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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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A cylinder and a cone have the same volume. The cylinder has a radius of 2 inches and a hieght of 3 inches. The cone has a radiu

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The height of the cone is inches, if the cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.

Step-by-step explanation:

The given is,

A cylinder and a cone have the same volume

Cylinder has a radius 2 inches and height of 3 inches.

Cone has a radius of 3 inches

Step:1

For Cylinder'

Formula to calculate the volume of cylinder is,

$V = \pi r^{2} h$ ..................................................(1)

where,

r - 2 inches

h - 3 inches

From the equation (1)

= $\pi$ × $2^{2}$ × 3

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Step:2

For cone,

Formula to calculate the volume of cone is,

$V = \pi r^{2} \frac{h}{3}$ ..................................................(2)

From the statement,

cylinder and a cone have the same volume

$V_{cylinder}$ = $V_{cone}$

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Height of the cone, h = 4 inches

Result:

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