MATH SOLVE

4 months ago

Q:
# help please!posted picture of question

Accepted Solution

A:

The region is in the first quadrant, and the axis are continuous lines, then x>=0 and y>=0

The region from x=0 to x=1 is below a dashed line that goes through the points:

P1=(0,2)=(x1,y1)βx1=0, y1=2

P2=(1,3)=(x2,y2)βx2=1, y2=3

We can find the equation of this line using the point-slope equation:

y-y1=m(x-x1)

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

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

m=1/1

m=1

y-2=1(x-0)

y-2=1(x)

y-2=x

y-2+2=x+2

y=x+2

The region is below this line, and the line is dashed, then the region from x=0 to x=1 is:

y<x+2 (Options A or B)

The region from x=2 to x=4 is below the line that goes through the points:

P2=(1,3)=(x2,y2)βx2=1, y2=3

P3=(4,0)=(x3,y3)βx3=4, y3=0

We can find the equation of this line using the point-slope equation:

y-y3=m(x-x3)

m=(y3-y2)/(x3-x2)

m=(0-3)/(4-1)

m=(-3)/3

m=-1

y-0=-1(x-4)

y=-x+4

The region is below this line, and the line is continuos, then the region from x=1 to x=4 is:

y<=-x+2 (Option B)

Answer: The system of inequalities would produce the region indicated on the graph is Option B

The region from x=0 to x=1 is below a dashed line that goes through the points:

P1=(0,2)=(x1,y1)βx1=0, y1=2

P2=(1,3)=(x2,y2)βx2=1, y2=3

We can find the equation of this line using the point-slope equation:

y-y1=m(x-x1)

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

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

m=1/1

m=1

y-2=1(x-0)

y-2=1(x)

y-2=x

y-2+2=x+2

y=x+2

The region is below this line, and the line is dashed, then the region from x=0 to x=1 is:

y<x+2 (Options A or B)

The region from x=2 to x=4 is below the line that goes through the points:

P2=(1,3)=(x2,y2)βx2=1, y2=3

P3=(4,0)=(x3,y3)βx3=4, y3=0

We can find the equation of this line using the point-slope equation:

y-y3=m(x-x3)

m=(y3-y2)/(x3-x2)

m=(0-3)/(4-1)

m=(-3)/3

m=-1

y-0=-1(x-4)

y=-x+4

The region is below this line, and the line is continuos, then the region from x=1 to x=4 is:

y<=-x+2 (Option B)

Answer: The system of inequalities would produce the region indicated on the graph is Option B