A quatrain is a stanza of four lines, especially one having alternate rhymes. (According to dictionary.com) With this in mind choose which line has these qualities to get your answer.
B. Compound, because it has a conjunction that combines segments that could be 2 separate thoughts.
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Your answer would be option A. ran, since the other option is a NOUN.
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For number 1, your option is correct (B). "Doggedly" is synonymous with "persistent," so "with great determination" matches that.
For number 2, your option is correct (D). "Stoutly" means "strong" and "sturdy," so "solid" would also work.
For number 3, your option is incorrect. The correct answer is B. "Boisterous" and "rowdy" both mean energetic and noisy. Since the children were bouncing off the walls, they were indeed energetic, boisterous, and rowdy.