(picture included) find the area of the circle
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Inequalities help us to compare two unequal expressions. There exists no solution to the given set of inequalities.
<h3>What are inequalities?</h3>Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given Inequalities can be solved as,
5 - x > 7
-x > 7 - 5
-x > 2
x < -2
2x + 3 ≥ 13
2x ≥ 10
x ≥ 5
As per the solution of the two inequalities, the value of x should be less than -2 but at the same time, it should be more than or equal to 5, which is impossible. Thus, there is no solution for the given inequalities.
This can be confirmed by graphing the two inequalities, as shown below. Since there is no area in common between the two inequalities, there exists no solution to the given set of inequalities.
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The center is (-1, -2) and the radius of the circle is 5.
<h3>What is the equation of a circle?</h3>The circle equation formula refers to the equation of a circle which represents the center-radius form of the circle.
A circle can be represented as;
Where; h and k are the center of the circle r is the radius of the circle.
The given equation of the circle is;
Comparing both the equations;
Hence, the center is (-1, -2) and the radius of the circle is 5.
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