In the standard form of an absolute value function given by f(x) = a|x – h| + k, the vertex of the function is represented by the coordinates (h, k). To break this down further: a: This coefficient affects the vertical stretch or compression of the absolute value graph. It also determines the direction of … Read more
The metric system is one of the most widely used measurement systems in the world, and it operates on a base-10 structure, which makes it quite intuitive. In the metric system, a kilogram is a fundamental unit of mass. To directly answer your question, there are 1,000 grams in a kilogram. This is a straightforward … Read more
To simplify the fraction of 724 divided by 3548, we start by expressing it as: Fraction: 724 / 3548 Next, we will find the greatest common divisor (GCD) of 724 and 3548 to reduce the fraction to its simplest form. The GCD is the largest number that divides both the numerator and denominator without leaving … Read more
To factor the quadratic expression x² + 14x + 48, we want to find two numbers that multiply to the constant term (48) and add up to the coefficient of the linear term (14). Let’s analyze the factors of 48: 1 and 48 2 and 24 3 and 16 4 and 12 6 and 8 … Read more
Graphing the Exponential Function y = 3^x Graphing the exponential function y = 3^x involves a few simple steps that will help you visualize the function’s behavior across different values of x. Here’s a detailed explanation and guide: 1. Understand the Basics of the Function The function y = 3^x is an exponential function where: … Read more
To determine the value that must be added to the expression x² + 16x in order to make it a perfect square trinomial, we can follow a systematic process. A perfect square trinomial takes the form of (a + b)², which expands to a² + 2ab + b². In our case, we have the quadratic … Read more
To solve the equation 11n + 1 = 35 + 3n, we will follow these steps: Start by isolating the variable terms on one side: First, we want to get all the terms involving n on one side of the equation and the constants on the other side. We can do this by subtracting 3n … Read more
In geometry, both medians and altitudes are crucial concepts related to triangles, yet they serve different purposes and possess unique properties. Understanding their differences can enhance your comprehension of triangle properties and geometry as a whole. Medians A median of a triangle is a line segment that connects a vertex to the midpoint of the … Read more
Dividing a number by zero is a mathematical operation that is undefined. To understand why, let’s explore the concept of division itself. When we divide a number, say A, by another number, B, we are essentially asking how many times B fits into A. For example, dividing 10 by 2 means we want to know … Read more