Learn Hardcore Russian: Полезная наука помогает людям.

Наука is a feminine noun of the 1st declension. In the nominative singular (the “subject” form), most feminine nouns end in -а or -я, so наука takes -а.

Why does the adjective полезная end with -ая?

Adjectives in Russian must agree with the noun they modify in gender, number, and case. Since наука is feminine, singular, and in the nominative case, the adjective полезная also takes the nominative feminine singular ending -ая.

Why is the verb помогает in the 3rd-person singular form?

The subject наука is singular, so the verb must match it in person and number. Помогает is the 3rd-person singular form of помогать (“to help”).

Why is людям in the dative case, and why plural?

The verb помогать requires its beneficiary (the one who receives help) to be in the dative case. The word for “people” is люди (nominative plural), and its dative plural form is людям.

Could we use the accusative case instead of the dative for людям?