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A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, where the numerator is an integer and the denominator is a non-zero integer. This means that both integers and non-integers can be classified as rational numbers, providing a broad spectrum of possibilities within this classification. … Read more

To find the other solution of the quadratic equation x² + 2x – 15 = 0, we can use the fact that quadratic equations can often be factored or solved using the quadratic formula. Since we already know one solution is x = 3, we can use this information to find the other solution. First, … Read more

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