Which system of linear inequalities is represented by the graph?

y > x + 3 and y < x + 2
y > x + 3 and y < x + 2
y > x + 3 and y > x + 2
y > x + 3 and y > x + 2

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

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.