ASAP NEED HELP ∩ω∩ Michael has $15 and wants to buy a combination of school lunches to feed at least three classmates. A sandwich costs $2, and hot lunch costs $3. This system of inequalities models the scenario: 2x + 3y ≤ 15 x + y ≥ 3 Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points) Part B: Is the point (5, 1) included in the solution area for the system? Justify your answer mathematically. (3 points) Part C: Choose a point in the solution set and interpret what it means in terms of the real-world context. (3 points)

Step-by-step explanation:

A. The first inequality is graphed as a shaded area below the solid line with x-and y-intercepts of 7.5 and 5, respectively. The second inequality is graphed as a shaded area above the solid line with x- and y-intercepts of 3.

The solution set is the set of integer-valued grid points one or between the lines.

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B. The point (5, 1) is included in the solution area. Mathematically, it can be shown to satisfy the two inequalities:

  2(5) +3(1) ≤ 15   ⇒   13 ≤ 15   True

  (5) +(1) ≥ 3   ⇒   6 ≥ 3   True

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C. The point (5, 1) is in the solution set. It means Michael can purchase 5 sandwiches and 1 hot lunch within his budget constraints. That will provide 6 meals, which is more than the minimum of 3 that he wants to provide.

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:

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step-by-step explanation: