(05.03 lc) determine the solution to f(x) = g(x) using the following system of equations: (5 points) f(x) = 5.5x − 13 g(x) = −5x + 18.5 x = 1 x = 2 x = 3 x = 4

If g(x) is equal to f(x), then they are the same value.

Put 5.5x - 13 in place of g(x) in the second equation.

5.5x - 13 = -5x + 18.5

Add 13 to both sides.

5.5x = -5x + 31.5

Add 5x to both sides.

10.5x = 31.5

Divide 10.5 on both sides.

x = 3

Hope this helps! :)

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< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

ac ≅ ab (given)< cax ≅ < bax   (given)ax ≅ ax (common side)

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

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

in δacy and δaby,

ac ≅ ab (given)< cay ≅ < bay (since < cax ≅ < bax is given and xy is the extension of line ax)ay ≅ ay (common side)

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)