AB has endpoints A(2,9) and B(5,8). A dilation, centered at the origin, is applied to AB. The image has endpoints A' (4/3,6) and B'(10/3,16/3).

scale factor =

Step-by-step explanation:

To determine the scale factor calculate the ratio of image coordinates to corresponding original coordinates, that is

Given A(2, 9 ) → A'(, 6 )

scale factor = = ← using y- coordinates

scale factor = = ← using the x- coordinates

The same scale factor is applied to B(5, 8 ) → B'( , )

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: