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Find the scale factor of each problem below. \( \begin{array}{lll}\text { 12. } 9 \text { inches: } 72 \text { inches } & \text { 13. } 5 \mathrm{~cm} \text { to } 145 \mathrm{~cm} & 14.2 \mathrm{ft:} 27 \mathrm{ft}\end{array} \)

Ask by Cox Fernandez. in the United States
Jan 23,2025

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- **Problem 12:** 8 - **Problem 13:** 29 - **Problem 14:** 13.5

Solution

To find the **scale factor** for each pair of measurements, you divide the larger measurement by the smaller one. The scale factor indicates how much larger (or smaller) one measurement is compared to the other. ### Problem 12 **Given:** 9 inches : 72 inches **Scale Factor Calculation:** \[ \text{Scale Factor} = \frac{72}{9} = 8 \] **Scale Factor:** **8** --- ### Problem 13 **Given:** 5 cm : 145 cm **Scale Factor Calculation:** \[ \text{Scale Factor} = \frac{145}{5} = 29 \] **Scale Factor:** **29** --- ### Problem 14 **Given:** 2 ft : 27 ft **Scale Factor Calculation:** \[ \text{Scale Factor} = \frac{27}{2} = 13.5 \] **Scale Factor:** **13.5** --- **Summary of Scale Factors:** - **Problem 12:** 8 - **Problem 13:** 29 - **Problem 14:** 13.5

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To find the scale factor, you need to divide the second measurement by the first. For the first problem, \( \frac{72 \text{ inches}}{9 \text{ inches}} = 8 \). So, the scale factor is 8. For the second problem, \( \frac{145 \text{ cm}}{5 \text{ cm}} = 29 \). Thus, the scale factor is 29. For the third problem, \( \frac{27 \text{ ft}}{14.2 \text{ ft}} \approx 1.9028 \). Therefore, the scale factor is approximately 1.90.

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