Graph the line and the circle (x-1)²+(y-2)²=2² and y=2x+2.

The graph of the line and the circle is in the attachment.

Step-by-step explanation:

In order to graph the circle, you have to use the circle equation formula to obtain the center and the radius.

(x-xo)² + (y-yo)² = r²

where the point (xo,yo) is the center and r is the radius.

Using the given formula, the center is:

xo=1, yo=2

(1,2)

And the radius is:

r=2

Now you have to graph the point (1,2) and draw a circle centered at that point, with a distance of 2 from the center.

To obtain the exact values of the intersection of the circle with the x-axis you have to replace y=0 in the equation and solve it for x. For the points of intersection with the y-axis you have to replace x=0 in the equation and solve it for y.

-For x=0, solving for y:

(0-1)²+(y-2)²=2²

1+(y-2)²=4

(y-2)²= 3

Applying the squareroot both sides

y-2 = ± √3

y1= -√3 +2

y2= √3 +2

P1(0, -√3 +2) and P2(0, √3 +2)

-For y=0

(x-1)²+(0-2)²=2²

(x-1)² + 4 = 4

(x-1)² = 0

Applying the squareroot both sides:

x-1 = √0

x-1=0

x=1

P3 (1,0)

In order to graph the linear equation, you have to obtain the intersection with the x-axis replacing y=0 in the equation and the intersection with the y-axis replacing x=0 in the equation. That way, you obtain two point of the line and then you have to trace the line containing those points.

-For x=0

y=2(0)+2 =2

P1 (0,2)

-For y=0

0= 2x+2

Adding -2 both sides

2x= -2

Dividing by 2 both sides

x= -1

P2(-1,0)

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

answer: your correct answer is b. d.

step-by-step explanation: