Points A, B, and C are collinear, and B lies between A and C. If AC = 48, AB = 2x + 2,
and BC = 3x + 6, what is BC? Show all work in a clear and organized manner.

BC = 30

Step-by-step explanation:

If the three points are collinear, it means they lie on the same straight line.

Now B lies between A and C

By mathematical convention;

AC = AB + BC

This means;

48 = 2x + 2 + 3x + 6

48 = 5x + 8

48-8 = 5x

5x = 40

x = 40/5

x = 8

From the question BC = 3x + 6

Substitute the value of x; 3(8) + 6 = 24 + 6 = 30

the answer is a i belaeve atleast thats what my calculator just gfave me

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)