Astudent writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle abc below is equal to the measure of the exterior angle. a triangle abc is shown. the base of the triangle extends into a straight line. the angle formed between this straight line and the edge of the triangle is marked as p. the angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n. step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle) step 2: m∠p − m∠o = 90 degrees (alternate interior angles) step 3: therefore, m∠m + m∠n + m∠o = m∠o + m∠p step 4: so, m∠m + m∠n = m∠p in which step did the student first make a mistake and how can it be corrected?

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:

this excerpt is taken from the book “we shall not be moved : the women’s factory strike of 1909 “ and is written by joan dash. it is the story of the great strike when almost 30thousand women working in factories in america formed a union to fight unsafe working conditions, long working hours and miserable wages.

question: which best states the author’s purpose for including this information in the text?

answer: to challenge the reader’s ideas about a historical event