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Finding the nth Term of a Geometric Sequence A geometric sequence, also known as a geometric progression, is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. The formula for finding the nth term of a geometric sequence … Read more

The Pythagorean identity in trigonometry states that for any angle θ, the following relationship holds: sin2(θ) + cos2(θ) = 1 In this case, we know that sin(8) = 15/17. To find cos(8), we first need to calculate sin2(8). Calculating sin2(8): sin2(8) = (15/17)2 = 225/289 Now we can substitute this back into the Pythagorean identity: … Read more

Let’s denote two consecutive positive integers as x and x + 1. The product of these integers can be expressed as: Product = x * (x + 1) = x2 + x The sum of these integers is: Sum = x + (x + 1) = 2x + 1 According to the problem, the product … Read more

To solve the problem, we start with the direct variation relationship where x varies directly with y, which can be expressed mathematically as: x = k * y where k is the constant of proportionality. Given the information that x is 25 when y is 10, we can substitute these values into the equation to … Read more

The best fit line, often referred to as a trend line, plays a crucial role in data analysis and statistical modeling, especially in the context of linear regression. Its primary purpose is to provide a visual representation of the relationship between two variables by minimizing the distance between the line and the data points plotted … Read more

To find the center of a circle given the endpoints of its diameter, we need to calculate the midpoint between these two points. The formula for the midpoint M = (x1 + x2, y1 + y2) / 2 In this case, the endpoints of the diameter are: Point 1 (x1, y1): (2, 8) Point 2 … Read more

The orthocentre of a triangle is the point where all three altitudes intersect. To find the orthocentre, you can follow these steps: Identify the vertices: Start by labeling the vertices of the triangle. Let’s say the vertices are A, B, and C. Calculate the slopes: Determine the slopes of the sides of the triangle. For … Read more

The equation 4x + 5y = 15 represents a linear relationship between the variables x and y. To understand what the graph looks like, we can rewrite the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. First, let’s isolate y: 4x + 5y = … Read more

The function f(x) = \frac{-x^2 – 9x – 20}{x + 4} is a rational function, meaning it is the ratio of a polynomial in the numerator to a polynomial in the denominator. To understand the graph of this function, we’ll analyze several key features: the x-intercepts, the y-intercept, vertical and horizontal asymptotes, and the overall … Read more

In an isosceles triangle, two sides are of equal length, and the angles opposite those sides are equal as well. When you know the measure of the vertex angle, you can easily find the measure of the base angles using the properties of triangles. The sum of the angles in any triangle is always 180 … Read more