Answer:
Part 2) the answer is the option A) [tex]x=4[/tex]
Part 3) the answer is the option C) I quadrant
Part 4) the answer is the option D [tex](1,1)[/tex]
Part 5) the graph in the attached figure
Step-by-step explanation:
Part 2) we have
[tex]x-2y\geq 4[/tex]
Find the x-intercept
the equation of the line is
[tex]x-2y= 4[/tex]
The x-intercept is the value of x when the value of y is equal to zero
For [tex]y=0[/tex]
substitute in the equation of the line
[tex]x-2(0)= 4[/tex]
[tex]x=4[/tex]
Part 3) If x>=0 and y>=0, then which quadrant holds the solution?
we know that
[tex]x\geq0[/tex] ------> the solution is in the I and IV quadrant
[tex]y\geq0[/tex] ------> the solution is in the I and II quadrant
The solution of the compound inequality is the common quadrant
so
The solution is in the I quadrant
Part 4) Which ordered pair is a solution of the inequality?
[tex]y\geq 4x-5[/tex]
we know that
If a ordered pair is a solution of the inequality. then the ordered pair must be satisfy the inequality
Substitute the value of x and y of the point [tex](1,1)[/tex] in the inequality
[tex]1\geq 4(1)-5[/tex]
[tex]1\geq -1[/tex] ------> is true
therefore
the point [tex](1,1)[/tex] is a solution of the inequality
Part 5) we have
[tex]y> -5x+3[/tex]
we know that
The solution is the shaded area above the dashed line
The equation of the line is [tex]y=-5x+3[/tex]
The slope of the line is negative
The y-intercept is the point [tex](0,3)[/tex]
The x-intercept is the point [tex](0.6,0)[/tex]
using a graphing tool
see the attached figure
