devyy 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
To find the value of i97, let’s first clarify what the imaginary unit i is. The imaginary unit i is defined as the square root of -1. When we raise i to various powers, it follows a recurring pattern: i1 = i i2 = -1 i3 = -i i4 = 1 This pattern repeats every … Read more
Sure! Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. This means they can only be divided evenly by these two numbers. Here are the first ten prime numbers: 2 3 5 7 11 13 17 19 23 29 These numbers play a crucial role in … Read more
A polygon with six sides and six angles is called a hexagon. The term ‘hexagon’ comes from the Greek words ‘hex’, meaning six, and ‘gonia’, meaning angle. Hexagons are interesting shapes that can be found in various forms in nature and human-made structures. One of the most well-known examples of hexagons in nature is the … Read more
The given expression is a quadratic polynomial written as 9x² – 24x + 16. To find the completely factored form, we will use the method of factoring by grouping or the quadratic formula, though in this case, factoring by grouping is more straightforward. First, we identify the coefficients: A = 9 (the coefficient of x²) … Read more