Awholesaler requires a minimum of 4 items in each order from its retail customers. the manager of one retail store is considering ordering a certain number of sofas, x, and a certain number of pillows that come in pairs, y. which graph represents the possible combinations of sofa and pillow orders the manager can have?

It is the last graph: solid line, shaded area over the line x = 2 - x/2

Explanation:

1) Set the algebraigic expression that represents the combinations of sofa and pillow orders:

Number of sofas: x (given)Number of pillows: 2y (given, since they come in pairs)Number of items = number of sofas + number of pillows = x + 2yMinimum of 4 items in each order (given) ⇒ x + 2y ≥ 4

2) Predict the graph of the inequality x + 2y ≥ 4

The border line is the equation x + 2y = 4You can choose two points to draw a lineChoose the axis-intercepst:

        x = 0 ⇒ 2y = 4 ⇒ y =4/2 ⇒ y = 2 ⇒ point (0,2)

        y = 0 ⇒ x = 4 ⇒ point (4,0)

        Then the lines goes through (0,2) and (4,0) ... [the four graphs meet this]

The shading area is above the line because when you solve for y you get y ≥   2 - x/2, and the line is included because the "equal to" part of the symbol (≥ means greater than or equal to).  To state that the line is included the graph uses a continous line instead of a dotted one.

3) Conclusion:

That means that the correct graph is the last one: solid line, shaded area over the line y = 2 - x/2.

Note: a more detailed graph would include the fact that the items cannot be negative, i.e. x ≥ 0 and y ≥ 0, which would result in that the shaded area would be on the first quadrant.

   

11/36 is .305 repeating