The x-intercept of a line is the point where the line crosses the x-axis. At this point, the value of y is always 0. To find the x-intercept of the equation given, which is 4x + 2y = 12, we can follow these steps: Step 1: Set y to 0 Start by replacing y with … Read more
An arithmetic sequence is defined as a sequence of numbers in which each term after the first is formed by adding a constant difference, known as the common difference, to the previous term. In the given sequence: 9, 11, 13, 15, we can observe that: The first term (a1) is 9. The common difference (d) … Read more
To approximate the value of y in the equation 10y = 5 using the graph of f(x) = log₁₀(x), follow these steps: Solve for y: First, start by simplifying the equation. We can rewrite it as: y = log₁₀(5). This transformation is derived from the property of logarithms that states if a = b, then … Read more
To determine the length of AE based on the provided information, we need to analyze the relationships between the segments in the diagram. If we assume that CE (12 units) and BE (5 units) are line segments connecting points C, E, and B, let’s define AE as another segment connecting points A and E. In … Read more
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