По сравнению с прошлой неделей орхидея выглядит лучше и уже не вянет.

По сравнению с means compared with or in comparison with.

It is a fixed expression:

• по сравнению с прошлой неделей = compared with last week

It is commonly used to compare one situation with another:

• По сравнению с зимой сейчас тепло. = Compared with winter, it’s warm now.
• По сравнению с братом он высокий. = Compared with his brother, he is tall.

So in your sentence, it sets up the comparison before the main statement.

Because по сравнению с requires the instrumental case.

The noun неделя becomes:

• nominative: прошлая неделя
• instrumental: прошлой неделей

And the adjective must match:

• прошлая → прошлой
• неделя → неделей

So:

• по сравнению с прошлой неделей = compared with last week

For feminine nouns ending in -я, the instrumental singular often ends in -ей:

• неделя → неделей
• Россия → Россией

Russian and English package comparisons differently.

In English, we say:

• compared to last week
• compared with last week

In Russian, the expression is literally built around comparison with:

• по сравнению с прошлой неделей

So even if the English translation uses to, Russian still uses с plus the instrumental case here.

This is something to learn as a set phrase rather than translate word for word.

Because орхидея is the subject of the sentence.

The sentence is saying what the orchid does:

• орхидея выглядит
• орхидея не вянет

So it stays in the nominative:

• орхидея = the orchid

If you changed the subject, the verb would match the new subject:

• цветы выглядят лучше = the flowers look better

Выглядит is the 3rd person singular present tense of выглядеть.

Dictionary form:

• выглядеть = to look, to appear

Conjugation:

• я выгляжу
• ты выглядишь
• он / она выглядит
• мы выглядим
• вы выглядите
• они выглядят

Here the subject is орхидея (singular), so:

• орхидея выглядит = the orchid looks / appears

Russian uses the present tense here just like English:

• The orchid looks better

Because лучше here is the comparative form meaning better, and it works with the verb выглядеть.

• выглядит лучше = looks better

You are not directly describing the orchid as the best or a better orchid. You are describing how it looks.

Compare:

• орхидея лучше = the orchid is better
• орхидея выглядит лучше = the orchid looks better

Also:

• лучшая means best or the better one in an adjective form:
  • лучшая орхидея = the best orchid

So лучше is correct because it is a comparison of condition/appearance, not an agreeing adjective before a noun.

Mostly yes: выглядеть is about how something looks or appears.

With a plant, выглядит лучше usually means:

• it seems healthier
• it looks less damaged
• its condition appears improved

So it is often visual, but it can imply general condition as judged from appearance.

For example:

• Он выглядит усталым. = He looks tired.
• Дом выглядит старым. = The house looks old.

In your sentence, the idea is that the orchid appears to be in better shape than it was last week.

Уже не means no longer or not anymore.

So:

• уже не вянет = is no longer wilting

Word by word:

• уже = already
• не = not

But in many sentences, already not is best translated naturally as:

• no longer
• not anymore

Examples:

• Он уже не спит. = He is no longer asleep.
• Я уже не работаю там. = I don’t work there anymore.

So in your sentence, уже signals a change from an earlier situation: before, the orchid was wilting; now it is not.

Because уже modifies the whole negated idea: not wilting anymore.

Russian commonly places уже before не in this kind of sentence:

• уже не вянет
• уже не болит
• уже не работает

This gives the meaning:

• previously yes
• now no

If you are an English speaker, it helps to think of уже не as one meaningful unit:

• already not → no longer

Вянет comes from вянуть, which means:

• to wilt
• to droop
• to fade (especially for plants or flowers)

So:

• орхидея вянет = the orchid is wilting

This is a very natural verb for flowers and plants.

Examples:

• Цветы вянут без воды. = Flowers wilt without water.
• Листья вянут на жаре. = The leaves wilt in the heat.

In your sentence:

• уже не вянет = it is no longer wilting

Because the sentence describes the orchid’s current state.

It says:

• compared with last week, the orchid looks better now
• and is no longer wilting now

Russian often uses the present tense exactly as English would here.

The comparison phrase по сравнению с прошлой неделей gives the time reference for the comparison, but the main verbs describe what is true at the present moment:

• выглядит
• не вянет

Because the sentence has one subject and two coordinated predicates:

• орхидея выглядит лучше
• (орхидея) уже не вянет

Both verbs belong to the same subject, орхидея, and they are joined by и. In that situation, Russian normally does not use a comma before и.

So this is standard:

• Орхидея выглядит лучше и уже не вянет.

Yes. Russian word order is flexible, though some versions sound more natural than others depending on emphasis.

The original:

• По сравнению с прошлой неделей орхидея выглядит лучше и уже не вянет.

This is very natural because it starts with the comparison frame.

You could also say:

• Орхидея по сравнению с прошлой неделей выглядит лучше и уже не вянет.

This is also understandable, but it puts more focus on орхидея first.

The original version is probably the most neutral and elegant in normal speech or writing.

Because these mean different things.

• на прошлой неделе = last week as a time expression
• прошлой неделей in по сравнению с прошлой неделей = with last week / compared with last week

Compare:

• На прошлой неделе орхидея вяла. = Last week the orchid was wilting.
• По сравнению с прошлой неделей орхидея выглядит лучше. = Compared with last week, the orchid looks better.

So на прошлой неделе answers when? But по сравнению с прошлой неделей answers compared with what?

Yes.

• не вянет = is not wilting
• уже не вянет = is no longer wilting

The version with уже clearly suggests a change:

• before, it was wilting
• now, that has stopped

Without уже, the sentence would simply describe the current state, without emphasizing improvement.

So in this sentence, уже is important because it supports the idea of recovery.

Absolutely. It can compare almost anything.

Examples:

• По сравнению с прошлым годом продажи выросли. = Compared with last year, sales increased.
• По сравнению с сестрой он очень спокойный. = Compared with his sister, he is very calm.
• По сравнению с этим домом тот дом маленький. = Compared with this house, that one is small.

So in your sentence, прошлой неделей is just the thing being used as the reference point for comparison.