determinado in English:

You can expect our adamant refusal.

I'm adamant that you should go.

He was so adamant in his refusal.

I've told her she should stay at home and rest but she's adamant that she's coming.

We tried to persuade her but she was adamant.

She's been adamant in her position for a long time.

But he was adamant.

adamant in support of, be adamant about sth

No one but her would know that her own adamant will had, in the end, failed her.

... at least were fairly adamant about wanting to sound...

I am adamant that he undertake it.