Birthday Party

Answer 1 To prove the sum of the interior angles of a triangle equals 180 degrees using parallel lines and transversals, extend one side of the triangle and draw a line parallel to the opposite side through the third vertex. The alternate interior...

Answer 1 To solve a quadratic equation using the quadratic formula, follow these steps: For a quadratic equation in the form ax^2 + bx + c = 0, the quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). Substitute the values of a, b, and c into the...

Answer 1 To find the vertex of a parabola in standard form y = ax^2 + bx + c, use the vertex formula: x = -b/(2a). Substitute this x-value back into the equation to find the y-coordinate. The vertex is at (x, y).[yarpp...

Answer 1 To find the derivative of a composite function using the chain rule, identify the outer function f(u) and the inner function u=g(x). The chain rule states that the derivative of f(g(x)) is f'(g(x)) * g'(x). Differentiate the outer function...

Answer 1 To prove that the sum of the interior angles of a regular polygon is (n-2)×180°, consider dividing the polygon into (n-2) triangles. Each triangle has an angle sum of 180°. Thus, the total interior angle sum is (n-2)×180°.[yarpp...