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(y-(4)/(5))^(2)+(x+(7)/(10))^(2)=30 A circle in the xy-plane has the equation. What is the radius of the circle? Round the answer to the nearest tenth.

(y−45)2+(x+710)2=30 \left(y-\frac{4}{5}\right)^{2}+\left(x+\frac{7}{10}\right)^{2}=30 \newlineA circle in the xy x y -plane has the equation. What is the radius of the circle? Round the answer to the nearest tenth.

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Find properties of circles from equations in general formright chevron icon

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Q. (y−45)2+(x+710)2=30 \left(y-\frac{4}{5}\right)^{2}+\left(x+\frac{7}{10}\right)^{2}=30 \newlineA circle in the xy x y -plane has the equation. What is the radius of the circle? Round the answer to the nearest tenth.
  1. Identify Center and Radius: The given equation is in the form of a circle's standard equation: x−h)²+(y−k)²=r2 where$h,kx - h)² + (y - k)² = r^2\, where \$h, k is the center of the circle and rr is the radius. Identify the center and the radius squared from the given equation.
  2. Compare with Standard Form: The given equation is (y−45)2+(x+710)2=30(y - \frac{4}{5})^2 + (x + \frac{7}{10})^2 = 30. Comparing this with the standard form, we can see that the radius squared, r2r^2, is equal to 3030.
  3. Calculate Square Root: To find the radius rr, we need to take the square root of the radius squared. Calculate the square root of 3030.
  4. Find Approximate Radius: The square root of 3030 is approximately 5.4775.477. Round this to the nearest tenth to find the radius of the circle.
  5. Final Radius Calculation: Rounding 5.4775.477 to the nearest tenth gives us 5.55.5. Therefore, the radius of the circle is approximately 5.55.5 units.

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