Yana is using an indirect method to prove that segment de is not parallel to segment bc in the triangle abc shown below:
a triangle abc is shown. d is a point on side ab and e is a point on side ac. points d and e are joined using a straight line. the length of ad is equal to 4, the length of db is equal to 5, the length of ae is equal to 6 and the length of ec is equal to 7.
she starts with the assumption that segment de is parallel to segment bc.
which inequality will she use to contradict the assumption?
4: 9 ≠ 6: 13
4: 9 ≠ 6: 7
4: 13 ≠ 6: 9
4: 5 ≠ 6: 13

  4:9 ≠ 6:13

Step-by-step explanation:

The ratios of corresponding segments will be equal if DE || BC. Yana can compare AD:AB versus AE:AC. She will find they're not equal, as expressed by ...

  4 : 9 ≠ 6 : 13

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: