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To find the inverse of the equation y = 5x² + 10, we follow several steps to simplify it and express x in terms of y. Step 1: Swap the Variables The first step in finding the inverse is to switch x and y in the equation. This gives us: x = 5y² + 10 … Read more

To determine the number of women in the city, we can use the given ratio of men to women, which is 3 to 1. This means that for every 3 men, there is 1 woman. Let’s break down the calculation step by step: 1. First, we need to express the ratio in terms of parts. … Read more

To factor the polynomial x² + 6x + 27, we will apply the methods of factoring polynomials. First, let’s check if it can be factored as a simple quadratic equation of the form ax² + bx + c. In our case: a = 1 b = 6 c = 27 To find the factors of … Read more

In triangle ABC, the incenter O is the point where the angle bisectors of the triangle intersect. The incenter is also the center of the circle inscribed within the triangle. To find the measure of angle QOB, we need to consider the relationship between the triangle’s angles and the angles formed by the incenter. Given … Read more

The product of two integers can be positive, negative, or zero depending on the integers involved. Here’s how it works: Product is Positive: When both integers are either positive or negative. For example: (3) * (4) = 12 and (-3) * (-4) = 12. In both cases, the result is a positive integer. Product is … Read more

To calculate the area of a shape, you’ll first need to identify the type of shape you’re working with, as the formula varies depending on the shape. Here are some common shapes and their area formulas: Rectangle: The area is calculated by multiplying the length by the width. Formula: Area = length × width Square: … Read more

To find f(g(x)), we first need to determine what g(x) is when we substitute a value for x. Given that g(x) = x^2, we can compute it by plugging in any valid value for x. Let’s keep it simple and use x = a (where a is any number other than 0), thus g(a) = … Read more

To understand the end behavior of the polynomial function y = 7×12 + 3×8 + 9×4, we need to focus on the leading term of the polynomial, which is the term with the highest degree. In this case, the leading term is 7×12. The degree of this polynomial is 12, which is an even number. … Read more

To find a function that has zeros at specific x-values, you can use the fact that a function is equal to zero at those points. In this case, we’re looking for a function that is equal to zero when x = 2 and x = 5. In polynomial functions, zeros correspond to the factors of … Read more

To solve the equation n + 4 = 3 + 3 + 2n + 3 + n, we first need to simplify both sides. Let’s break it down step by step. 1. **Simplifying the Right Side:** The right side consists of a few constants and terms with ‘n’. Start by adding the constants: 3 + … Read more