Ihave three distinct mystery novels, three distinct fantasy novels, and three distinct biographies. i'm going on vacation, and i want to take two books of different genres. how many possible pairs can i choose?

You can pick your books in 27 possible ways

Step-by-step explanation:

First, lets choose the 2 genders you want. From the 3 genders available, you pick 2. There are 3 ways to do this (you are picking 1 book not to be taken, thus you have 3 possibilities).

After you pick the 2 genders, you have to choose one book from 3 books on each one, so you have 3 possibilities on each gender, giving a total of 3*3 = 9.

Therefore, you can pick your books in 3*9 = 27 possible ways.

i dont know

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)