Question

astronomers have been able to determine the density of some exoplanets by using information from the radial velocity method. the transit and radial velocity methods. the direct imaging method. the transit and direct imaging lmethods.

Explanation:

The transit method provides information about the size of an exoplanet (radius) by measuring the dimming of a star as the planet passes in front of it. The radial - velocity method gives information about the mass of the exoplanet by detecting the wobble of the star caused by the gravitational pull of the planet. Density is mass divided by volume, and volume is related to the size (radius). So, both transit and radial - velocity methods are needed to determine density. Direct imaging method is mainly used for detecting large planets at large distances and is not the main way to determine density.

Answer:

the transit and radial velocity methods.