Brick Co. has 170,000 shares of common stock outstanding at January 1, year 8. On May 1, year 8, it issued 30,000 additional shares of common stock. Outstanding all year were 12,000 shares of convertible cumulative preferred stock. Each share of the convertible preferred stock, which was dilutive in year 8, is convertible into one share of Bricks common stock. What is the number of shares that Brick should use to calculate year 8 diluted earnings per share

202,000 shares

Explanation:

170,000 common stocks outstanding, January 1

30,000 additional common stock issued, May 1 ⇒ 30,000 x 8/12 = 20,000

diluted shares = 12,000 (since each preferred stock is convertible to common stock, then all of them must be included as diluted stocks)

total number of shares = 170,000 +20,000 + 12,000 = 202,000 shares

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.