2. Two lines are represented by equations: 2x + 4y = 21 and y = kx - 12. What value of k will make lines parallel?

-1/2

Step-by-step explanation:

- arrange the equation in the y=mx+b form

2x + 4y =21, subtract 2x from both sides of the equation

4y= -2x +21 , divide both sides by 4

y= -1/2x +21/4

-compare the slopes m of the 2 equations

y= kx -12, has the slope k

y= -1/2x +21/4, has the slope -1/2

- If the lines are parallel then they have the same slope

Therefore, k= -1/2

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: