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 will be forced to go to your competition. I'm afraid they won't help you either. You see, in our line of work, a man has to present to the customer a convincing air of healthful vitality. Not to mention trustworthiness and incorruptibility. Please, please, please, please. I'll do anything. (..)2014 TvShow: The Knick Title: The Golden Lotus Season: 1 Episode 9