A subject with two or more nouns joined by the word and is called a compound subject. A compound subject takes a plural verb, even if some or all of the nouns are singular. Here are some examples of compound subjects joined by and:
Sometimes the nouns in a compound subject are joined by or. If all the nouns are singular, the verb is also singular. If all of the nouns are plural, the verb is also plural. Here are some examples of compound subjects joined by or:
If one of the nouns is plural and another is singular, the choice between a singular or plural verb depends on context and personal habit. The grammar rule that many teachers and grammarians teach is that the verb agrees with the noun closest to it, but in actual usage, this rule is often broken.
Therefore, in formal writing, a sentence like the one below would probably be written with the singular verb is, but in actual conversation you would be just as likely to hear someone use the plural verb are—and no one would notice.
I hope this is helpful.