Asap will mark factor x2 − 7x + 8. (x + 8)(x − 1) prime (x − 8)(x − 1) (x + 8)(x + 1)

Prime.

Step-by-step explanation:

First let's multiply our outer coefficients in this case 1 and 8, so we have 1x8=8.  Now the point of this is to get the factors of 8 and see if we can get that middle term -7.  Factors of 8 are 1x8, 2x4 and that's it.  From there I notice that -8+1 = -7 and so:

Notice that the (x-8) and (x+8) are not the same factors, therefore the factors are not any of those answer choices and so it's prime.  You can calculate the factors by using the quadratic formula, however I think that is beyond the scope of this question.

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

< 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)