The sum of the interior angles of a polygon can be calculated using the formula: Sum = (n – 2) × 180 Where n is the number of sides in the polygon. Given that the sum of the interior angles is 720 degrees, we can set up the equation: (n – 2) × 180 = … Read more
To find the probability of drawing two marbles of different colors from the bag, we first need to determine the total number of marbles in the bag. The bag contains: 6 Red marbles 4 Blue marbles 7 Green marbles 3 Yellow marbles Adding these together gives us the total number of marbles: Total Marbles = … Read more
Factoring the expression x² + 7x + 8 involves finding two numbers that multiply to the constant term (8) and add up to the linear coefficient (7). Let’s break it down step-by-step: We start with the expression: x² + 7x + 8. Next, we look for two numbers that multiply to 8
To simplify the fraction formed by the numbers 64 and 32, we need to divide both the numerator (64) and the denominator (32) by their greatest common divisor (GCD). 1. **Find the GCD**: The GCD of 64 and 32 is 32, since 32 is the largest number that divides both of these without leaving a … Read more
To find the value of x in the inverse variation equation given by xy = k, where y = 4 and k = 7, we can follow a simple calculation. 1. Start with the equation: xy = k 2. Substitute the known values of y and k: x * 4 = 7 3. To isolate … Read more
The area of a triangle can be easily calculated using the formula: Area = (Base × Height) / 2 In this case, we have one side of the triangle which we’ll consider as the base, measuring 10 inches, and the height from that base to the opposite vertex is 7 inches. Substituting these values into … Read more
When dealing with quadratic equations, the discriminant plays a crucial role in determining the nature of the roots of that equation. The discriminant, denoted as D, is the part of the quadratic formula that is under the square root: D = b² – 4ac, where a, b, and c are the coefficients of the equation … Read more
To find the arc length function for the curve given by the equation y = 2x³ from the starting point P(0, 12), we will use the formula for arc length. The arc length L from point a to point b is given by the integral: L = ∫ab sqrt(1 + (dy/dx)²) dx First, we need … Read more
Finding the Vertex of a Quadratic Function The vertex of a quadratic function in the standard form f(x) = ax² + bx + c can be found using the vertex formula, which is given as: x = -b / (2a) In your case, the function is f(x) = x² + 8x + 3. Here, we … Read more
Creating Venn Diagrams for Sets A, B, and C Venn diagrams are a great way to visually represent the relationships between different sets. In this case, we’re looking at three sets: A, B, and C. Below, you’ll find detailed instructions on how to draw Venn diagrams for their various combinations, such as A ∩ B, … Read more