To solve the equation 2cos(2x) * cos(x) = 1, we will follow a series of steps: Start by simplifying the equation: We begin with: 2cos(2x) * cos(x) – 1 = 0 Next, we can use the double angle identity: cos(2x) = 2cos²(x) – 1 By substituting this into our equation, we have: 2(2cos²(x) – 1) … Read more
To find the value of x when given the numbers 14, 15, 16, and 17, we first need to clarify the context in which x relates to these numbers. Let’s analyze different scenarios: Statistical Average: If you want to determine the average (mean) of these numbers, you would add them together and divide by the … Read more
To find another factor of the expression y² + 10y + 24, we can start by using the given information that one of the factors is (y + 4). We can perform polynomial division to divide y² + 10y + 24 by (y + 4). Here’s how it works: Set up the division: y + … Read more
Solving the System of Equations We start with the two equations: Equation 1: y = x² – 5x + 4 Equation 2: y = x² – 9x + 18 Since both equations are equal to y, we can set them equal to each other: x² – 5x + 4 = x² – 9x + 18 … Read more
Solving the Equation: 5x² + 4x – 9 = 0 To solve the quadratic equation 5x² + 4x – 9 = 0, we can use the quadratic formula: x = \frac{{-b \pm \sqrt{{b^2 – 4ac}}}}{{2a}}, where a, b, and c are coefficients from the equation in the form ax² + bx + c = 0. … Read more
To solve the equation if 3t = 7, we need to find the value of t first. We can do this by isolating t. Dividing both sides of the equation by 3 gives us: t = 7 / 3 or approximately t = 2.33. Now that we have the value of t, we can find … Read more
If you’re looking for the equation of a graph with its vertex at the point (3, 2), you’re likely referring to a quadratic function, which can be expressed in vertex form. The vertex form of a quadratic equation is given by: y = a(x – h)² + k In this equation, (h, k) represents the … Read more
The function f(x) = 23x is a linear function where the coefficient of x is 23. Domain The domain of a function refers to the set of all possible input values (x-values) that the function can accept. For f(x) = 23x, there are no restrictions on the value of x; you can input any real … Read more
Understanding the Expression To determine which expression is a factor of 3xy + 2x + 18y + 12, we first need to simplify and analyze the terms of the provided expression. The expression can be rearranged to facilitate factoring. Rearranging the Expression The expression can be grouped as follows: 3xy + 18y + 2x + … Read more