Given what we know, we can confirm that amongst the wave types mentioned both X-rays and radio waves are able to transmit energy through a vacuum.
This is due to the fact that unlike sound, water, and seismic waves that transmit energy through air, water, or the earth, the waves mentioned above, those being radio and x-rays, do not need a medium through which to propagate. This allows them to exist and transmit energy even in a vacuum such as outer space, which is corroborated by their existence in space.
Therefore, we can confirm that amongst the wave types mentioned both X-rays and radio waves are able to transmit energy through a vacuum.
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