Engangstallerkenen og papkruset er tomme.

Because Danish usually writes compound nouns as a single word.

So engangstallerkenen is built like this:

• engangs- = disposable / single-use
• tallerken = plate
• -en = the for a common-gender singular noun

So the whole word means the disposable plate.

This is very normal in Danish. Where English often uses several words, Danish often joins them into one noun.

Engangs- literally comes from the idea of one time or for one use. In compounds, it often means:

• single-use
• disposable

So:

• engangstallerken = disposable plate
• engangskop = disposable cup
• engangshandsker = disposable gloves

It is a very common prefix in modern Danish.

The endings are different because the nouns have different grammatical genders.

• tallerken is a common gender noun, so the definite singular ending is -en

  • en tallerken = a plate
  • tallerkenen = the plate

• krus is a neuter noun, so the definite singular ending is -et

  • et krus = a cup / mug
  • kruset = the cup / mug

Since the sentence uses the definite form, you get:

• engangstallerkenen = the disposable plate
• papkruset = the paper cup

It is another compound noun:

• pap = cardboard / paper
• krus = cup / mug
• -et = the for a neuter singular noun

So papkruset means the paper cup.

Depending on context, pap can mean cardboard or paper, but in a sentence like this, paper cup is the most natural English translation.

In Danish, the is often attached to the end of the noun instead of appearing as a separate word.

So:

• tallerken = plate

• tallerkenen = the plate

• krus = cup
• kruset = the cup

That means Danish often expresses definiteness with an ending, not a separate word.

Because the subject is made up of two things joined by og (and):

• Engangstallerkenen
• og
• papkruset

Together, they form a plural subject: the disposable plate and the paper cup.

So the adjective after er must also be plural:

• one common-gender thing: tom
• one neuter thing: tomt
• more than one thing: tomme

That is why the sentence says er tomme.

It depends on the gender of the noun:

• Tallerkenen er tom. = The plate is empty.
• Kruset er tomt. = The cup is empty.

And with a plural subject:

• Tallerkenen og kruset er tomme. = The plate and the cup are empty.

So the forms are:

• tom = singular common gender
• tomt = singular neuter
• tomme = plural

Because Danish verbs do not change according to person or number the way English verbs sometimes do.

So Danish uses er for:

• jeg er = I am
• du er = you are
• han er = he is
• vi er = we are
• de er = they are

That is why both singular and plural subjects use er.

No, this sentence has very basic Danish main-clause word order:

• Subject: Engangstallerkenen og papkruset
• Verb: er
• Complement: tomme

So it works much like English:

• The disposable plate and the paper cup are empty.

The sentence is straightforward and neutral.

Danish does have ways to say a and the, but they work differently.

For a/an, Danish uses separate articles:

• en tallerken = a plate
• et krus = a cup

For the, Danish usually adds the definite ending to the noun:

• tallerkenen = the plate
• kruset = the cup

So Danish marks indefiniteness with a separate word (en / et) and definiteness very often with an ending (-en / -et).

Possibly, depending on what kind of cup you mean.

• kop usually means a cup more like a drinking cup with a handle, or sometimes just cup in general
• krus often means mug, but it can also be used more broadly depending on context

In real life, usage can overlap, and learners will notice that Danish sometimes uses words a little differently from English. In this sentence, papkruset is completely natural if the intended meaning is a paper drinking cup.

Unfortunately, you usually have to learn the noun together with its article:

• en tallerken
• et krus

That is the best habit. If you memorize the article with the noun, it becomes much easier to form:

• the definite form
• adjective agreement
• pronouns later on

So instead of learning just tallerken, learn en tallerken. Instead of just krus, learn et krus.

If you wanted to say A disposable plate and a paper cup are empty, you would use the indefinite forms:

• En engangstallerken og et papkrus er tomme.

Notice the changes:

• engangstallerkenen → en engangstallerken
• papkruset → et papkrus

But er tomme stays the same, because the subject is still plural overall.