This table shows direct variation. Find k.

k=2/3

Step-by-step explanation:

As said, this table shows direct variation. The equation is y=kx.

we can solve the equation to isolate the variable to see what the equation is to find k.

divide by x on both sides

y/x=k

that means that k is y/x

so we can divide 2/3 for example. Or 4/6 and see it simplifies to 2/3. You can do this for the other numbers to see that they are all equal to 2/3

That means that k is 2/3

Hope this helps!

< 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)