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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

When the mean and median of a data set are close to one another, it typically indicates that the distribution of the data is relatively symmetrical. In more informal terms, the numbers are clustered together in a way that doesn’t significantly skew the average (mean) away from the middle value (median). Let’s break this down … Read more

An equilateral triangle is defined as a triangle in which all three sides are equal in length and all three angles are equal in measure. To prove that a triangle is equilateral, you can apply several methods: 1. Measuring the Sides The simplest way to verify if a triangle is equilateral is by measuring its … Read more

An isosceles triangle is a unique shape in the world of geometry, primarily defined by having two sides of equal length. This characteristic not only gives it a distinct appearance but also determines its symmetry properties. In terms of lines of symmetry, an isosceles triangle has exactly one line of symmetry. This line runs from … Read more

To find a number that is both a factor of 450 and a multiple of 25, we first need to break down what these terms mean: Factors of 450: A factor is a number that divides another number without leaving a remainder. The factors of 450 can be calculated by identifying the numbers that divide … Read more

To find the exact value of cos 225 degrees using the half-angle formula, we can break it down into simple steps. The half-angle formula for cosine is given by: cos(θ/2) = ± √((1 + cos θ)/2) In our case, since 225 degrees is equivalent to 2 * 112.5 degrees, we can find cos 225 degrees … Read more

A quintillion is a large number that is equal to 1 followed by 18 zeros. To write it out numerically, a quintillion looks like this: 1,000,000,000,000,000,000 In the United States and most parts of the world that use the short scale, quintillion represents 1018. The term ‘quintillion’ is derived from the Latin word ‘quintus,’ which … Read more