Asked by NICKOLAS
Fill in the blank question.
Jim has a yard sign measuring 45 centimeters by 60 centimeters for his mayoral campaign. He wants to use the same image for a sticker. Jim reduces the image by a scale factor of 15, and to print the sticker, he reduces the second image by a scale factor of 13.
What are the dimensions of the sticker? Write the smaller dimension first and the larger dimension second.
Answers
Answered by
GPT-4o mini
To find the dimensions of the sticker, we first need to reduce the original dimensions of the yard sign (45 cm by 60 cm) by a scale factor of 15, and then further reduce the resulting dimensions by a scale factor of 13.
1. **Reduce by a scale factor of 15:**
- Smaller dimension: \( 45 \, \text{cm} \div 15 = 3 \, \text{cm} \)
- Larger dimension: \( 60 \, \text{cm} \div 15 = 4 \, \text{cm} \)
After this step, the dimensions are 3 cm and 4 cm.
2. **Reduce by a scale factor of 13:**
- Smaller dimension: \( 3 \, \text{cm} \div 13 = \frac{3}{13} \, \text{cm} \)
- Larger dimension: \( 4 \, \text{cm} \div 13 = \frac{4}{13} \, \text{cm} \)
Thus, the final dimensions of the sticker are \( \frac{3}{13} \, \text{cm} \) (smaller dimension) and \( \frac{4}{13} \, \text{cm} \) (larger dimension).
Therefore, the dimensions of the sticker are:
**\(\frac{3}{13} \, \text{cm}, \frac{4}{13} \, \text{cm}\)**.
1. **Reduce by a scale factor of 15:**
- Smaller dimension: \( 45 \, \text{cm} \div 15 = 3 \, \text{cm} \)
- Larger dimension: \( 60 \, \text{cm} \div 15 = 4 \, \text{cm} \)
After this step, the dimensions are 3 cm and 4 cm.
2. **Reduce by a scale factor of 13:**
- Smaller dimension: \( 3 \, \text{cm} \div 13 = \frac{3}{13} \, \text{cm} \)
- Larger dimension: \( 4 \, \text{cm} \div 13 = \frac{4}{13} \, \text{cm} \)
Thus, the final dimensions of the sticker are \( \frac{3}{13} \, \text{cm} \) (smaller dimension) and \( \frac{4}{13} \, \text{cm} \) (larger dimension).
Therefore, the dimensions of the sticker are:
**\(\frac{3}{13} \, \text{cm}, \frac{4}{13} \, \text{cm}\)**.
Answered by
NICKOLAS
Are the reduced images similar to the original? Write yes or no.
Answered by
GPT-4o mini
Yes.
Answered by
NICKOLAS
What are the dimensions of the sticker?
Answered by
GPT-4o mini
Let's recalculate the dimensions of the sticker based on the original dimensions of the yard sign (45 cm by 60 cm) and the provided scale factors.
1. **Reduce by a scale factor of 15:**
- Smaller dimension: \( 45 \, \text{cm} \div 15 = 3 \, \text{cm} \)
- Larger dimension: \( 60 \, \text{cm} \div 15 = 4 \, \text{cm} \)
Now, the dimensions are 3 cm and 4 cm.
2. **Reduce this image by a scale factor of 13:**
- Smaller dimension: \( 3 \, \text{cm} \div 13 = \frac{3}{13} \, \text{cm} \)
- Larger dimension: \( 4 \, \text{cm} \div 13 = \frac{4}{13} \, \text{cm} \)
Thus, the dimensions of the sticker are:
**\(\frac{3}{13} \, \text{cm}, \frac{4}{13} \, \text{cm}\)**.
Please note that if the first reduction was indeed the intended operation, the answer holds true. However, if the original dimensions were to first reduce the height 45 cm by a factor of 15 and then the width of 60 cm also by a factor of 15, it would lead to different dimensions. Let me know if you would like that calculation instead!
1. **Reduce by a scale factor of 15:**
- Smaller dimension: \( 45 \, \text{cm} \div 15 = 3 \, \text{cm} \)
- Larger dimension: \( 60 \, \text{cm} \div 15 = 4 \, \text{cm} \)
Now, the dimensions are 3 cm and 4 cm.
2. **Reduce this image by a scale factor of 13:**
- Smaller dimension: \( 3 \, \text{cm} \div 13 = \frac{3}{13} \, \text{cm} \)
- Larger dimension: \( 4 \, \text{cm} \div 13 = \frac{4}{13} \, \text{cm} \)
Thus, the dimensions of the sticker are:
**\(\frac{3}{13} \, \text{cm}, \frac{4}{13} \, \text{cm}\)**.
Please note that if the first reduction was indeed the intended operation, the answer holds true. However, if the original dimensions were to first reduce the height 45 cm by a factor of 15 and then the width of 60 cm also by a factor of 15, it would lead to different dimensions. Let me know if you would like that calculation instead!