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3 years ago

What is the value of x

Mathematics

1 answer:

kati45 [8]3 years ago

6 0

Answer:8

Step-by-step explanation:

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Which system of linear inequalities is represented by the graph?

azamat

Answer:

The system of linear inequalities represented by the graph is:

y > (2/3) x + 3 and y <= - (1/3) x + 2

Step-by-step explanation:

In the graph we can see the region on and below the red line, and above the black dashed line.

1) The red line goes through the points:

P1=(0,2)=(x1,y1)→x1=0, y1=2

P2=(3,1)=(x2,y2)→x2=3, y2=1

The slope of this line is:

s=(y2-y1)/(x2-x1)

Replacing the known values:

s=(1-2)/(3-0)

s=(-1)/(3)

s=-(1/3)

The equation of the red line is:

y-y1=s(x-x1)

y-2=-(1/3)(x-0)

y-2=-(1/3)x

y-2+2=-(1/3)x+2

y=-(1/3)x+2

The area on and below the red line is: y<=-(1/3)x+2

2) The black dashed line goes through the points:

P1=(-3,1)=(x1,y1)→x1=-3, y1=1

P2=(0,3)=(x2,y2)→x2=0, y2=3

The slope of this line is:

s=(y2-y1)/(x2-x1)

Replacing the known values:

s=(3-1)/(0-(-3))

s=(2)/(0+3)

s=(2)/(3)

s=(2/3)

The equation of the red line is:

y-y2=s(x-x2)

y-3=(2/3)(x-0)

y-3=(2/3)x

y-3+3=(2/3)x+3

y=(2/3)x+3

The area above the black dashed line is: y>(2/3)x+3

Then, the system of linear inequalities represented by the graph is:

y>(2/3)x+3 and y<=-(1/3)x+2

6 0

3 years ago

Read 2 more answers

The graph of a linear relationship has a slope of -5 and passes through the point (2, -12). Write the equation of the line in sl

DerKrebs [107]

<h3>Answer:</h3>

y=-5x-2

<h3>Solution:</h3>

We are given the line's slope and a point that it passes through.
Using the given information, we can write the equation of the line in Point-Slope Form:
$y-y_1=m(x-x_1)$
In this formula, y₁ stands for the y-coordinate of the point, m stands for the slope of the line, and x₁ stands for the x-coordinate of the point.
In this case, y₁ is equal to -12, m is equal to -5, and x₁ is equal to 2.
Plug in the values:
y-(-12)=-5(x-2)
y+12=-5(x-2)
Now, convert into Slope-Intercept Form, y=mx+b:
y+12=-5x+10
y=-5x+10-12
y=-5x-2