To find the x-intercept of the function f(x) = x² – 16x + 64, we need to determine the points where the graph intersects the x-axis. This occurs when the value of f(x) equals 0. Therefore, we set the equation equal to zero: x² – 16x + 64 = 0 This is a quadratic equation, … Read more
To determine the y-intercept of the line given by the equation x + 5y – 12 = 0, we need to find the value of y when x is equal to 0. 1. **Start with the equation:** x + 5y – 12 = 0 2. **Substitute x = 0:** 0 + 5y – 12 = … Read more
To find the distance between two complex numbers in the complex plane, we can treat them as points in a two-dimensional space. The complex number 1 + 3i corresponds to the point (1, 3) and 2 + 4i corresponds to the point (2, 4). We can use the distance formula, which is derived from the … Read more
To find the next number in the series 2, 5, 11, 20, 32, 47, let’s first examine the differences between consecutive numbers: 5 – 2 = 3 11 – 5 = 6 20 – 11 = 9 32 – 20 = 12 47 – 32 = 15 Here are the differences: 3 6 9 12 … Read more
To rewrite the inequality 6x + 2y ≤ 46 in slope-intercept form, we need to isolate y on one side of the inequality. Slope-intercept form is typically structured as y = mx + b, where m represents the slope and b denotes the y-intercept. Here are the detailed steps to perform the conversion: Start with … Read more
To write the equation of a line that passes through two points, you can use the two-point form of a line equation. The basic steps are as follows: Identify the points: In this case, the points are (1, 3) and (2, 2). Calculate the slope (m): The slope formula is m = (y_2 – y_1) … Read more
The simplest form of a factor tree for the number 1225 involves breaking it down into its prime factors. Here’s a step-by-step explanation of how to create the factor tree and find the simplest form: Step 1: Determine if 1225 is divisible by smaller prime numbers First, let’s check if 1225 is divisible by the … Read more
To determine the value of the constant b when x² is a factor of the expression x² + bx + b, we can use the rules of polynomial factorization. Since x² is a factor, this means that we can express the given polynomial as: (x²)(Ax + B), where A and B are constants. This means … Read more
To complete the square for the quadratic equation x² + 6x + 9 = 0, follow these steps: Start with the equation: x² + 6x + 9 = 0. Notice that the expression on the left side can be expressed as a perfect square. The expression x² + 6x + 9 can be factored. The … Read more