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Harrizon [31]
3 years ago
12

If a system of two inequalities has a solution, then their two half planes intersect , true or false ?

Mathematics
1 answer:
Nana76 [90]3 years ago
7 0

Answer: The answer is true.


Step-by-step explanation:  The given statement is

'If a system of two inequalities has a solution, then their two half planes intersect'.

We are to check whether the statement is true or false.

Let a system of two inequalities be

x+y\geq 3,\\\\2x+5y\leq 10.

These inequalities has a solution, for example, x = 2, y = 1.

Plotting these inequalities on a graph paper (please see the attached graph), we see that the two half planes intersect, which is represented by the double shaded region in the graph.

Thus, the given statement is TRUE.

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Step-by-step explanation:

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<h3><u>Explanation</u></h3>
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The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with σ = 30 hours. A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038 hours.

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