A6 cm object is 15 cm from a convex lens that has a focal length of 5 cm. what is the distance of the image from the lens, to the nearest hundredth?
–33.33 cm
–7.69 cm
7.69 cm
33.33 cm

So we want to know what is the distance d of the object from the lens if the height of the object is h=6 cm, focal length of the lens is f=5 cm and the distance d=15 cm is the distance of the object from the lens. From the formula for the convex lens 1/f=(1/D + 1/d) where D is the distance of the image from the lens we can get D after solving for D: 1/D=(1/f) - (1/d),
1/D=(1/5)-(1/15)=0.2-0,06667=0.13333 so f=1/0.13333=7.500187 cm. Rounded to the nearest hundredth D=7.50 cm.  That is very close to 7.69 cm so the correct answer is the third one.