These bagels are stale.
determiner or pronoun

Determiner.

Explanation:

Determiners are words, most times pronouns placed before a noun, that qualifies/determines something about the noun placed after it or shows who possess it.

Pronouns (possessive) on the other hand do not require a noun after it.

Examples of determiners: the, this, some, your, my, enough, their, etc

Examples below:

(In the first sentence some books is explicit in qualifying the number of books while in the second sentence the word some replaces books)

( The placed before project determines that we are talking about the project while, yours is the possessive pronoun that replaces your project).

Therefore, These bagels are stale. These determines which bagels are stale followed by the word Bagels, a noun.

he is honest with congress and america about the difficulty of the war ahead.

son.