To solve the equation 11n + 1 = 35 + 3n, we will follow these steps: Start by isolating the variable terms on one side: First, we want to get all the terms involving n on one side of the equation and the constants on the other side. We can do this by subtracting 3n … Read more
In geometry, both medians and altitudes are crucial concepts related to triangles, yet they serve different purposes and possess unique properties. Understanding their differences can enhance your comprehension of triangle properties and geometry as a whole. Medians A median of a triangle is a line segment that connects a vertex to the midpoint of the … Read more
Dividing a number by zero is a mathematical operation that is undefined. To understand why, let’s explore the concept of division itself. When we divide a number, say A, by another number, B, we are essentially asking how many times B fits into A. For example, dividing 10 by 2 means we want to know … Read more
When any number is raised to the power of 1, the result is simply the number itself. This is based on the fundamental properties of exponents. For example, if we take the number 5: 51 = 5 Similarly, if we take the number 10: 101 = 10 As you can see, it doesn’t matter what … Read more
To find the average rate of change of the function f(x) = 17x² over the interval from 1 to 5, we use the formula for the average rate of change, which is: Average Rate of Change = (f(b) – f(a)) / (b – a) In this case, a = 1 and b = 5. Now, … Read more
To calculate the distance between two points on a coordinate grid, we use the distance formula, which is derived from the Pythagorean theorem. The distance formula is given by: d = √((x2 – x1)² + (y2 – y1)²) Here, (x1, y1) is the first point and (x2, y2) is the second point. In this case, … Read more
The sequence provided is part of the Fibonacci series, where each number is the sum of the two preceding ones. To understand this better, let’s break it down: The first two numbers are 55 and 34. If we add these together (55 + 34), we get 89. Next, looking at the following numbers, 34 and … Read more
To find the sum of the measures of the interior angles of a polygon, you can use the formula: Sum of interior angles = (n – 2) × 180° Where n represents the number of sides in the polygon. For a 14-sided polygon, we plug in n = 14: Sum of interior angles = (14 … Read more
To find the discriminant of the quadratic equation, we need to identify the standard form of the equation, which is ax² + bx + c = 0. In this case, the given equation is: 6x² + 4x + 3 = 0 Based on this equation, we can identify the coefficients: a = 6 (the coefficient … Read more