That settles something (such as an argument) definitely and conclusively(adjective)
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Use "clinching" in a sentence
"Matsui's 3 RBI's in the title clinching game: $13,000,000.00"
"Tim Tebow threw for three touchdowns and ran for two more, and the No. 4 Gators routed Vanderbilt 42-14 in clinching the SEC Eastern Division title for the second time in three years."
"While he was held to 17 aces, he lost only 13 points on his serve to improve to 10-0 in clinching situations for the U.S."