Answer :
To determine the appropriate equation for the area of Marissa's patio that will be painted, given that there is a bench that does not need painting, let's examine the options provided.
### Step-by-Step Analysis:
1. Identify the equations provided:
- Option 1: [tex]\( A = (x+20)(x+11) \)[/tex]
- Option 2: [tex]\( A = (x+15)(x+10) + 5 \)[/tex]
- Option 3: [tex]\( A = (x+15)(x+10) - 5 \)[/tex]
- Option 4: [tex]\( A = (x+9)(x+10) \)[/tex]
2. Understand the scenario:
- The total area to be painted excludes the area of a bench.
- This implies that the equation representing the painted area should subtract the bench’s area from the total patio area.
3. Examine each option:
- Option 1: [tex]\( A = (x+20)(x+11) \)[/tex]
- This represents the total area of a rectangle with dimensions [tex]\( (x+20) \)[/tex] and [tex]\( (x+11) \)[/tex].
- It does not account for any exclusion (like a bench), so this does not seem correct.
- Option 2: [tex]\( A = (x+15)(x+10) + 5 \)[/tex]
- This represents an area with added value, suggesting that more area is being painted than the product of the dimensions provided. Since we need to subtract the area of the bench, this is unlikely to be correct.
- Option 3: [tex]\( A = (x+15)(x+10) - 5 \)[/tex]
- This represents the area of a rectangle with dimensions [tex]\( (x+15) \)[/tex] and [tex]\( (x+10) \)[/tex], but it subtracts an additional 5 units.
- This subtraction indicates that part of the area (presumably the bench) is not painted, which matches our scenario.
- Option 4: [tex]\( A = (x+9)(x+10) \)[/tex]
- This represents the total area of a different rectangle with dimensions [tex]\( (x+9) \)[/tex] and [tex]\( (x+10) \)[/tex].
- There is no indication of exclusion for the bench area, so this is also incorrect.
4. Conclusion:
- Considering the need to exclude the bench area from being painted, the equation that best fits the scenario is:
[tex]\[ A = (x+15)(x+10) - 5 \][/tex]
Thus, the correct equation to determine the area of the patio that will be painted is:
[tex]\[ A = (x+15)(x+10) - 5 \][/tex]
Therefore, the appropriate selection is:
Option 3: [tex]\( A = (x+15)(x+10) - 5 \)[/tex].
### Step-by-Step Analysis:
1. Identify the equations provided:
- Option 1: [tex]\( A = (x+20)(x+11) \)[/tex]
- Option 2: [tex]\( A = (x+15)(x+10) + 5 \)[/tex]
- Option 3: [tex]\( A = (x+15)(x+10) - 5 \)[/tex]
- Option 4: [tex]\( A = (x+9)(x+10) \)[/tex]
2. Understand the scenario:
- The total area to be painted excludes the area of a bench.
- This implies that the equation representing the painted area should subtract the bench’s area from the total patio area.
3. Examine each option:
- Option 1: [tex]\( A = (x+20)(x+11) \)[/tex]
- This represents the total area of a rectangle with dimensions [tex]\( (x+20) \)[/tex] and [tex]\( (x+11) \)[/tex].
- It does not account for any exclusion (like a bench), so this does not seem correct.
- Option 2: [tex]\( A = (x+15)(x+10) + 5 \)[/tex]
- This represents an area with added value, suggesting that more area is being painted than the product of the dimensions provided. Since we need to subtract the area of the bench, this is unlikely to be correct.
- Option 3: [tex]\( A = (x+15)(x+10) - 5 \)[/tex]
- This represents the area of a rectangle with dimensions [tex]\( (x+15) \)[/tex] and [tex]\( (x+10) \)[/tex], but it subtracts an additional 5 units.
- This subtraction indicates that part of the area (presumably the bench) is not painted, which matches our scenario.
- Option 4: [tex]\( A = (x+9)(x+10) \)[/tex]
- This represents the total area of a different rectangle with dimensions [tex]\( (x+9) \)[/tex] and [tex]\( (x+10) \)[/tex].
- There is no indication of exclusion for the bench area, so this is also incorrect.
4. Conclusion:
- Considering the need to exclude the bench area from being painted, the equation that best fits the scenario is:
[tex]\[ A = (x+15)(x+10) - 5 \][/tex]
Thus, the correct equation to determine the area of the patio that will be painted is:
[tex]\[ A = (x+15)(x+10) - 5 \][/tex]
Therefore, the appropriate selection is:
Option 3: [tex]\( A = (x+15)(x+10) - 5 \)[/tex].
