Find the variation constant and an equation of variation for the given situation. y varies directly as x, and y = 7 when x = 1/2.

Step-by-step explanation:

Directly Proportion

It's said that y varies directly proportional as x, if:

Where k is a constant of proportionality.

We know that y=7 when x=1/2.

Using the above condition, we can find the value of k:

Solving for k:

k=14

Thus, the equation is:

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:

i think the amount would be $140.62