a standard DP to HDMI one way adapter should work at the DP output source.   You should not use an adapter to convert DisplayPort to HDMI anywhere in the signal chain other than right at the source. If not working, a few possibilities.  7010 DP has no signal out, the adapter is defective, or the TV is not configured to receive HDMI signal.  for the last option, test TV and same HDMI cable using another video source that has HDMI out such as your laptop.  one way to prove that adapter and HDMI cable work is test them on another PC that has DP out.  If that work, then something wrong with 7010 DP out or connection.  sometimes it could be a bad connection.  unplug and adapter/cable and plug it into the 7010 a couple of times to ensure a good connection.
Greetings I have an optiplex 7010MT the mobo model 0773vg. I am trying to use the display port to get an image to an led tv without any success. - I am also using a display port to hdmi adapter to get the signal to the tv but nosignal input is detected    - I am not using a gpu but the display port on the motherboard itself. -The hdmi  cable seems. fine I changed it tested it with a laptop and android tv box. -Maybe it needs to be an even higher quality or should I not be using a dp to hdmi adapter? This model has no hdmi out. Any help is appreciated thanks
Optiplex 7010 display port problems