Factoring the Quadratic Equation: 6x² + 5x + 6 To factor the quadratic equation 6x² + 5x + 6, we need to find two binomials that multiply to give us this expression. The general form for factoring a quadratic equation is: ax² + bx + c = (px + q)(rx + s) Where: a = … Read more
To find the number that should be subtracted from 23 to get 16, you can set up a simple mathematical equation. Start by letting ‘x’ represent the number we want to find. The equation can be expressed as: 23 – x = 16 Now, to isolate ‘x’, you need to rearrange this equation. You can … Read more
Finding the Equation of a Line To determine the equation of the line that passes through the points (4, 1) and (2, 3), we can follow these steps: Step 1: Calculate the Slope The first step is to find the slope (m) of the line using the formula: m = (y2 – y1) / (x2 … Read more
The probability of an event and the probability of its complement always sum up to 1. This is a fundamental principle in probability theory that helps us understand how events and their outcomes are related. To break it down, let’s define a few terms: Probability of an Event (P(A)): This refers to how likely the … Read more
To solve the equation √x – 5 = 7, we will follow a few simple steps: Isolate the square root: Start by adding 5 to both sides of the equation to get rid of the constant on the left side: √x = 7 + 5 √x = 12 Square both sides: To eliminate the square … Read more
To create a consistent and independent system of equations with the given equation 3x + 4y = 8, we need to find a second equation that differs in slope.
The numbers 0, 1, 2, 3, and 4 belong to various categories in mathematics, and understanding these classifications can provide insight into their unique properties. 1. Whole Numbers: All these numbers are considered whole numbers. Whole numbers include all non-negative integers starting from zero. Hence, 0, 1, 2, 3, and 4 fit perfectly into this … Read more
The polynomial function f(x) = 4×7 – 40×6 + 100×5 is characterized by its degree, which is the highest power of x present in the expression. In this case, the degree is 7, indicating that the graph will have a series of turning points and will extend to infinity in both positive and negative directions. … Read more
To find the sum of the polynomials 7x³ + 4x² and 2x³ + 4x², we start by combining like terms. First, we can rewrite the polynomials as: First polynomial: 7x³ + 4x² Second polynomial: 2x³ + 4x² Now, let’s add them together: (7x³ + 4x²) + (2x³ + 4x²) Next, we group the similar terms: … Read more
To find the slope of the equation 9x + 3y = 15, we will first rewrite the equation in the slope-intercept form, which is y = mx + b. In this form, m refers to the slope of the line. Here are the steps to isolate y: Start with the original equation: 9x + 3y … Read more