Learn Arabic (Modern Standard): المرأة فقيرة.

Arabic does not use a present tense verb for "is" or "are". Instead, you create a nominal sentence simply by placing the subject المرأة (the woman) and the descriptive word فقيرة (poor) side by side.

Why does the word for "woman" have the "al-" prefix but "poor" does not?

This is the core rule for making "is" sentences with adjectives in Arabic. The subject usually has the definite article ال (the), while the adjective describing it does not. If both words had ال, reading المرأة الفقيرة, it would not be a full sentence but just a descriptive phrase meaning "the poor woman".

Why is there a taa marbuta (ة) at the end of the word for "poor"?

Adjectives must match the gender of the noun they describe. Since المرأة (the woman) is a feminine noun, the basic adjective فقير (poor) gets the feminine ending ة to become فقيرة.

Why does the spelling of the word for woman look different here compared to when it means "a woman"?

This noun has a unique spelling quirk. Without "the", the word for "a woman" is written as امرأة. When you add ال to make it "the woman", the first letter drops out entirely and it becomes المرأة.