To find the solutions to the equation 4x – 8 = 2 + 5x, let’s first rearrange it step by step. 1. Start by simplifying the equation: 4x – 8 = 2 + 5x 2. To isolate the variable, we can subtract 5x from both sides: 4x – 5x – 8 = 2 3. This … Read more
Calculating the original price of a discounted item can seem tricky at first, but it’s quite straightforward once you understand the process. Here’s how you can do it in a few simple steps: Identify the Discounted Price: Start by noting the price after the discount has been applied. This is the amount you see on … Read more
Solving the Equation x² + 2x + 6 = 0 To solve the quadratic equation x² + 2x + 6 = 0, we can use several methods. However, in this case, the quadratic formula is likely the most effective method because it provides a solution for any quadratic equation. Step 1: Identifying Coefficients The general … Read more
To convert a percentage to a fraction, you can follow a simple process. A percentage is a way of expressing a number as a fraction of 100. Therefore, when dealing with 2 percent, we can express it as: 2 percent = rac{2}{100} Next, we can simplify the fraction. To do this, we need to find … Read more
To find the area of a circle when its circumference is given, we’ll use the formulas for circumference and area. The circumference (C) of a circle is calculated using the formula: C = 2πr where r is the radius of the circle. Given that the circumference is 8π meters, we can set up the equation: … Read more
The side length of a square can be determined by taking the square root of its area. If the measurements mentioned (30 units, 35 units, 42 units, and 49 units) represent the lengths of the sides of squares, we can calculate the approximate side lengths as follows: For 30 units: The side length is already … Read more
A term in a polynomial is a single mathematical expression that can vary in complexity. It typically consists of a coefficient, a variable, and an exponent. Understanding the components of a term can help clarify its role in the context of polynomials. Here’s a breakdown of the elements that comprise a term: Coefficient: This is … Read more
To find the product of the terms 4y, 32y2, 3y, and 5, we will multiply them together step by step. 1. First, let’s group the coefficients (the numerical parts) together and the variable parts together: Coefficients: 4, 32, 3, and 5 Variables: y, y2, and y 2. Now, we will multiply the coefficients: 4 * … Read more
To find the area of a regular hexagon given a radius (or circumradius) of 5 inches, you can use the formula: Area = (3√3/2) × r², where r is the radius. Step 1: First, square the radius: r² = 5² = 25. Step 2: Multiply the squared radius by (3√3/2): Area = (3√3/2) × 25. … Read more
The sequence defined by the formula an = 6n + 1 can be evaluated by substituting the values of n starting from 1. Here’s how to find the first five terms: For n = 1: a1 = 6(1) + 1 = 6 + 1 = 7 For n = 2: a2 = 6(2) + 1 … Read more