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Which of the following is the area of the region that includes all the points that satisfy the inequalities:
x + y - 3 ≤ 0, x ≥ 0, y ≥ 0?
x + y - 3 ≤ 0, x ≥ 0, y ≥ 0?
- a)1.5
- b)2.5
- c)3
- d)4.5
- e)5
Correct answer is option 'D'. Can you explain this answer?
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Which of the following is the area of the region that includes all the...
To find the area of the region that satisfies the given inequalities, we first need to graph the inequalities on a coordinate plane.
The first inequality, x + y - 3 ≤ 0, can be rearranged to y ≤ -x + 3. This represents a line with a y-intercept of 3 and a slope of -1.
The second inequality, x ≥ 0, represents the positive x-axis.
The third inequality, y ≥ 0, represents the positive y-axis.
To determine the area of the region that satisfies all the inequalities, we need to identify the enclosed region on the graph.
Since x ≥ 0 and y ≥ 0, we know that the region is bounded by the positive x-axis and the positive y-axis.
The line y ≤ -x + 3 intersects the x-axis at (3, 0) and the y-axis at (0, 3).
To find the area of the region, we can calculate the area of the triangle formed by the points (0, 0), (3, 0), and (0, 3).
The base of the triangle is the line segment from (0, 0) to (3, 0), which has a length of 3.
The height of the triangle is the line segment from (0, 0) to (0, 3), which has a length of 3.
Therefore, the area of the triangle is (base * height) / 2 = (3 * 3) / 2 = 9 / 2 = 4.5.
Therefore, the correct answer is D. 4.5.
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Which of the following is the area of the region that includes all the points that satisfy the inequalities:x + y - 3≤ 0, x ≥ 0, y≥ 0?a)1.5b)2.5c)3d)4.5e)5Correct answer is option 'D'. Can you explain this answer?
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