A greenhouse contained both 6-inch high geraniums and 3 inch high geraniums. The 6-inch high geraniums were taken out of the greenhouse in early spring and grew at a rate of 1 inch per week. The 3 inch high geraniums remained in the greenhouse and grew at a rate of 1 (1/2) inches per week. After the 6-inch high geraniums were taken outside, in how many weeks were both groups of geraniums the same height.

What is the next step in the given proof? choose the most logical approach. a. statement: m 1 + m 2 + 2(m 3) = 180° reason: angle addition b. statement: m 1 + m 3 = m 2 + m 3 reason: transitive property of equality c. statement: m 1 = m 2 reason: subtraction property of equality d. statement: m 1 + m 2 = m 2 + m 3 reason: substitution property of equality e. statement: 2(m 1) = m 2 + m 3 reason: substitution property of equality

Abilliard ball is struck by a cue. it travels 1 0 0 cm 100cm before ricocheting off a rail and traveling another 1 2 0 cm 120cm into a corner pocket. the angle between the path as the ball approaches the rail and the path after it strikes the rail is 4 5 ∘ 45 ∘ . how far is the corner pocket from where the cue initially struck the ball? do not round during your calculations. round your final answer to the nearest centimeter.

In a recent year, the weather was partly cloudy 2/5 of the days. assuming there are 356 days in a year, how many days were partly cloudy?