown below is at least 45 square units and at most 100 square units. write an inequality that shows the possible values for m.

Explanation:

Step1: Recall the formula for the area of a rectangle

The area \(A\) of a rectangle is given by \(A = \text{length}\times\text{width}\). Here, the width is \(5\) and the length is \(m\), so \(A = 5m\).

Step2: Set up the inequality based on the area constraints

The area is at least \(45\) (so \(5m\geq45\)) and at most \(100\) (so \(5m\leq100\)). Combining these two inequalities gives \(45\leq5m\leq100\).

Step3: Solve the compound - inequality for \(m\)

Divide each part of the compound - inequality \(45\leq5m\leq100\) by \(5\).
For \(45\leq5m\), we have \(\frac{45}{5}\leq\frac{5m}{5}\), which simplifies to \(9\leq m\).
For \(5m\leq100\), we have \(\frac{5m}{5}\leq\frac{100}{5}\), which simplifies to \(m\leq20\).

Answer:

\(9\leq m\leq20\)