Rewriting the Quadratic in Vertex Form To convert the quadratic function f(x) = x² + 6x + 4 into vertex form, we need to complete the square. The vertex form of a quadratic function is given by: f(x) = a(x – h)² + k where (h, k) is the vertex of the parabola. Steps to … Read more
To solve the equation 1 3 7x 1 1 4, we first need to clarify the format and structure of this expression. It seems there might be some confusion with the formatting. Let’s break it down step by step: If we interpret 1 3 7x 1 1 4 as a linear equation in the form … Read more
Understanding the Value of 1/10 To find the value of 1/10 in relation to the provided number 103162, we simply need to perform a calculation using division. Calculation: The fraction 1/10 represents one part of ten, which means it is equal to 0.1. Now, to find 1/10 of 103162, you need to multiply 103162 by … Read more
To determine the ranges of the functions f(x) = 45x and g(x) = 45x + 6, let’s analyze each function one by one. 1. Range of f(x) = 45x: This function is a linear function with a slope of 45. Linear functions are defined for all real numbers, which means the output can take any … Read more
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