To find the measure of arc BC in the scenario where circle O has diameters AC and BD, we first need to understand the relationships between the arcs and their associated angles. We know the following: Arc AB = 3x – 70 degrees Arc DC = x + 10 degrees Since AC and BD are … Read more
Finding the exact values of trigonometric functions without relying on the unit circle can seem daunting, but it is entirely feasible with a few useful techniques and properties of trigonometric functions. Here’s a detailed breakdown of how you can accomplish this: 1. Understanding Special Angles There are certain angles, specifically 0°, 30°, 45°, 60°, and … Read more
To determine the common ratio of a geometric sequence, we can divide any term by the previous term. In this sequence, the terms are: 625, 125, 25, 5, and 1. Let’s calculate the common ratio using the first two terms: Common ratio (r) = second term / first term = 125 / 625 Calculating that … Read more
To determine the value of f(1) for a step function, we first need to understand the characteristics of a step function. A step function is a piecewise constant function that jumps from one value to another without taking on any values in between. It is often represented visually as a series of horizontal lines that … Read more
The sum of an arithmetic sequence can be found using the formula: Sn = (n/2) * (a + l) Where: Sn = Sum of the first n terms n = Number of terms a = First term l = Last term In this case, we have the following: a = 3 (the first term) l … Read more
To prove that the product of √2 and √5 is irrational, we can use a proof by contradiction. This method helps us show that assuming the opposite leads to an impossible situation. 1. **Assumption**: First, let’s suppose that √2 * √5 is rational. This means we can express it as a fraction of two integers … Read more
Creating a graph for the linear equation y = 2x + 6 involves a few straightforward steps. Here’s a detailed guide: 1. Understand the Equation This equation is in the slope-intercept form, which is generally written as y = mx + b. In this equation: m (the slope) is 2, which indicates that for every … Read more
When we talk about an expression like x0, we’re delving into a fundamental rule of exponents in mathematics. This rule states that any non-zero number raised to the power of 0 is equal to 1. So, regardless of what x represents (as long as it is not zero), the expression x0 will always equal 1. … Read more
The x-intercept of a graph is the point where the line crosses the x-axis. This occurs when the value of y is zero. To find the x-intercept for the equation 4x + 5y = 40, you can follow these steps: Substitute y = 0 into the equation: 4x + 5(0) = 40 This simplifies to: … Read more
To determine the most precise name for the quadrilateral ABCD with vertices A(3, 2), B(1, 4), C(4, 4), and D(2, 2), we follow a systematic approach involving basic geometry principles. First, let’s plot the points to visualize the shape: A(3, 2) B(1, 4) C(4, 4) D(2, 2) Next, we calculate the lengths of the sides … Read more