Math Problem Statement
Solution
Looking at the graph provided, we can observe that the shaded region is bounded by two lines and specific constraints:
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Line 1 (y ≥ x + 1): This line has a slope of 1 and y-intercept at (0, 1), which forms the boundary of the shaded region on the left side. The shading is above this line, so the inequality would be .
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Line 2 (y ≤ 10): This is the horizontal line at that forms the top boundary of the shaded region. The region is below this line, so the inequality would be .
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Constraint on x (x ≥ 0): The graph shows that the region is limited to the right of the y-axis, meaning .
Therefore, the correct system of inequalities is:
This matches Option C.
Final Answer: C.
Let me know if you want more details or if you have any questions!
Here are 5 related questions to expand on this:
- How do you determine if a region is above or below a line in inequalities?
- What does the inequality represent in a graph?
- How do boundary lines affect shading in inequalities?
- Can a region be bounded by curves instead of straight lines? How would that change the inequalities?
- How do you interpret a system of inequalities geometrically?
Tip: When graphing inequalities, use test points (like ) to check which side of the boundary should be shaded!
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Math Problem Analysis
Mathematical Concepts
Linear Inequalities
Graphing Systems of Inequalities
Formulas
y ≥ x + 1
y ≤ 10
x ≥ 0
Theorems
Inequalities in Two Variables
Suitable Grade Level
Grades 7-10