Final answer:
The image of the woman's face formed by the concave makeup mirror is three times as large as her actual face.
Step-by-step explanation:
The image of the woman's face formed by the concave makeup mirror can be determined using the mirror formula: 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance. In this case, the object distance is 20 cm and the focal length is 30 cm. Plugging these values into the formula, we can solve for the image distance:
1/30 = 1/v - 1/20
5/600 = 1/v
v = 600/5 = 120 cm
Since the image distance is positive, the image is real. The magnification of the image is given by M = -v/u, where M is the magnification. Plugging in the values, we get:
M = -120/20 = -6
Therefore, the image of the woman's face is 6 times larger than her actual face. So, the correct answer is D. three times as large as her face.