Solve the absolute value equation last and check for extraneous solution |2x-8|=-4x-2

Last one and the bottom answer choice is y=(x-4)^2+1 you guys!

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)

Answer this two poles, ab and ed, are fixed to the ground with the of ropes ac and ec, as shown: two right triangles abc and edc have a common vertex c. angle abc and edc are right angles. ab is labeled 13 feet, ac is labeled 15 feet, ec is labeled 10 feet, and ed is labeled 4 feet.what is the approximate distance, in feet, between the two poles? 11.14 feet16.65 feet14.35 feet15.59 feet