1. Problem 38: Determine which sequences of transformations maintain congruence of a figure. - Congruence means the figure's size and shape do not change. - Transformations that maintain congruence include reflections, rotations, and translations. - Dilations change size, so they do not maintain congruence. Check each option: A. Reflection and then rotation: Both maintain size and shape, so congruence is maintained. ✔ B. Dilation and then translation: Dilation changes size, so congruence is not maintained. ✘ C. Translation and then reflection: Both maintain size and shape, so congruence is maintained. ✔ D. Rotation and then dilation: Dilation changes size, so congruence is not maintained. ✘ E. Rotation and then translation: Both maintain size and shape, so congruence is maintained. ✔ 2. Problem 39: Estimate the number of steps the average man takes in 1 year using scientific notation. - Given: Average steps per day = 7,192 steps - Number of days in a year = 365 Formula: $$\text{Total steps in a year} = \text{steps per day} \times \text{days per year}$$ Calculate: $$7,192 \times 365$$ Approximate calculation: $$7,192 \approx 7.192 \times 10^{3}$$ $$365 \approx 3.65 \times 10^{2}$$ Multiply: $$7.192 \times 10^{3} \times 3.65 \times 10^{2} = (7.192 \times 3.65) \times 10^{3+2} = 26.25 \times 10^{5}$$ Convert to proper scientific notation: $$26.25 \times 10^{5} = 2.625 \times 10^{6}$$ Rounded to three significant figures: $$2.62 \times 10^{6}$$ Answer choice: ⓒ 2.62 × 10⁶