a) Nola and I prepared dinner for the family
The underlined nominative pronoun is used in the sentence as a compound subject. A compound subject is a subject made up of two or more simple subjects joined by a coordinating conjunction and that share the same predicate.
In a) the coordinating conjunction "and" is joining the two subjects ("Nola" and "I") and the verbal predicate they share is "prepared dinner for the family".
