To find out how many games the soccer team won, we need to calculate 65% of the total games played, which is 160. The formula to calculate the number of wins is: Number of Wins = Total Games Played × Win Percentage In this case: Number of Wins = 160 games × 0.65 Now, performing … Read more
To convert the expression x² + 10x into a perfect square trinomial, we need to find a specific value that, when added, completes the square. A perfect square trinomial takes the form (x + a)², which expands to x² + 2ax + a². In this case, we have: The coefficient of x is 10 In … Read more
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