To find the probability of not rolling a 3 on a regular number cube, we can start by looking at how a standard six-sided die works. Each face of the cube has an equal chance of landing face up, and there are a total of 6 faces: 1, 2, 3, 4, 5, and 6. When … Read more
To determine the equivalent system of the given equations, we first need to analyze the equations: 1. Equation 1: 23x + y = 2 2. Equation 2: x + 12y = 3 Next, we will solve these equations to find an equivalent system that may present the same solution set. Step 1: Solve Equation 1 … Read more
To find the value of b² – 4ac for the given quadratic equation 2x² + 2x + 1 = 0, we first identify the coefficients a, b, and c from the standard form of a quadratic equation, which is ax² + bx + c = 0. a = 2 b = 2 c = 1 … Read more
The Rational Root Theorem provides a way to identify all potential rational roots of a polynomial equation. To apply this theorem to the polynomial equation 3x³ + 9x + 6 = 0, follow these steps: Identify the coefficients: The polynomial can be expressed as: a3 = 3 (coefficient of x³) a2 = 0 (coefficient of … Read more
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