Question

question
enter the missing values in the area model to find 7(5t + 1)
answer
attempt 2 out of 2

Explanation:

Step1: Analyze the area model for \(7(5t + 1)\)

The area model for a product \(a(b + c)\) is split into two rectangles: one with area \(a\times b\) and the other with area \(a\times c\). Here, \(a = 7\), \(b = 5t\), and \(c = 1\).

Step2: Find the area of the first rectangle (with \(5t\))

The area of the first rectangle (top part) is \(7\times5t\). Calculating that, we get \(7\times5t = 35t\).

Step3: Find the area of the second rectangle (with the missing value)

The second rectangle (bottom part) has a height of \(7\) and a width corresponding to the constant term in \(5t + 1\), which is \(1\). So the area is \(7\times1 = 7\). Wait, but looking at the diagram, the right - hand side of the bottom rectangle (the small square) should be the width, which is \(1\) (since the expression inside the parentheses is \(5t+1\), so the two terms are \(5t\) and \(1\)). And the area of the bottom rectangle (the one with \(+7\)) is \(7\times1 = 7\), but the missing value in the small square (the width of the bottom rectangle) is \(1\), and the area of the top rectangle (the one with \(5t\)) is \(7\times5t=35t\).

Wait, re - examining the problem: We need to fill in the missing values in the area model for \(7(5t + 1)\). The area model is a big rectangle split into two smaller rectangles. The big rectangle has a height of \(7\), and the base is split into \(5t\) and \(1\). So:

• The top rectangle (with base \(5t\) and height \(7\)) has area \(7\times5t = 35t\).
• The bottom rectangle (with base \(1\) and height \(7\)) has area \(7\times1 = 7\), and the missing value in the small square (the base of the bottom rectangle) is \(1\), and the area of the top rectangle is \(35t\).

Answer:

The missing value in the top rectangle (the one with \(5t\)) is \(35t\), and the missing value in the small square (the base of the bottom rectangle) is \(1\). If we consider the two missing values: the top - most (area of the top rectangle) is \(35t\) and the small square (the width of the bottom rectangle) is \(1\).