Ten sweter jest brzydki, ale bardzo ciepły.

Because ten has to agree with the noun in gender, number, and case.

• sweter is a masculine singular noun
• in this sentence it is in the nominative case
• so the correct demonstrative is ten

Compare:

• ten sweter = this sweater
• ta koszula = this shirt/blouse
• to krzesło = this chair

So ten is the masculine form.

Usually, yes. In Polish, a noun ending in a consonant is often masculine.

So:

• sweter → masculine
• dom → masculine
• stół → masculine

This is a very common pattern, though there are some exceptions elsewhere in the language. For sweter, masculine is the normal gender.

It is in the nominative case.

Why?

Because sweter is the subject of the sentence:

• Ten sweter = the thing being talked about
• jest brzydki = is ugly
• ale bardzo ciepły = but very warm

The adjectives brzydki and ciepły also match the noun in nominative masculine singular.

Both adjectives are still masculine singular nominative, but Polish adjectives can have different dictionary endings:

• -y
• -i

So:

• brzydki = ugly
• ciepły = warm

This does not mean they are in different cases or genders here. It is just part of how different adjective stems behave.

A useful beginner rule is:

• many masculine adjectives end in -y
• some end in -i, especially after certain consonants

So in this sentence, both forms are completely normal and both agree with sweter.

Jest is the 3rd person singular form of być = to be.

So:

• sweter jest brzydki = the sweater is ugly

In standard Polish, you normally do use jest in this kind of sentence.

Unlike in Russian, for example, Polish does not usually drop to be in the present tense in ordinary sentences.

So:

• Ten sweter jest brzydki. = correct, normal
• Ten sweter brzydki. = not standard in normal speech

Because ale means but, and in Polish it is normally preceded by a comma.

So:

• Ten sweter jest brzydki, ale bardzo ciepły.

This is standard punctuation.

You will see the same with many contrasting clauses:

• Chciałem iść, ale padało. = I wanted to go, but it was raining.

Because bardzo is an adverb meaning very, and it modifies the adjective ciepły.

In Polish, adverbs like bardzo usually come before the adjective they modify:

• bardzo ciepły = very warm
• bardzo ładny = very pretty
• bardzo zimny = very cold

So bardzo ciepły is the natural order.

Yes, Polish word order is more flexible than English, but the version in the sentence is the most neutral and natural.

Neutral order:

• Ten sweter jest brzydki, ale bardzo ciepły.

You can sometimes move things for emphasis, but not every rearrangement sounds equally natural.

For example, you might hear:

• Ten sweter jest bardzo ciepły, ale brzydki.

This changes the emphasis a bit: first you focus on it being very warm, then add the contrast that it is ugly.

So yes, word order can move, but the original sentence is a very standard way to say it.

Because Polish does not have articles like English a and the.

That means Polish often just says:

• sweter = sweater / a sweater / the sweater

The exact meaning depends on context.

Here, ten sweter is more specific. It usually means:

• this sweater
• sometimes something close to that sweater
• in some contexts it can simply point to a particular sweater the speaker has in mind

So ten is not just the English article the. It is a demonstrative word.

Yes, absolutely.

• Sweter jest brzydki, ale bardzo ciepły.

This is grammatically correct and means The sweater / A sweater is ugly, but very warm, depending on context.

Adding ten makes it more specific:

• Ten sweter... = this particular sweater / that sweater

So the difference is about specificity and pointing something out, not basic grammar.

Here are rough English-style approximations:

• ten ≈ ten
• sweter ≈ SVE-ter
• jest ≈ yest
• brzydki ≈ BZHYT-kee
• ale ≈ AH-leh
• bardzo ≈ BAR-dzo
• ciepły ≈ CHYEP-wy

A few useful pronunciation notes:

• w in Polish sounds like English v
• rz often sounds like the s in measure
• ł sounds like English w
• y is a vowel that does not exist exactly in English
• in brzydki, the d is not pronounced strongly as an English d because of the following k

So the hardest words for many English speakers are usually brzydki and ciepły.

Because Polish can omit the repeated jest when two adjectives describe the same subject.

So:

• Ten sweter jest brzydki, ale bardzo ciepły.

is completely natural.

You could also say:

• Ten sweter jest brzydki, ale jest bardzo ciepły.

That is also grammatical, but it sounds a bit more explicit or slightly heavier. The version with just one jest is usually more natural here.