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A regular pentagon is a five-sided polygon where all sides and angles are equal. To find the measure of each exterior angle, we can use a simple formula related to polygons. The sum of all exterior angles of any polygon is always 360 degrees, regardless of the number of sides. Since a regular pentagon has … Read more

To determine if two line segments are perpendicular, you can employ several methods. Here are the most common approaches: Using the Slope Method: In a two-dimensional Cartesian coordinate system, a line segment’s slope is determined by the ratio of the change in y (vertical) to the change in x (horizontal) between the two endpoints. If … Read more

Completing the Square To find the number that should be added to the expression x² + 4x to make it a perfect square, we can follow these steps: Start with the given expression: x² + 4x. Identify the coefficient of the linear term (4x). In this case, the coefficient is 4. Take half of the … Read more

The Latin word for the digit 9 is nove. In the context of Latin numerals, it is often written as ‘IX’, which is derived from the combination of ‘I’ (1) placed before ‘X’ (10), indicating one less than ten. The word ‘nove’ has roots in the Proto-Indo-European language, where it is connected to other numeral … Read more

To make the number 100 using exactly six 9s, you can utilize mathematical operations in a clever way. Here’s how you can do it: One common method is to express the six 9s as follows: 99 + (9 / 9) = 100 Here’s the breakdown: The first two 9s are combined to form 99. The … Read more

To determine the value of f(3) for the quadratic function graphed with the points (9, 3) and (0, 9), we first need to derive the equation of the quadratic function. A quadratic function can be expressed in the standard form as: f(x) = ax² + bx + c Given the points (9, 3) and (0, … Read more

The sequence defined by the formula an = 3n + 1 is quite straightforward to compute. Each term is generated by substituting successive integer values of n into the formula. Let’s break it down step by step: For n = 1: a1 = 3(1) + 1 = 3 + 1 = 4 For n = … Read more

The question of whether 0 is a rational or irrational number is an interesting one in the field of mathematics. Let’s break it down: A rational number is defined as any number that can be expressed as the quotient of two integers, where the denominator is not zero. In simpler terms, a rational number can … Read more

To convert the mixed number 6 7 into a fraction with a denominator of 42, we first need to understand how to represent this mixed number as an improper fraction. The mixed number 6 7 consists of the whole number 6 and the fraction 7/1. To convert it into an improper fraction: Multiply the whole … Read more

The sequence provided is 8, 16, 32, and 64. We can observe that this is a geometric progression where each term is multiplied by 2 to get the next term. To express this mathematically, we can identify the first term (a) and the common ratio (r). The first term in this sequence, a, is 8. … Read more