An even function is defined as a function that satisfies the condition f(-x) = f(x) for all x in its domain. To determine which of the given functions are even, we’ll evaluate each one: f(x) = 12: This is a constant function. When we evaluate f(-x), we get f(-x) = 12. Since f(-x) = 12 … Read more
Rewriting f(x) = x² – 4x + 1 in Vertex Form To rewrite the function f(x) = x² – 4x + 1 in vertex form, we will use the completing the square method. Vertex form of a quadratic function is expressed as: f(x) = a(x – h)² + k where (h, k) is the vertex … Read more
To find the radius of a circle when you know its circumference, you can follow a straightforward mathematical approach. The relationship between the circumference (C) and the radius (r) of a circle is given by the formula: C = 2 * π * r Here, π (pi) is a constant approximately equal to 3.14159. To … Read more
To find the measure of angle x in the figure, we need a few key details about the angles related to it. If we have a diagram you are working with, it could provide additional information, such as adjacent angles, supplementary angles, or any relationships involving parallel lines and transversals. Here’s a general method to … Read more
To determine the probability of drawing a red face card from a standard deck of 52 playing cards, you first need to know how many total face cards there are and how many of those are red. In a standard deck, there are three face cards in each suit: the King, Queen, and Jack. Since … Read more
To find the product of the two mixed numbers, 4 2/3 and 11 1/4, we first need to convert them into improper fractions. 1. Convert 4 2/3 to an improper fraction: 4 2/3 = (4 * 3 + 2) / 3 = (12 + 2) / 3 = 14/3 2. Convert 11 1/4 to an … Read more
To find an ordered pair that satisfies both inequalities y > 3x + 1 and y < x + 4, we need to analyze what these inequalities represent. 1. **Understanding the inequalities**: The first inequality, y > 3x + 1, represents all the points that lie above the line defined by the equation y = … Read more
To solve the equation x6 + 9×3 + 8 = 0, we can utilize a technique called u-substitution. The idea is to simplify the equation by substituting a new variable for the expression involved. Step 1: Make the substitutionLet’s set u = x3. This means that x6 = (x3)2 = u2. Rewriting the original equation … Read more
To determine the polar coordinates of the point (3, 3), we first need to convert these Cartesian coordinates to polar coordinates. In polar coordinates, a point is represented by the radius (r) and the angle (θ). 1. **Calculating the Radius (r)**: The radius can be calculated using the formula: r = √(x2 + y2) where … Read more
A regular 30-sided polygon, also known as a triacontagon, can be rotated around its center, and the degree of rotation refers to the angle at which the polygon can be rotated while still appearing unchanged. To find the degree of rotation for any regular polygon, you can use the formula: Degree of Rotation = 360° … Read more