بطاقة الدعوة وهدية الزفاف جاهزتان.

In Arabic, present-tense nominal sentences usually do not use a separate word for is/are/am.

So the sentence is simply:

بطاقة الدعوة وهدية الزفاف = the subject
جاهزتان = the predicate

Literally, it is something like The invitation card and the wedding gift ready.

If you wanted were, Arabic would use a verb, for example:

بطاقة الدعوة وهدية الزفاف كانتا جاهزتين
= The invitation card and the wedding gift were ready

Because it is a dual feminine form.

The sentence is talking about exactly two things:

• بطاقة الدعوة
• هدية الزفاف

So Arabic uses the dual, not the singular or regular plural.

The pattern here is:

• جاهزة = ready, for one feminine thing
• جاهزتان = ready, for two feminine things
• جاهزات = ready, for more than two feminine things

So جاهزتان means ready with agreement for two feminine nouns.

Because both nouns are grammatically feminine:

• بطاقة
• هدية

A very common sign of feminine nouns is ة at the end, and both of these words have it.

Since the two nouns are feminine, the predicate must agree with them, so Arabic uses:

جاهزتان = feminine dual

not:

جاهزان = masculine dual

Because both phrases are iḍāfa constructions, often called the construct phrase.

• بطاقة الدعوة
• هدية الزفاف

In an iḍāfa, the first noun normally does not take الـ and does not take tanwīn.
The second noun determines definiteness.

So:

• بطاقة الدعوة = literally card of the invitation, naturally the invitation card
• هدية الزفاف = literally gift of the wedding, naturally the wedding gift

Because الدعوة and الزفاف are definite, the whole phrases are definite too.

Each one is an iḍāfa phrase made of:

1. a first noun
2. a second noun that specifies it

So:

• بطاقة الدعوة = invitation card
• هدية الزفاف = wedding gift

More literally, Arabic is saying:

• card of the invitation
• gift of the wedding

English often translates iḍāfa either with of or with a compound noun.

Also, in an iḍāfa, the second noun is in the genitive case.

Because ة (tāʾ marbūṭa) is usually pronounced:

• -a / -ah when you stop on the word by itself
• t when another word or ending follows

For example:

• بطاقة by itself: biṭāqa
• بطاقة الدعوة: biṭāqat ad-daʿwa

And:

• جاهزة by itself: jāhiza
• جاهزتان: the t appears before the dual ending

So the t is not random; it is part of how ة behaves in connected speech and before suffixes.

Because this word is nominative.

In MSA, the feminine dual endings are:

• -تانِ for the nominative
• -تينِ for the accusative and genitive

Here, جاهزتان is the predicate of a nominal sentence, so it is nominative.

That is why the form is:

جاهزتان

not:

جاهزتين

With full case endings, the sentence is:

بِطَاقَةُ الدَّعْوَةِ وَهَدِيَّةُ الزَّفَافِ جَاهِزَتَانِ

Here is the case of each part:

• بطاقةُ: nominative
  It is part of the subject.

• الدعوةِ: genitive
  It is the second noun in the iḍāfa.

• هديةُ: nominative
  It is coordinated with بطاقةُ by و.

• الزفافِ: genitive
  It is the second noun in the iḍāfa.

• جاهزتانِ: nominative
  It is the predicate, and it is feminine dual.

In standard MSA, when you are describing exactly two feminine things together, the expected form is the feminine dual:

جاهزتان

Compare:

• جاهزة = one feminine thing is ready
• جاهزتان = two feminine things are ready
• جاهزات = more than two feminine things are ready

So for this sentence, جاهزتان is the standard form.

و means and.

It connects the two noun phrases:

• بطاقة الدعوة
• هدية الزفاف

Together, they form a compound subject:

بطاقة الدعوة وهدية الزفاف
= the invitation card and the wedding gift

Because there are two items joined by و, the predicate is dual: جاهزتان.

A fully vocalized version is:

بِطَاقَةُ الدَّعْوَةِ وَهَدِيَّةُ الزَّفَافِ جَاهِزَتَانِ

A careful reading is:

biṭāqatu d-daʿwati wa hadiyyatu z-zafāfi jāhizatāni

If you pause at the end of the sentence, many readers pronounce the last word as:

jāhizatān

Also notice that the ل of الـ assimilates before the sun letters د and ز, so you hear:

• ad-daʿwa
• az-zafāf

rather than pronouncing a clear l sound.