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Calculating Area and Perimeter of Triangles Triangles are one of the most basic geometric shapes, and understanding how to calculate their area and perimeter is essential in geometry. Let’s break down the process step by step. Step 1: Identification of the Triangle Type First, it’s important to identify the type of triangle you are working … Read more

To solve the problem, we start by understanding the concept of direct variation. When we say that y varies directly as x, it means that there is a constant ratio between y and x. This relationship can be expressed mathematically as: y = kx Where k is the constant of variation. To find the value … Read more

Converting an improper fraction to a mixed number is a straightforward process. An improper fraction is one where the numerator (the top number) is greater than or equal to the denominator (the bottom number). A mixed number, on the other hand, consists of a whole number and a proper fraction. Here’s how to do the … Read more

To find the length of EG in the parallelogram EFHG, we start by understanding the properties of a parallelogram. In any parallelogram, opposite sides are equal in length. Thus, in parallelogram EFHG, the lengths of sides EG and FH will be equal, and the lengths of sides EF and HG will also be equal. We … Read more

To find the values of the vectors AB, BC, and CA for the triangle formed by the vertices A, B, and C, we first need to understand what these vectors represent. If we denote the vertices of the triangle as: A(x1, y1) B(x2, y2) C(x3, y3) Then the vectors can be expressed as follows: Vector … Read more

To find the equation of a line given a point and a slope, we can use the point-slope form of the equation of a line, which is: y – y1 = m(x – x1) Here, (x1, y1) is the point through which the line passes, and m is the slope of the line. In your … Read more

The axis of symmetry is an essential feature of a quadratic function. For the function h(x) = 2×2 + 12x – 3, the axis of symmetry can be determined using the formula: x = -b / (2a) In this quadratic equation, a is the coefficient of x2, and b is the coefficient of x. Here, … Read more

The value of the product 3 * 2 * i * 3 * 2 * i can be calculated as follows: First, we break it down into parts. The product involves both real and imaginary numbers, where i is the imaginary unit, defined as i = sqrt(-1). We can rearrange the multiplication: 3 * 2 … Read more

To check if a vector is an eigenvector of a matrix, you need to follow these steps: Understand Eigenvectors and Eigenvalues: An eigenvector of a matrix A is a non-zero vector v that, when multiplied by A, yields a scalar multiple of v. Mathematically, this is expressed as: A * v = λ * v, … Read more

To find out what percentage one number (let’s call it A) is of another number (let’s call it B), you can follow a simple mathematical formula: Percentage = (A / B) × 100 Here’s a step-by-step guide to help you through the process: Identify Your Numbers: Determine the two numbers you want to analyze. For … Read more