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A rhombus is a type of quadrilateral, which means it has four sides. One of the key properties of all quadrilaterals is that the sum of their interior angles is always 360 degrees. This is true for a rhombus as well. In the case of a rhombus, not only do we have the total sum … Read more

The growth described by the population increasing at rates of 2, 4, 8, 16, and 32 is an example of exponential growth. In exponential growth, the quantity increases at a consistent percentage rate over time, leading to larger increments as time progresses. To better understand this, let’s break down the numbers: Starting with 2, each … Read more

To find the equation of a line that passes through the origin (0, 0) and a given point, in this case, (1, 2), we can use the slope-intercept form of a line, which is: y = mx + b Here, m represents the slope and b is the y-intercept. Since the line passes through the … Read more

To determine whether the function f(x) = 3x² + 1 is even, odd, or neither, we need to evaluate the function using its definition. 1. **Definition of Even Function:** A function is called even if for every x in the domain of the function, f(-x) = f(x). This means that the graph of the function … Read more

To find csc(x) given the equation sin(x) * cot(x) = cos(x) * √3, we can start rewriting the equation using trigonometric identities. First, recall the identity for cot(x): cot(x) = cos(x) / sin(x). Thus, we can substitute it into our equation: sin(x) * (cos(x) / sin(x)) = cos(x) * √3 This simplifies to: cos(x) = … Read more

To identify the initial amount (a) and the growth factor (b) in the exponential function g(x) = 14 * 2x, we can analyze the components of the function. The general form of an exponential function is typically represented as: g(x) = a * bx In this format: a is the initial amount, which represents the … Read more

The expression given is: x, 5x, 5, x², 10x, 25, x², 10x, 25, x², 25, x², 25. To find the product, we need to multiply all these terms together. Let’s break it down step-by-step: First, combine all the coefficients (the numerical parts): 5 (from 5x) * 5 (constant) * 10 (from 10x) * 25 (constant) … Read more

Understanding the Angles of an Isosceles Triangle In an isosceles triangle, two sides are of equal length, and the angles opposite those sides are also equal. This property is crucial when determining the measures of the angles. Given Information We know that one angle is 28 degrees. We will denote the equal angles as θ. … Read more

To solve for x in the ratio 2:x:4:2 using the proportional method, follow these steps: Understand the ratio: The notation 2:x:4:2 signifies that we are considering a proportion between these four quantities. For our purpose, we can clarify this by writing it in fraction form: 2/x = 4/2 Cross-multiply: In the case of proportions, you … Read more

A geometric sequence is a series of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio. In this case, we can identify the terms of the given sequence: 1, 6, and 36. First, let’s determine the common ratio. We can find it by … Read more