To solve the quadratic equation 2×2 + 40x + 2 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a Here, the coefficients are: a = 2 b = 40 c = 2 Now, we will calculate the discriminant, which is b² – 4ac: … Read more
The y-intercept of a function is the point where the graph intersects the y-axis. This occurs when the value of x is zero. To find the y-intercept for the function f(x) = 4 + 5x, we substitute x with 0: f(0) = 4 + 5(0) This simplifies to: f(0) = 4 + 0 = 4 … Read more
To find the y-intercept of the line given by the equation 3y + 4x = 15, we need to determine the value of y when x is equal to 0. The y-intercept is the point where the line crosses the y-axis, which occurs when the value of x is zero. Let’s solve for y: 3y … Read more
When we talk about multiples that are shared between two or more numbers, what we’re often referring to are the common multiples of those numbers. A common multiple is any number that is a multiple of each of the given numbers. To better understand common multiples, let’s take two numbers as an example: 4 and … Read more
An ellipse is a geometric shape that looks like a stretched circle or an elongated oval. In mathematical terms, it is defined as a set of points in a plane such that the sum of the distances from two fixed points, known as the foci, is constant. This unique property gives ellipses their distinct shape … Read more
When considering events that cannot occur at the same time, it’s essential to understand the concept of exclusivity in terms of timing and resources. Here are some key categories of events that typically cannot coexist: 1. Mutually Exclusive Events In probability and statistics, mutually exclusive events are those that cannot happen simultaneously. For example, when … Read more
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