To determine the area [tex]\( A \)[/tex] of the patio that Marissa will paint, we need to consider the different given equations and find the one that logically fits the scenario where there is a rectangular patio with a bench excluded.
Here are the steps to analyze each given equation:
1. Understanding the given equations:
- [tex]\( A=(x+20)(x+11) \)[/tex]
- [tex]\( A=(x+15)(x+10)+5 \)[/tex]
- [tex]\( A=(x+15)(x+10)-5 \)[/tex]
- [tex]\( A=(x+9)(x+10) \)[/tex]
2. Identifying a typical patio area:
- Typically, the area of a patio can be represented by a product of two dimensions, such as [tex]\( (length \times width) \)[/tex].
3. Considering exclusion of a bench:
- If the bench occupies some specific area, this should be subtracted from the total patio area to get the actual painted area.
4. Analysis of Correct Equation:
- Let's break down each equation logically:
a. Equation [tex]\(A=(x+20)(x+11)\)[/tex]:
- This represents the total area without any exclusion.
b. Equation [tex]\(A=(x+15)(x+10)+5\)[/tex]:
- This represents an area adding an additional fixed part, which doesn't fit our scenario because we are excluding an area.
c. Equation [tex]\(A=(x+15)(x+10)-5\)[/tex]:
- This equation seems promising as it represents the total area minus 5 units, aligning with the idea of excluding a fixed area (the bench).
d. Equation [tex]\(A=(x+9)(x+10)\)[/tex]:
- This is another configuration of the patio dimensions but doesn't account for excluding any area.
5. Identifying the correct option:
- Among these, equation [tex]\( A=(x+15)(x+10)-5 \)[/tex] is the one that fits the scenario of having a bench area subtracted from the total patio area.
Therefore, the correct equation to determine the area [tex]\( A \)[/tex] of the patio that Marissa will paint is:
[tex]\[ A=(x+15)(x+10)-5 \][/tex]
Thus, the corresponding option is:
[tex]\[ \boxed{3} \][/tex]
