To find the value of x that satisfies the equation 5x + 15 = 10 + 20x, we can start by rearranging the terms. Step 1: Move all terms involving x to one side and constant terms to the other side. We can do this by subtracting 5x from both sides of the equation: 5x … Read more
A polygon with all sides of the same length is referred to as a regular polygon. In a regular polygon, not only are all the sides equal in length, but all the interior angles are also equal. This characteristic gives regular polygons a level of symmetry and uniformity that makes them visually appealing. For example, … Read more
Finding Input Values for Function Matches The question involves identifying an input value that returns the same output for two distinct functions. In this case, we are considering the function f(x) = x³ – 2x – 3. To solve the problem, we can analyze the equation: x³ – 2x – 3 = 0 This cubic … Read more
To calculate the slope of a line that passes through two points, you can use the formula: Slope (m) = (y2 – y1) / (x2 – x1) In this case, the points given are (2, 12) and (6, 11). We will label these points as follows: (x1, y1) = (2, 12) (x2, y2) = (6, … Read more
To solve the equation 6y + 20 = 2y + 4, we need to isolate the variable y. Here’s a step-by-step breakdown: Start with the equation: 6y + 20 = 2y + 4 Move the terms involving y to one side: Subtract 2y from both sides: 6y – 2y + 20 = 2y – 2y … Read more
Understanding Shapes Made of Straight Lines When we talk about shapes made up of perfectly straight lines, the term that best encapsulates this concept is polygon. A polygon is defined as a two-dimensional geometric figure that is bounded by a finite number of straight line segments. These line segments are known as the edges or … Read more
To determine the length of WZ in inches, we need to express it based on the information provided. We know that: TZ = 3x inches WZ = 2x + 3 inches However, without additional information or a relationship between the segments TZ and WZ, we can’t directly compute the length of WZ in terms of … Read more
To graph the function f(x) = x² + 4x + 5, follow these steps: 1. Understand the Function: This is a quadratic function in the form of f(x) = ax² + bx + c, where: a = 1 b = 4 c = 5 Since a > 0, the parabola opens upwards. 2. Find the … Read more
To find the equation of the line that passes through the point (2, 2) and is parallel to the given line y = rac{1}{2}x + 8, we need to follow these steps: Identify the slope: The given line has a slope (m) of rac{1}{2}, as indicated by the coefficient of x in the slope-intercept form … Read more