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The phrase "are very persuasive" is correct and usable in written English.
You can use it to describe someone or something that effectively convinces or influences others.
Example: "Her arguments are very persuasive, making it difficult for anyone to disagree with her point of view."
Alternatives: "are highly convincing" or "are quite compelling."
Dictionary
Exact(6)
"We've been led to believe these companies have all these powers and are very persuasive in their advertising," Gameau says.
"Rich people are very persuasive and they swing their weight around and they know you're anxious to make a deal," Mr. Hubert added.
He amiably concedes, however, that he doesn't think there is a concrete answer, and that "there are very persuasive arguments to be made for the idea" that Tony has, in fact, been shot dead in the final scene (one such argument is put forth, at great length, in an online essay titled "The Sopranos: Definitive Explanation of 'The END' ").
The data on the benefits of consuming high levels of phytonutrients in fruit and vegetables to prevent or ameliorate chronic disease are very persuasive.
And they are very persuasive.
Neither of these are very persuasive arguments for using a therapy.
Similar(52)
And she's very persuasive.
"He is very persuasive".
But Ms. Burstein was very persuasive.
(The Baron is very persuasive).
"They can be very persuasive," she said.
More suggestions(17)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com