The equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².
Based on the calculations, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5²
The equation of a circle.
Mathematically, the standard form of the equation of a circle is given by;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center.
r is the radius of a circle.
The midpoint of the given points represents the center of this circle:
h = (4 + 4)/2 = 4
k = (5.5 + 10.5)/2 = 8
Next, we would determine the radius by using the distance formula for coordinates:
r = √[(x₂ - x₁)² + (y₂ - y₁)²]
r = √[(4 - 4)² + (10.5 - 5.5)²]
r = √[0² + 5²]
r = √25
r = 5 units.
Therefore, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².
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<h3>
Answer: 16 square units</h3>
Let x be the height of the parallelogram. Right now it's unknown, but we can solve for it using the pythagorean theorem. Focus on the right triangle. It has legs a = 3 and b = x, with hypotenuse c = 5
a^2 + b^2 = c^2
3^2 + x^2 = 5^2
9 + x^2 = 25
x^2 = 25-9
x^2 = 16
x = sqrt(16)
x = 4
This is a 3-4-5 right triangle.
The height of the parallelogram is 4 units.
We have enough info to find the area of the parallelogram
Area of parallelogram = base*height
Area of parallelogram = 4*4
Area of parallelogram = 16 square units
Coincidentally, the base and height are the same, which isn't always going to be the case. The base is visually shown as the '4' in the diagram. The height is the dashed line, which also happens to be 4 units long.
The sales tax is .075 so she would pay 23.65 for the earbuds
Answer:
760
Step-by-step explanation:
