An advanced civilization lives on a planet orbiting a close binary star system that consists of a 15msun red giant and a 10msun black hole. assume that the two stars are quite close together, so that an accretion disk surrounds the black hole. the planet on which the civilization lives orbits the binary star at a distance of 10 au.
sometime within the next million years or so, their planet is likely to be doomed because

Because the red giant is likely to blow into a supernova within the next million years.

Explanation:

A red giant is one of the final phases of a dying star. Usually, in small stars such as our sun, the cycle would end with the star as a white dwarf.  The star will start to blow out the outer layers of the star in enormous clouds of gas and stellar dust that are known as a planetary Nebulae, as the core continues to collapse itself, it will end its life as a white dwarf.

But in this case, we have a massive star, since it has a larger mass, this will start to fall inwards until the gas and dust will be blown off in a strong explosion called a supernova. The fact that the black hole is so close to the star will only speed up the process, as will destabilize the core faster, and soon, this advanced civilization will have serious habitability issues with their planet.

(4,-2)

explanation:

6x+4y=16

-6x-9y=-6

-5y=10

y=-2

x=4