Here are the answers to each question:
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A participle is a type of verb that can function as a(n adjective in a sentence. Participles can be present or past participles. Present participles always end in -ing and past participles end in -ed unless they are irregular verbs.
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The word that is the past tense of an irregular verb is tapped.
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The participle that functions as an adjective in the sentence "There is a walking path that leads from the middle school to the high school." is walking.
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The sentence that contains a participle functioning as a verb is The blinking sign warns drivers of a sharp curve ahead. ("blinking" is a participle functioning as a verb here).
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The sentence that contains a participle functioning as an adjective is The swimming pool in my neighborhood is closed for the winter. ("closed" is a participle functioning as an adjective here).