
abhängen von
to depend on
To be determined or influenced by something or someone; to rely on something.
Ob wir den Ausflug machen, hängt ganz vom Wetter ab.
Whether we go on the trip depends entirely on the weather.
to depend / to hang out / to take down
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to depend on
To be determined or influenced by something or someone; to rely on something.
Ob wir den Ausflug machen, hängt ganz vom Wetter ab.
Whether we go on the trip depends entirely on the weather.

to hang out
(Colloquial) To relax and spend time doing nothing in particular, often with friends.
Am Wochenende will ich einfach nur mit meinen Freunden im Park abhängen.
At the weekend, I just want to hang out with my friends in the park.

to leave behind
(Colloquial) To leave someone behind in a competition or pursuit; to outperform someone.
Im letzten Sprint hat die Läuferin ihre Konkurrentin deutlich abgehängt.
In the final sprint, the runner clearly left her competitor behind.

to take down
To take down or remove something that has been hung up.
Nach der Party müssen wir die ganze Dekoration wieder abhängen.
After the party, we have to take all the decorations down again.
'Abhängen' is a separable verb. In a main clause, the prefix 'ab' stands at the end of the sentence or clause.
Ich hänge nach der Schule oft mit meinen Freunden ab.
I often hang out with my friends after school.
In the meaning of 'angewiesen sein' (to depend on / rely on), 'abhängen' is always used with the preposition 'von' and the dative. A very common structure is 'Es hängt davon ab, ob/wie/wann ...' (It depends on whether/how/when ...).
Der Erfolg des Projekts hängt von der guten Zusammenarbeit im Team ab.
The success of the project depends on good teamwork.
The meaning 'sich entspannen' (to relax) is colloquial and is used especially by younger people in informal situations. It often appears with the preposition 'mit' (with).
Was machst du so? Ich hänge nur ein bisschen auf dem Sofa ab.
What are you up to? I’m just hanging out on the sofa a bit.
When 'abhängen' means 'hinter sich lassen' (to leave behind), the verb needs an accusative object. You always leave behind 'jemanden' (someone) or 'etwas' (something).
Der Radfahrer konnte die Verfolger am letzten Berg abhängen.
The cyclist was able to leave the pursuers behind on the final mountain.
This meaning is the literal, physical action. It is used for things that you remove from a hook, a line, or a wall.
Kannst du mir helfen, die Gardinen abzuhängen?
Can you help me take down the curtains?
to lie / be located
An etwas liegen identifies the actual cause of an outcome. Von etwas abhängen, by contrast, describes a factor or condition that determines or influences the outcome. For an established cause, liegen is appropriate; when the outcome can still change, abhängen is appropriate.

Ob die Feier stattfindet, hängt vom Wetter ab.
Whether the celebration takes place depends on the weather.
Dass die Feier ausfällt, liegt am starken Regen.
The celebration is being canceled because of the heavy rain.