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nekit [7.7K]
3 years ago
7

Identify the inequalities A, B, and C for which the given ordered pair is a solution: (0,0)​

Mathematics
1 answer:
professor190 [17]3 years ago
5 0

Answer:

Options (A) and (C)

Step-by-step explanation:

A). The given inequality is,

    x + y ≤ 2

    Solution area of the inequality is the shaded area below the line.

    Since (0, 0) lies in the shaded region, ordered pair will be a solution of this inequality.

B). For the inequality y ≤ \frac{3}{2}x-1

   Since, (0, 0) doesn't lie in the shaded region of this inequality, ordered pair will not be a solution of the inequality.

C). y > -\frac{1}{3}x-2

    In this graph (0, 0) lies in the shaded region of the inequality therefore, it will be a solution of the given inequality.

Therefore, Options (A) and (C) are the correct options.

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Can someone help me with number 8 please? Thank you.
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------------------------------------------------------------------------------

Explanation:

The domain is the set of possible x input values. Look at the left most point (-4,-1). The x coordinate here is x = -4. This is the smallest x value allowed. The largest x value allowed is x = 5 for similar reasons, but on the other side of the graph.

So that's how I got -4 \le x \le 5 (x is between -4 and 5; inclusive of both endpoints)

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Writing \left\{x|x\in\mathbb{R}, \ -4\le x\le 5\right\} is the set-builder notation way of expressing the domain. The x\in\mathbb{R} portion means "x is a real number"

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