Question
Annabelle measured her bedroom as 11 ft Times 13 ft, which is 143 square feet. She wants to change the units to square inches. Which statements should she consider when converting? Check all that apply.
There are 12 inches in every foot.
The length and width will change by a factor of 1.2 times 10 Superscript 1.
The length and width will change by a factor of 1.2 times 10 Superscript 0.
The area will change by a factor of (1.2 times 10 Superscript 1 Baseline) (1.2 times 10 Superscript 1 Baseline) = 1.44 times 10 Superscript 2 Baseline = 144, since area is length times width.
The area will change by a factor of 2 (1.2 times 10 Superscript 1 Baseline) = (2 times 10 Superscript 1 Baseline) (1.2 times 10 Superscript 1 Baseline) = 2.4 times 10 Superscript 2 Baseline = 240, since both the length and width increase by that factor.
There are 12 inches in every foot.
The length and width will change by a factor of 1.2 times 10 Superscript 1.
The length and width will change by a factor of 1.2 times 10 Superscript 0.
The area will change by a factor of (1.2 times 10 Superscript 1 Baseline) (1.2 times 10 Superscript 1 Baseline) = 1.44 times 10 Superscript 2 Baseline = 144, since area is length times width.
The area will change by a factor of 2 (1.2 times 10 Superscript 1 Baseline) = (2 times 10 Superscript 1 Baseline) (1.2 times 10 Superscript 1 Baseline) = 2.4 times 10 Superscript 2 Baseline = 240, since both the length and width increase by that factor.
Answers
Answered by
GPT-4o mini
To convert the area from square feet to square inches, Annabelle should consider the following statements:
1. **There are 12 inches in every foot.**
- This statement is true and is crucial for the conversion since it establishes the relationship between feet and inches.
2. **The length and width will change by a factor of 1.2 times 10 Superscript 1 (which is 12).**
- This statement is incorrect in context because it misrepresents the conversion factor; it should just say that each dimension will be multiplied by 12 (1.2 times 10^1 = 12), not that the dimensions change by a factor of 1.2 times 10^1. The factor for length and width should just be specified as 12.
3. **The length and width will change by a factor of 1.2 times 10 Superscript 0 (which is 1).**
- This statement is incorrect in this context as well. It's not relevant to the conversion since the conversion factor is clearly 12, not 1.
4. **The area will change by a factor of (1.2 times 10 Superscript 1)(1.2 times 10 Superscript 1) = 1.44 times 10 Superscript 2 = 144, since area is length times width.**
- This statement is correct. The area changes by the factor of the conversion of both dimensions, which is \(12 \times 12 = 144\).
5. **The area will change by a factor of 2 (1.2 times 10 Superscript 1) = (2 times 10 Superscript 1)(1.2 times 10 Superscript 1) = 2.4 times 10 Superscript 2 = 240, since both the length and width increase by that factor.**
- This statement is incorrect. The area does not change by a factor of just 2; it actually changes by a factor of 144, as explained in point 4.
In summary, the statements Annabelle should consider are:
- **There are 12 inches in every foot.**
- **The area will change by a factor of (1.2 times 10 Superscript 1)(1.2 times 10 Superscript 1) = 1.44 times 10 Superscript 2 = 144, since area is length times width.**
1. **There are 12 inches in every foot.**
- This statement is true and is crucial for the conversion since it establishes the relationship between feet and inches.
2. **The length and width will change by a factor of 1.2 times 10 Superscript 1 (which is 12).**
- This statement is incorrect in context because it misrepresents the conversion factor; it should just say that each dimension will be multiplied by 12 (1.2 times 10^1 = 12), not that the dimensions change by a factor of 1.2 times 10^1. The factor for length and width should just be specified as 12.
3. **The length and width will change by a factor of 1.2 times 10 Superscript 0 (which is 1).**
- This statement is incorrect in this context as well. It's not relevant to the conversion since the conversion factor is clearly 12, not 1.
4. **The area will change by a factor of (1.2 times 10 Superscript 1)(1.2 times 10 Superscript 1) = 1.44 times 10 Superscript 2 = 144, since area is length times width.**
- This statement is correct. The area changes by the factor of the conversion of both dimensions, which is \(12 \times 12 = 144\).
5. **The area will change by a factor of 2 (1.2 times 10 Superscript 1) = (2 times 10 Superscript 1)(1.2 times 10 Superscript 1) = 2.4 times 10 Superscript 2 = 240, since both the length and width increase by that factor.**
- This statement is incorrect. The area does not change by a factor of just 2; it actually changes by a factor of 144, as explained in point 4.
In summary, the statements Annabelle should consider are:
- **There are 12 inches in every foot.**
- **The area will change by a factor of (1.2 times 10 Superscript 1)(1.2 times 10 Superscript 1) = 1.44 times 10 Superscript 2 = 144, since area is length times width.**