Completing the square is a useful method in algebra for rewriting a quadratic equation in a standard form. To complete the square for any quadratic expression of the form ax² + bx + c, you want to transform it into a perfect square trinomial. The first step is to focus on the b coefficient and … Read more
To solve the expression 4b + 6 – 2b + 4, you’ll want to combine like terms to simplify it. 1. **Identify the like terms**: In the expression, the like terms are the terms involving b and the constant terms: Like terms with b: 4b and -2b Constant terms: 6 and 4 2. **Combine the … Read more
To find an equation that has specific solutions, such as m = 5 and m = 9, we can use the concept of factored forms in algebra. The general approach is to create a polynomial equation where the specific solutions are the roots. In this case, we can create the equation by finding the factors … Read more
To find the solution to the system of equations y = 3x + 8 and y = 5x + 2, we need to determine the values of x and y that simultaneously satisfy both equations. This can be done using the substitution method or the elimination method. Here, we will use the substitution method. First, … Read more
To confirm that two functions, f and g, are inverses of each other, we need to show that applying one function to the result of the other returns us to the original input. This requires evaluating two specific expressions: f(g(x)) = x g(f(x)) = x Let’s break down the process step by step: Step 1: … Read more
To calculate the volume of a sphere, we can use the formula: Volume (V) = (4/3) × π × r³ Where: V = volume of the sphere π = pi (approximately 3.14159) r = radius of the sphere In this case, the radius (r) of the sphere is 6 centimeters. Plugging this value into the … Read more
Solving the Quadratic Equation x² + 6x + 18 To solve the quadratic equation x² + 6x + 18 = 0, we can employ the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a In this formula, a, b, and c are coefficients from the equation in the standard … Read more
To find the solution set of the equation x * (x3) * (x – 5) = 0, we can begin by setting the expression equal to zero: x * (x3) * (x – 5) = 0 This equation is satisfied when any of the factors equals zero. Therefore, we will look at each factor separately: … Read more
To find the product of 3.23 and 14.25, we simply need to multiply the two numbers together. Here’s the calculation: 3.23 × 14.25 = 46.0725 Therefore, the product of 3.23 and 14.25 is 46.0725.
To solve the problem, let’s denote the two numbers as x and y. According to the information provided, we know two things: The sum of the two numbers is 39, which can be represented mathematically as: x + y = 39 Additionally, it is stated that one number is twice as large as the other. … Read more