To solve the quadratic equation 6x² + 13x + 5 = 0, we can use the quadratic formula, which is given by: x = \frac{-b \pm \sqrt{b² – 4ac}}{2a} In this equation, the variables are: a = 6 b = 13 c = 5 First, we need to calculate the discriminant: b² – 4ac = … Read more
To find the median of a dataset with an odd number of observations, follow these steps: Organize the Data: Begin by sorting the dataset in ascending order. This arrangement is crucial because the median is the middle value, and you need to know the exact order of the numbers. Identify the Count: Count the total … Read more
To determine the number of solutions for the equation 12x + 34x + 2 = 0, we first need to simplify the equation: 1. Combine like terms: 12x + 34x = 46x So, the equation becomes: 46x + 2 = 0 2. Next, we will isolate the variable x. We do this by first moving … Read more
To find the measure of an angle that is equal to its complement, we need to understand what complementary angles are. Complementary angles are two angles whose measures add up to 90 degrees. Let’s denote the angle we are trying to find as x. According to the definition of complementary angles, the complement of x … Read more
To construct a perpendicular line through a point that does not lie on any given line, follow these step-by-step instructions: Gather Your Materials: You will need a pencil, a ruler, and a compass. Identify Your Point: First, identify the point (let’s call it P) through which you want to draw the perpendicular line. Make sure … Read more
The distance between two points in a coordinate system can be calculated using the distance formula, which is derived from the Pythagorean theorem. If you have two points, represented as (x1, y1) and (x2, y2), the distance (d) between these points is calculated as follows: Distance Formula: d = √((x2 – x1)2 + (y2 – … Read more
To solve the inequality 8z + 3 < 2z + 51, follow these steps: Isolate the variable: Start by moving all the terms involving z to one side of the inequality and the constant terms to the other side. This allows us to isolate z. Subtract 2z from both sides: 8z + 3 – 2z … Read more
The sequence defined by the formula an = 5n + 1 can be calculated by substituting the values of n For n = 1: a1 = 5(1) + 1 = 5 + 1 = 6 For n = 2: a2 = 5(2) + 1 = 10 + 1 = 11 For n = 3: a3 … Read more
The likelihood that a particular event will occur is commonly referred to as probability. Probability is a fundamental concept in statistics and mathematics that expresses the chance of an event happening. It provides a numerical value between 0 and 1, where 0 indicates that the event cannot occur, and 1 signifies that the event is … Read more
To solve the polynomial equation 9×4 + 2×2 + 7 = 0, we will employ the method of u-substitution. This approach simplifies the equation by reducing its degree. Step 1: Perform u-substitution Let u = x2. Therefore, we can rewrite x4 as (x2)2 = u2. Substituting these values into the original equation gives us: 9u2 … Read more