Die Tonanlage ist sehr laut.

Because Tonanlage is a feminine noun in German, so its nominative singular article is die.

A useful thing to know is that German nouns have grammatical gender:

• der = masculine
• die = feminine
• das = neuter

So in this sentence, die Tonanlage is the subject, and feminine nouns in the nominative take die.

Also, die can mean:

• the for a feminine singular noun
• the for any plural noun

Here it is feminine singular, not plural.

Tonanlage is a compound noun, which is very common in German.

It is made from:

• Ton = sound, audio
• Anlage = system, installation, setup

So Tonanlage means something like:

• sound system
• stereo system
• audio system

In German, compound nouns are written as one word, not as separate words.

German main clauses usually follow the verb-second rule, often called V2.

In Die Tonanlage ist sehr laut:

1. Die Tonanlage = first element
2. ist = verb in second position
3. sehr laut = rest of the sentence

This is one of the most important word-order patterns in German. In a normal statement, the finite verb usually comes second.

Sein is the infinitive, meaning to be.
In a sentence, you usually need a conjugated form.

Here the subject is die Tonanlage, which is third person singular, so sein becomes ist.

A few forms of sein are:

• ich bin
• du bist
• er/sie/es ist
• wir sind
• ihr seid
• sie/Sie sind

So die Tonanlage ist = the sound system is.

Because laut is being used as a predicate adjective, not an adjective directly before a noun.

Compare:

• Die Tonanlage ist sehr laut.
  Here laut comes after ist, so it does not take an ending.

• die sehr laute Tonanlage
  Here the adjective comes before the noun, so it does take an ending: laute

This is a very common German pattern:

• after sein, werden, bleiben, adjectives usually stay in the base form
• before a noun, adjectives usually take endings

Sehr means very and it modifies the adjective laut.

So:

• laut = loud
• sehr laut = very loud

This works much like English:

• very loud
• very big
• very expensive

In German:

• sehr laut
• sehr groß
• sehr teuer

In this sentence, yes, laut means loud.

But depending on context, laut can also appear in another meaning:

• laut dem Bericht = according to the report

That is a different use of the same word.

In Die Tonanlage ist sehr laut, the meaning is clearly the adjective loud, describing how much noise the sound system makes.

Because all nouns are capitalized in German.

So:

• die Tonanlage
• das Haus
• der Tisch

But adjectives, verbs, and adverbs are usually not capitalized unless they begin the sentence:

• ist
• sehr
• laut

This is one of the easiest visual clues in German: if a word is capitalized in the middle of a sentence, it is often a noun.

It is singular here.

Even though die can also be the plural article, the verb tells you what is happening:

• Die Tonanlage ist ... = singular
• Die Tonanlagen sind ... = plural

So:

• die Tonanlage ist sehr laut = singular
• die Tonanlagen sind sehr laut = plural

The noun form also helps:

• singular: Tonanlage
• plural: Tonanlagen

A simple learner-friendly pronunciation guide would be:

dee TOHN-an-lah-guh ist zair lowt

A few helpful details:

• die sounds like dee
• Ton has a long o sound
• Anlage is roughly AHN-lah-guh
• sehr is roughly zair
• laut rhymes roughly with English out

The r in sehr is often very soft in standard German.

Yes. That would still be correct.

• Die Tonanlage ist laut. = The sound system is loud.
• Die Tonanlage ist sehr laut. = The sound system is very loud.

So sehr just adds extra intensity.

Here is the breakdown:

• Die = definite article
• Tonanlage = noun
• ist = verb, finite form of sein
• sehr = adverb
• laut = adjective

So the structure is basically:

article + noun + verb + adverb + adjective

More grammatically:

• Die Tonanlage = subject
• ist = linking verb
• sehr laut = predicate adjective phrase

The subject die Tonanlage is in the nominative case, yes.

That is because it is the thing that is something:

• Die Tonanlage is very loud.

After sein, the subject is nominative. The adjective laut does not show case here because it is a predicate adjective and has no ending in this position.

So the main case point in this sentence is:

• die Tonanlage = nominative subject