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3 years ago

Which system of linear inequalities is represented by the graph x+5y>5 y<2x+4

Mathematics

2 answers:

grandymaker [24]3 years ago

7 0

Answer:

The lines represent the inequalities .

Further explanation:

The linear equation with slope m and intercept c is given as follows.

The formula for slope of line with points and can be expressed as,

Given:

The inequalities are as follows.

a. x – 5y < –5 and y < –2x – 4

b. x + 5y > 5 and y < 2x + 4

c. x – 5y < –5 and y < –2x + 4

d. x + 5y > 5 and y < 2x – 4

Step-by-step explanation:

The blue line intersects y-axis at , therefore the y-intercept is 4.

The blue line intersect the points that are and .

The slope of the line can be obtained as follows.

The slope of the line is m = 2.

Now check whether the inequality included origin or not.

Substitute in equation y=x+1.

0 is not greater than 1 which means that the inequality doesn’t include origin.

Therefore, the blue line is y < 2x + 4.

The orange line intersects y-axis at , therefore the y-intercept is 1.

The orange line intersect the points that are and .

The slope of the line can be obtained as follows.

The slope of the line is m = .

Now check whether the inequality included origin or not.

Substitute in equation y > .

0 is not greater than 1 which means that the inequality doesn’t include origin.

Therefore, the orange line is y > .

Solve the equation y > .

The equation of orange line is 5y + x > 5.

Option (a) is not correct as it satisfy the inequalities of the graph.

Option (b) is correct as it satisfy the inequalities of the graph.

Option (c) is not correct as it satisfy the inequalities of the graph.

Option (d) is is not correct as it satisfy the inequalities of the graph.

Hence, is correct.

Black_prince [1.1K]3 years ago

6 0

Answer:

Step-by-step explanation:

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Step-by-step explanation:

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Generally the margin of error is mathematically represented as

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Generally 90% confidence interval is mathematically represented as

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Considering question b

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The margin of error is E = 0.03

From the question we are told the confidence level is 99% , hence the level of significance is

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Generally from the normal distribution table the critical value of is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the sample size is mathematically represented as

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=> $n = [\frac{2.58}{0.03} ]^2 * 0.59 (1 - 0.59 )$

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