هذه آلة جديدة.

Because آلة is a feminine singular noun, and the demonstrative must match it.

• هذا = this for masculine singular
• هذه = this for feminine singular

So with آلة, you say هذه.

In Arabic, many nouns are feminine because they are inherently feminine in the language, and very often they also show the feminine ending ة.

آلة ends in ة (called tāʾ marbūṭa), which is a very common sign of a feminine noun.

That is why both the demonstrative and the adjective are feminine:

• هذه because the noun is feminine
• جديدة because it describes a feminine noun

Because in Arabic, adjectives normally come after the noun they describe.

So:

• آلة جديدة = a new machine

This is the normal pattern:

• noun + adjective

Unlike English, Arabic does not usually put the adjective before the noun.

Because adjectives in Arabic must agree with the noun they describe.

Since آلة is:

• feminine
• singular
• indefinite

the adjective must also be:

• feminine
• singular
• indefinite

So:

• جديد = masculine singular
• جديدة = feminine singular

That is why جديدة is correct here.

In the present tense, Arabic usually does not use a separate word for is/am/are in sentences like this.

So:

• هذه آلة جديدة literally looks like this a new machine
• but it means this is a new machine

This kind of sentence is very normal in Arabic. The idea of is is understood automatically.

Arabic has no indefinite article like English a/an.

So آلة جديدة can mean:

• a new machine

Indefiniteness is usually shown by context, and in fully vocalized Arabic often by tanwīn on the noun and adjective:

• آلةٌ جديدةٌ

That tells you the phrase is indefinite.

A fully vocalized version is:

هٰذِهِ آلَةٌ جَدِيدَةٌ

Here is what is happening:

• هٰذِهِ = this (feminine singular)
• آلَةٌ = machine, with -un because it is nominative
• جَدِيدَةٌ = new, also nominative because it agrees with آلة

In normal everyday writing, these short vowel endings are usually not written, so you just see:

هذه آلة جديدة

It is usually pronounced roughly as ʾaala or ʾāla.

A few useful points:

• it begins with a glottal stop sound, like a quick catch before the vowel
• the ا gives a long aa sound
• the final ة is usually pronounced like -a in pause

So in normal citation-style pronunciation, it sounds like ʾāla.

If fully read with case ending, it can be ʾālatun.

The letter ة is called tāʾ marbūṭa.

In most pause pronunciation, it sounds like -a or -ah:

• آلة → ʾāla
• جديدة → jadīda

But when grammatical endings are pronounced in full, the t sound appears:

• آلةٌ → ʾālatun
• جديدةٌ → jadīdatun

So the same letter can sound different depending on how carefully the sentence is being read.

Because Arabic normally places the demonstrative before the noun:

• هذه آلة = this machine / this is a machine

Then the adjective comes after the noun:

• آلة جديدة = new machine

So the natural order is:

• demonstrative + noun + adjective

That gives:

هذه آلة جديدة

You would make the noun and adjective definite:

هذه الآلة الجديدة

Here:

• الآلة = the machine
• الجديدة = the new

Notice that the adjective also becomes definite with الـ because adjectives must match the noun in definiteness too.

So compare:

• هذه آلة جديدة = this is a new machine
• هذه الآلة الجديدة = this is the new machine / this new machine

It is a complete sentence in Arabic.

Arabic often forms present-tense sentences without a verb like is, so:

• هذه functions like the topic: this
• آلة جديدة gives the information about it: a new machine

So the whole thing naturally means:

• This is a new machine

Even though there is no separate word for is, it is still a full sentence.