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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

Understanding the Relationship Between Surface Area and Volume of a Cube A cube is a three-dimensional shape where all sides are equal in length. To express the surface area of a cube as a function of its volume, we first need to recall the formulas for both the surface area and volume of a cube. … Read more

Finding the Minimum Value of the Product xy To determine the minimum value of the product xy given the equation y = 2x + 8, we can start by rewriting the product in terms of a single variable. First, replace y in the product: xy = x(2x + 8) = 2x^2 + 8x Now, we … Read more

To determine the number of sides in a regular polygon when given the measure of its exterior angle, we can use the formula: Exterior Angle = 360° / n, where n represents the number of sides of the polygon. In this case, we know that the exterior angle is 24 degrees. We can set up … Read more

A rectangle is a type of quadrilateral that possesses certain properties which qualify it as a convex shape. To understand why a rectangle is a convex quadrilateral, we first need to clarify what these terms mean. A quadrilateral is a polygon with four sides. Convex quadrilaterals, specifically, are those where all interior angles are less … Read more