dead / shrunk / received
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dead
Refers to plants that have died, usually because of lack of water or disease.
Während unseres Urlaubs sind leider alle Blumen auf dem Balkon eingegangen.
Unfortunately, all the flowers on the balcony died while we were on vacation.
'Eingegangen' is the past participle form of the separable verb 'eingehen'. The verb is conjugated with the auxiliary verb 'sein' (to be), because it describes a change of state or movement.
Meine Lieblingspflanze ist leider eingegangen.
Unfortunately, my favorite plant has died.
You can recognize the meaning of 'eingegangen' from the subject of the sentence. If it is about plants, it means 'died'. With textiles, it means 'shrunk'. With mail, money, or messages, it means 'arrived'.
Die Tomatenpflanzen sind in der Hitze eingegangen.
The tomato plants died in the heat.
In the meaning 'arrived', 'eingegangen' is very often used as an adjective before a noun, especially in office and business language.
Alle eingegangenen Rechnungen müssen bis Freitag bezahlt werden.
All received invoices must be paid by Friday.
to receive / preserve / support
'erhalten' and 'eingegangen' can both be used with mail, messages, or payments. 'erhalten' describes the action from the point of view of the person or organization that receives something. 'eingegangen' describes more of a status: a message, application, or payment has arrived and been registered. That is why 'eingegangen' often sounds natural in offices, with authorities, or in written notifications. They can be confused because both say that something has arrived. In practice: a person or company 'erhält' something; an email, payment, or application 'ist eingegangen'.
Heute ist die Zahlung auf unserem Konto eingegangen.
The payment was received in our account today.
Haben Sie unsere Nachricht von gestern erhalten?
Did you receive our message from yesterday?