To solve the quadratic equation x² + 4x – 18 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a In our equation, we can identify the coefficients as follows: a = 1 (the coefficient of x²) b = 4 (the coefficient of x) … Read more
To solve the equations for x and y, we start with the given equation: 7y + 3 = 2x^2 + 14 + 4y – 2 + 3x. First, we need to simplify the equation. Reorganizing terms, we get: 1. Move all terms involving y to one side and those involving x to the other side: … Read more
To find the greatest number that can be formed using the digits 5, 3, 1, 4, and 7, we need to arrange these digits in descending order. The descending order means we start with the largest digit and proceed to the smallest. Here are the digits in the set: 5 3 1 4 7 Arranging … Read more
To solve the equation x2 + 4x + 5 = 0 by graphing, you’ll first need to understand the process of converting the quadratic equation into a function that can be plotted. Here’s a step-by-step guide: Define the function: Rewrite the equation in the standard quadratic function format. In this case, you can express it … Read more
The quadratic formula is a useful tool for finding the solutions to any quadratic equation of the form ax² + bx + c = 0. The formula is: x = (-b ± √(b² – 4ac)) / (2a) In this case, your equation is: x² – 2x – 20 = 0 Here, we can identify the … Read more
The present value (PV) of an amount of money is calculated using the following expression: PV = FV / (1 + r)^n Where: PV: Present Value – the current worth of a given amount of money in the future. FV: Future Value – the amount of money you expect to receive in the future. r: … Read more
To determine the x-intercept of the line given by the equation 6x + 2y = 18, we follow a straightforward process. The x-intercept is the point where the line crosses the x-axis, which occurs when the value of y is zero. Here are the steps to find the x-intercept: Set y = 0 in the … Read more
To determine how many cups of tomato are needed for a salsa batch of 105 cups, we first need to understand how the ingredients are proportioned according to the given ratio of 3:5:7 for green pepper, onion, and tomato. The total parts in the ratio can be calculated as follows: Green pepper: 3 parts Onion: … Read more
To find the point on the line y = 2x + 4 that is closest to the origin (0, 0), we can use the concept of distance between points in a Cartesian plane. The distance d from any point (x, y) to the origin is given by: d = √(x2 + y2) In our case, … Read more
The sum of the interior angles of any quadrilateral is 360 degrees. This can be understood through a simple geometric principle. To visualize this, think of a quadrilateral as a four-sided figure, which can be any shape with four edges and four vertices. One effective way to see why the interior angles add up to … Read more