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The phrase "are very optimistic" is correct and usable in written English.
You can use it when expressing a positive outlook or hopeful attitude about a situation or future events.
Example: "Despite the challenges we face, the team are very optimistic about achieving our goals this quarter."
Alternatives: "are quite hopeful" or "are extremely positive".
Exact(59)
"We are very optimistic," Dr. Maray said.
"We are very optimistic," he said, calling his condition favorable.
"We are very optimistic about the future," he said.
And they are very optimistic about defeating five Republican incumbents.
"We are very optimistic about where it stands".
"We are very optimistic that Jimmy is fit to play.
"We are very optimistic, but there are a few issues remaining".
We are very optimistic that there will be more investment over the next few years.
"I would say we are very optimistic right now," Ms. Kelly said.
We are very optimistic, but we have to wait until the final rules are settled".
"We are very optimistic, and hopefully the court will bring the justice the victims deserve," he added.
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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