To find the solution to the equation 4x = 100, you need to isolate the variable x. Here’s how you can do it step by step: Divide both sides by 4: Since x is being multiplied by 4, you can eliminate the 4 by dividing both sides of the equation by 4. This looks like … Read more
To understand the probability of rolling an odd number on a fair six-sided die, let’s first identify the characteristics of the die itself. A standard six-sided die, often referred to as a number cube, has the numbers 1 through 6 displayed on its faces. Out of these six numbers, the odd numbers are 1, 3, … Read more
To find the equation for the nth term of the arithmetic sequence given by the numbers 3, 5, 7, and 9, we start by identifying the common difference of the sequence. The sequence can be described as: Term 1 (n=1): 3 Term 2 (n=2): 5 Term 3 (n=3): 7 Term 4 (n=4): 9 We can … Read more
The solutions x = 1 ± √5 indicate that we have two distinct values for x: one is x = 1 + √5 and the other is x = 1 – √5. To find the quadratic equation that corresponds to these solutions, we can start from the general property of roots in a quadratic equation, … Read more
To solve the quadratic equation 3x² – 18x + 15 = 0 by completing the square, we’ll follow several clear steps. Here’s how: Divide the entire equation by the coefficient of x²: Since the coefficient of x² is 3, we divide every term by 3 to simplify the equation. Rewrite the equation: x² – 6x … Read more
To understand the probability of a value being more than one standard deviation away from its mean, we need to dive into the concept of the normal distribution, often depicted as a bell curve. In a normal distribution: The mean is the center of the distribution. About 68% of the data falls within one standard … Read more
In mathematics, especially in the field of geometry, a plane is defined as a flat, two-dimensional surface that extends infinitely in all directions. You can think of it as a vast sheet of paper that has no edges and goes on forever. Mathematicians use the concept of a plane to understand relationships between points, lines, … Read more
To identify the solution set for the equation x³ + 4x + 5 = 2x, we first need to rearrange the equation into standard form. This involves moving all terms to one side of the equation. 1. **Rearranging the Equation**: Start by subtracting 2x from both sides: x³ + 4x + 5 – 2x = … Read more
To simplify the difference between the two expressions, we first need to write them down clearly: Expression 1: 7x + 5×4 + 5 Expression 2: 7×4 + 5 + 9x Now, we want to find the difference: Difference: (7x + 5×4 + 5) – (7×4 + 5 + 9x) Next, we can distribute the negative … Read more
Understanding the Sine Function in Trigonometry The primary aim is to find the sine of an angle where the terminal side of the angle intersects the point (15, 8). First, let’s understand the scenario involving the angle in standard position. The terminal side of the angle is determined by a point (x, y) in the … Read more