She argued 'convincingly' [='persuasively'] that more money should be given to public schools.
There is no 'convincing' evidence to support his theory.
Your argument/story isn't very 'convincing'.
(..) I do. No, you don't. I think you're an exceptional lawyer. I watch the court members. They respond to you. They like you. I see you convincing them, and I think Dawson and Downey... are gonna end up owing their lives to you. Jo, I think-- I think you should prepare yourself (..)1992 A Few Good Men