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Mandarinka [93]
3 years ago
11

Which system of linear inequalities has the point (2, 1) in its solution set?

Mathematics
2 answers:
neonofarm [45]3 years ago
7 0

Answer:

y\leq-x+3

y\leq \frac{1}{2}x+3

Step-by-step explanation:

we know that

If a point is a solution of a system of linear inequalities, then the point must satisfy both inequalities of the system

<u><em>Verify each system of inequalities</em></u>

case 1) we have

y ----> inequality A

y\leq \frac{1}{2}x+3 -----> inequality B

Verify if the ordered pair (2,1) is a solution of the system

<em>Inequality A</em>

1

1 ----> is not true

so

The ordered pair not satisfy the inequality A

therefore

The ordered pair is not a solution of the system of inequalities

case 2) we have

y\leq-\frac{1}{2}x+3 ----> inequality A

y< \frac{1}{2}x -----> inequality B

Verify if the ordered pair (2,1) is a solution of the system

<em>Inequality A</em>

1\leq-\frac{1}{2}(2)+3

1\leq2 ----> is true

so

The ordered pair satisfy the inequality A

<em>Inequality B</em>

1< \frac{1}{2}(2)

1< 1 -----> is not true

so

The ordered pair not satisfy the inequality B

therefore

The ordered pair is not a solution of the system of inequalities

case 3) we have

y\leq-x+3 ----> inequality A      

y\leq \frac{1}{2}x+3 -----> inequality B

Verify if the ordered pair (2,1) is a solution of the system

<em>Inequality A</em>

1\leq-(2)+3

1\leq 1 ----> is true

so

The ordered pair satisfy the inequality A

<em>Inequality B</em>

1\leq \frac{1}{2}(2)+3

1\leq 4 ----> is true

so

The ordered pair satisfy the inequality B

therefore

The ordered pair satisfy the system of inequalities

case 4) we have

y< \frac{1}{2}x ----> inequality A      

y\leq -\frac{1}{2}x+2 -----> inequality B

Verify if the ordered pair (2,1) is a solution of the system

<em>Inequality A</em>

1< \frac{1}{2}(2)

1< 1 ----> is not true

so

The ordered pair satisfy the inequality A

therefore

The ordered pair not satisfy the system of inequalities

asambeis [7]3 years ago
7 0

Answer:

Your answer is Graph 3

Step-by-step explanation:

Look at the picture I included.

It is this graph because:

- Graph D is incorrect because you cannot have a point on a dashed line

- Even though for Graph D the point (2, 1) has a solid and dashed line running through it, you cannot plot a point on a dashed line, regardless if there is another solid line running through it.

- For options A and B, (2, 1) lands on a dashed line

- Your answer is option C

- This is right on edg2020 and quizlet!

I hope this helps!

- sincerelynini

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Answer:

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Step-by-step explanation:

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3 years ago
Please help me again
gulaghasi [49]

Answer:

65 degrees

Step-by-step explanation:

<u>Step 1:  Find what the measure of JLK is</u>

JLM + JLK = 180

140 + JLK - 140 = 180 - 140

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<u>Step 2:  Find what the measure of KJL is</u>

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5 0
3 years ago
The graph of a quadratic function is shown. Check all of the following statements that are true of the function.
Fed [463]

Answer:

a < 0

The vertex is (1,2)

Step-by-step explanation:

Looking at the graph

we have a vertical parabola open downward

The leading coefficient is negative

The vertex is a maximum

The vertex is the point (1,2)

The axis of symmetry is equal to the x-coordinate of the vertex, so the axis of symmetry is x=1

The y-intercept is the point (0,1)

The function has two real solutions (zeros of the function) one positive and one negative

The positive zero of the function is greater than 2

The negative zero of the function is greater than -1

<u><em>Verify each statement</em></u>

case 1) a < 0

The statement is true

Because the parabola open downward

case 2) The vertex is (1,2)

The statement is true

The vertex in this problem is the maximum of the function

case 3) The axis of symmetry is y =2

The statement is false

Because the axis of symmetry is x=1

case 4) x = 2 is a zero of the function

The statement is false

Because the positive zero of the function is greater than 2

case 5) (1,2) is a minimum

The statement is false

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