devyy Factoring the Expression 16x² + 25 The expression 16x² + 25 is a sum of squares, which does not factor into real numbers using traditional methods. However, we can attempt to express it using complex numbers. Recognizing the Form The expression can be recognized as: A² + B² where: A = 4x B = 5 … Read more
The sum of the measures of the exterior angles of any polygon is a fascinating geometric fact that applies regardless of the number of sides the polygon has. For any polygon, including a decagon (which has 10 sides), the sum of the exterior angles is always 360 degrees. To understand why this is the case, … Read more
To calculate 81 to the power of 14 (or 8114), we can break it down as follows: First, we can rewrite 81 as a power of 3, since it is equal to 34. Therefore: 8114 = (34)14 Using the power of a power property in exponents, which states that (am)n = am*n, we can simplify … Read more
The sine function, denoted as sin(x), equals zero at specific intervals on the unit circle. Understanding when this occurs is essential, especially in trigonometry and calculus. In mathematical terms, sin(x) = 0 at the following points: x = n imes \\pi for any integer n. This means that sine is zero at: 0, \\pi, 2\\pi, … Read more
A polygon with seven sides is called a heptagon. This term comes from the Greek word hepta, meaning seven. Heptagons can be regular, where all sides and angles are equal, or irregular, where they differ in length and measure. In geometry, understanding the properties of polygons is crucial. Regular heptagons have interesting characteristics, such as: … Read more
To find out what percentage 1 in 5 represents, you can follow a simple mathematical calculation. Here’s how to break it down: First, understand that ‘1 in 5’ means 1 unit out of a total of 5 units. Next, to convert that ratio into a percentage, you divide 1 by 5. So, the calculation would … Read more
The equation y = 5x is in the slope-intercept form, which is expressed as y = mx + b, where m represents the slope of the line and b is the y-intercept. In this specific equation, the coefficient of x is 5, which means the slope m is equal to 5. This slope indicates the … Read more
A regular octagon, which is an eight-sided polygon where all sides and angles are equal, possesses a fascinating property known as symmetry. Specifically, a regular octagon has 8 lines of symmetry. To understand this better, let’s break it down: Vertex Symmetry: For every vertex, there is a line of symmetry that runs through that vertex … Read more
Determining if two line segments are parallel is an essential skill in geometry. Here’s how you can do it: 1. Compare Their Slopes If you have the equations of the lines on which the segments lie, you can calculate their slopes. For lines in the form of y = mx + b, the slope m … Read more
Understanding the Inverse Function In mathematics, the inverse of a function essentially reverses the operations of the original function. If you start with a function and then apply its inverse, you will retrieve your original value. For example, if we have a function defined as y = f(x), the inverse operation would be to express … Read more