Answer:
2
Step-by-step explanation:
The discriminant is the quantity under the radical in the quadratic formula ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[tex]
When that quantity is positive, the square root is real, and the formula gives two real values for x.
The standard equation of a circle is
(x-h)^2 + (y-k)^2 = r^2
where the center is at point (h,k)
From the statement of the problem, it is already established that h = 2 and k = -5. What we have to determine is the value of r. This could be calculated by calculating the distance between the center and point (-2,10). The formula would be
r = square root [(x1-x2)^2 + (y1-y2)^2)]
r = square root [(2--2)^2 + (-5-10)^2)]
r = square root (241)
r^2 = 241
Thus, the equation of the circle is
w = width
w + 50 = length {length is 50 longer than the width}
Perimeter of a rectangle = 2(width) + 2(length)
2w + 2(w + 50) = 220 {substituted width and length into perimeter formula}
2w + 2w + 100 = 220 {used distributive property}
4w + 100 = 220 {combined like terms}
4w = 120 {subtracted 100 from each side}
w = 30 {divided each side by 4}
w + 50 = 80 {substituted 30, in for w, into w + 50}
width = 30 cm
length = 80 cm
The center of a triangle must always be found inside the triangle given that it is concurrent point of the three median lines of the triangle all three of which are located only inside of the triangle
The examples of the properties of the center of a triangle are;
- The center of the triangle is the centroid of the triangle which is the point of concurrency of the three medians of the triangle, where a median line is the line which connects a vertex to the midpoint of the side opposite the vertex inside the triangle
- Each median line divides the area of the triangle in half, and given that the area of the triangle is equal to half the altitude, multiplied by the length of the base side of the triangle, the three medians of a triangle are related and share a common concurrent point <em>inside</em> the triangle such the perpendicular distance from the concurrent point of the three medians to each of the three side is less than the altitude of the triangle
Given that the three medians are located inside the triangle therefore, based on the location of the center of the triangle on the medians of the triangle, the center of the triangle must always be found inside the triangle
Learn more about the centroid of a triangle here;
brainly.com/question/16482898
boi
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Step-by-step explanation: