Expert Answer to "To graph: The solution set to (x+37)2+y2=9."

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

sputavanomr

Answered question

2021-11-26

To graph: The solution set to

{(x + 37)}^{2} + y^{2} = 9

Answer & Explanation

Todd Williams

Beginner2021-11-27Added 18 answers

Graph:
Consider the provided inequality,

{(x - 3)}^{2} + y^{2} \geq 9

Consider the inequality as an equality first:

{(x + 3)}^{2} + y^{2} = 9

‘The equation represents a circle centered at (-3, 0) with radius 3.
Construct the graph using the points obtained.
‘The curves divide the graph into two regions.
Test a point from each region into the inequality to obtain the solution set:
From region inside the circle:
Test the point (-2, 0).

{(- 2 + 3)}^{2} + 0^{2} \geq 9 (1 \geq 9)

The result is false.
From region outside the circle:
Test the point (1,0)

{(1 + 3)}^{2} + 0^{2} \geq 9 (16 \geq 9)

‘The result is true.
‘Now, shade the solution region where the inequality holds true as:
Interpretation:
The inequality is

{(x + 3)}^{2} + y^{2} \geq 9

greeter then equal to, the inequality does not contain inner circle region. It implies the solution set consistoutside of the circle.

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