A határozat érvényes.

In Hungarian, the verb to be is usually left out in the present tense, third person singular.

So:

• A határozat érvényes. = The decision is valid.

But in other persons, the verb appears:

• Én fáradt vagyok. = I am tired.
• Te fáradt vagy. = You are tired.

So this omission is completely normal here.

A is the definite article, meaning the.

So:

• a határozat = the decision / the resolution

Hungarian has two forms of the definite article:

• a before most consonants
• az before vowels

For example:

• a határozat
• az ügy = the case / matter

Határozat is a noun. It often means:

• decision
• resolution
• ruling
• formal determination

The exact English translation depends on context. It is often used in official, legal, administrative, or institutional language, so it can sound more formal than a simple everyday decision.

Érvényes is an adjective meaning:

• valid
• effective
• in force

In this sentence, it functions as a predicate adjective:

• A határozat érvényes. = The decision is valid.

Compare:

• érvényes határozat = a valid decision
  Here it comes before the noun and directly describes it.
• A határozat érvényes. = The decision is valid.
  Here it is the main statement about the noun.

Because here it is not part of the noun phrase. It is the predicate of the sentence.

Compare the two patterns:

• az érvényes határozat = the valid decision
  (érvényes is attributive: it modifies the noun directly)
• A határozat érvényes. = The decision is valid.
  (érvényes is predicative: it says something about the subject)

So the position changes depending on the role of the adjective.

The structure is:

• A határozat = the subject
• érvényes = predicate adjective

So the pattern is:

• Subject + adjective

Because Hungarian omits is in this kind of sentence, that is enough to form a complete statement.

No, that would be incorrect in standard Hungarian.

In the present tense, third person singular, you normally do not use van with this type of adjective:

• Correct: A határozat érvényes.
• Incorrect: A határozat van érvényes.

Hungarian does use van in other situations, but not here.

A simple pronunciation guide is:

• A határozat érvényes
  roughly: aw haw-TAA-ro-zawt AAYR-vay-nyesh

A few helpful points:

• Stress in Hungarian is always on the first syllable of each word.
• á is a long vowel, pronounced longer than a.
• é is also long.
• ny is like the ny in canyon.
• s is pronounced like English sh.

So érvényes sounds roughly like AIR-vay-nyesh.

No. Határozat is in the nominative form, which is the basic dictionary form of the noun.

Hungarian often shows grammatical roles with endings, but here there is no extra ending:

• határozat = decision / resolution

Since it is the subject of the sentence, the basic form is exactly what you would expect.

Yes, it sounds somewhat formal or official, mainly because of the noun határozat.

This is the kind of sentence you might see in:

• legal texts
• administrative documents
• institutional decisions
• official notices

In everyday speech, a different noun might be more natural depending on context, but A határozat érvényes is perfectly normal in formal Hungarian.

Yes, depending on context.

Because érvényes can mean:

• valid
• effective
• in force

So if határozat refers to an official resolution or ruling, a natural English translation might be:

• The resolution is valid.
• The resolution is in force.

The exact choice depends on what kind of text you are translating.