10. This model shows the area of a garden. Write two expressions that represent the area. \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}\hline\( x \) & \( x \) & \( x \) & \( x \) & \( x \) & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline\end{tabular}

To determine the area of the garden based on the given model, let's analyze the provided table: \[ \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline \( x \) & \( x \) & \( x \) & \( x \) & \( x \) & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline \end{tabular} \] ### Interpretation of the Model - **Number of \( x \)'s:** 5 - **Number of 1's:** 9 - **Total Cells:** 14 (combining both \( x \)'s and 1's) This model suggests that the garden's area is partitioned into segments represented by \( x \) and 1. To express the total area, consider the following interpretations: 1. **Sum of Segments:** - **Expression:** \( 5x + 9 \) - **Explanation:** Here, the five \( x \)'s represent one dimension (e.g., length), and the nine 1's represent another dimension (e.g., width). Summing them gives an expression for the area. 2. **Product of Dimensions:** - **Expression:** \( 5x \times 9 = 45x \) - **Explanation:** Alternatively, if we interpret the five \( x \)'s as the length and the nine 1's as the width, the area can be calculated by multiplying these two dimensions. ### Conclusion The area of the garden can be represented by either of the following expressions: 1. **Additive Expression:** \( 5x + 9 \) 2. **Multiplicative Expression:** \( 45x \) Both expressions accurately model the total area based on the given table. Answer: One expression is 5 x + 9 and another is 45 times x. Thus, • Area = 5x + 9 • Area = 45 x