Prove The Following
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Below.

Step-by-step explanation:

m < PCA = m  < CAD ( alternate angles)

m < BAD = m <CAD ( given)

Also m < CAB = m < PCA + m < CPA  ( exterior angle of a triangle theorem).

Also m < CAB = m< CAD + m < BAD (given)

So  m < PCA + m < CPA =  m < CAD + m < BAD

But m < PCA = m  < CAD

so  m < CAD + m < CPA = m < CAD + m BAD

So m < CPA = m < BAD

But m < PCA = m < CAD = m BAD

therefore m < CPA = m < PCA

That makes triangle CAP isosceles

Therefore AP = AC.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: