Find the
f(k-8) = 1/2(k-8)-4​

f = (k - 16) / (2k - 16)

k = (16f - 16) / (2f - 1)

Step-by-step explanation:

f(k-8) = 1/2(k-8)-4​

Solve for f:

Divide both sides by (k-8)

f = (k - 16) / (2k - 16)

Solve for k:

Subtract 1/2 * k from both sides.

fk - 8f - (1/2)k = -8

Add 8f to both sides.

fk - 1/2*k = k * (2f - 1)/2 = 8f -8

Divide both sides by (2f - 1)/2

k = (16f - 16) / (2f - 1)

See below.

Step-by-step explanation:

Triangle ABC is congruent to triangle DEF (Given)

Angle ACB is congruent to angle ECG. (Vertical angles theorem)

Angle CEG is congruent to angle DEF. (Vertical angles theorem)

Angle DEF is congruent to angle ABC. (Definition of congruent triangles)

Angle CEG is congruent to angle ABC. (Substitution property of equality).

Triangle ABC is similar to triangle GEC. (Angle angle similarity postulate- if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.)