In algebra, when we multiply a number and a variable together in a term, the number is referred to as the numerical coefficient. This coefficient plays a crucial role in defining the value of the term. For example, in the expression 5x, the 5 is the numerical coefficient, and x is the variable. The coefficient … Read more
To determine if the statement is true or false, we first need to solve the equation x² + 6x + 8 = 0. This is a quadratic equation which we can solve using factoring, the quadratic formula, or completing the square. In this case, we can factor the equation. We look for two numbers that … Read more
The expression 4×2 + 19x + 5 is a quadratic equation in the standard form ax2 + bx + c, where: a = 4 b = 19 c = 5 To determine the properties of this quadratic equation, we can analyze its coefficients: 1. Parabola Orientation: Since the coefficient of x2 (which is 4) is … Read more
To solve the equation a² = 4, we will take the following steps: Understand the Equation: The equation states that a squared is equal to 4. We need to find the values of a that satisfy this equation. Isolate the Variable: To find a, we can take the square root of both sides of the … Read more
To find the vertex of the quadratic function f(x) = 3x² + 6x + 3, we can use the formula for the vertex of a parabola given in the standard form f(x) = ax² + bx + c. The coordinates of the vertex (h, k) can be found using the formulas: h = -b / … Read more
To complete the square for the quadratic equation x² + 12x – 11, we need to focus on the quadratic and linear terms, which are x² + 12x. Here’s a step-by-step process to determine the number to add: Take the coefficient of the linear term (which is 12 in this case) and divide it by … Read more
To find the length of one side of a square when given its perimeter, you can use the formula for the perimeter of a square, which is: Perimeter = 4 × side length In this case, we know that the perimeter is 36. So we can set up the equation: 36 = 4 × side … Read more
The relative maximum and minimum points of a function can be found by analyzing its critical points. A critical point occurs when the first derivative of the function is zero or undefined. Let’s go through the steps to find the critical points of the function f(x) = 2x³ + x² + 11x. Step 1: Find … Read more
To find the number of onto functions (surjective functions) from set A to set B, we can use the concept from combinatorial mathematics involving Stirling numbers of the second kind and inclusion-exclusion principle. Assuming that set A has m elements and set B has n elements, where m >= n, the formula for the number … Read more