To solve the equation x² – 36 – 5x = 0, we can rearrange it into the standard form of a quadratic equation, which is: x² – 5x – 36 = 0 Now, we’ll use the quadratic formula to find the solutions for x. The quadratic formula is: x = (-b ± √(b² – 4ac)) … Read more
To convert the improper fraction 11/7 into a mixed number, we follow a simple process. Step 1: Divide the Numerator by the Denominator We start by dividing the numerator (11) by the denominator (7). 11 divided by 7 equals 1 with a remainder of 4. Step 2: Write the Whole Number Part The result from … Read more
To solve the equation 2x + 10 = 13, we need to isolate the variable x. Follow these steps: Start with the original equation: 2x + 10 = 13. Subtract 10 from both sides to eliminate the constant term on the left side: 2x + 10 – 10 = 13 – 10 Which simplifies to: … Read more
To find the factors of the quadratic expression x² + 4x + 5, we can use the method of factoring or the quadratic formula. A standard quadratic expression can be factored into the form: (x + a)(x + b), where ab = c (the constant term) and a + b = b (the coefficient of … Read more
A regular hexagon is a six-sided polygon where all sides and angles are congruent (equal). To find the measure of one interior angle in a regular hexagon, we need to use a specific formula for calculating the interior angles of any regular polygon. The formula for finding the measure of one interior angle is: Interior … Read more
To integrate the function 1/x2, we can follow these steps: Rewrite the integrand in a more convenient form. We can express 1/x2 as x-2. Now, we set up the integral: ∫ x-2 dx We can apply the power rule of integration, which states: ∫ xn dx = &frac{xn+1}{n+1} + C, for n ≠ -1 In … Read more
To calculate the distance between the points (1, 4) and (6, 2), we use the distance formula derived from the Pythagorean theorem. The formula for the distance ( d) between two points (x1, y1) and (x2, y2) in a 2D plane is: d = √((x2 – x1)² + (y2 – y1)²) Substituting our points into … Read more
The circumference of a circle can be calculated using the formula: C = π × d where C is the circumference and d is the diameter of the circle. In this case, the diameter (d) is 18. Plugging this value into the formula: C = π × 18 Using the approximate value of π (3.14), … Read more
In any triangle, the sum of the interior angles is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry. Regardless of the type of triangle—be it an equilateral triangle, where all angles are 60 degrees; an isosceles triangle, featuring two equal angles; or a scalene triangle, where all angles are different—the … Read more
The area of a circle can be calculated using the formula: Area = π × r² Where: π (Pi) is a mathematical constant approximately equal to 3.14159. r is the radius of the circle. In your case, the radius (r) is 5. Now, let’s plug that value into the formula: Area = π × (5)² … Read more