Question

1. Is C

2. In the graph of the inequality x-2y >= 4, which is a value for x on the boundary line and the x-axis?

A. 4
B. -2
C. 2
D. -4

3. If x>=0 and y>=0, then which quadrant holds the solution?

A. IV
B. III
C. I
D. II

4. Which ordered pair is a solution of the inequality?
y>=4x-5

A. (3, 4)
B. (2, 1)
C. (3, 0)
D. (1, 1)

5. Graph the inequality.
y>-5x+3

Answer 1

1) C. (1,0)
2) A. 4
3) C. I
4) D. (1,1)
5) D

Answer 2

Part 2) the answer is the option A)
`x=4`

Part 3) the answer is the option C) I quadrant

Part 4) the answer is the option D
`(1,1)`

Part 5) the graph in the attached figure

Explanation:

Part 2) we have

`x-2y\geq 4`

Find the x-intercept

the equation of the line is

`x-2y= 4`

The x-intercept is the value of x when the value of y is equal to zero

For
`y=0`

substitute in the equation of the line

`x-2(0)= 4`

`x=4`

Part 3) If x>=0 and y>=0, then which quadrant holds the solution?

we know that

`x\geq0` ------> the solution is in the I and IV quadrant

`y\geq0` ------> 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?

`y\geq 4x-5`

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
`(1,1)` in the inequality

`1\geq 4(1)-5`

`1\geq -1` ------> is true

therefore

the point
`(1,1)` is a solution of the inequality

Part 5) we have

`y> -5x+3`

we know that

The solution is the shaded area above the dashed line

The equation of the line is
`y=-5x+3`

The slope of the line is negative

The y-intercept is the point
`(0,3)`

The x-intercept is the point
`(0.6,0)`

using a graphing tool

see the attached figure