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The divisor represented by the synthetic division notation you provided, which is written as 5 5 x 5 x 5, is referring to a polynomial being divided by the binomial (x – 5). In synthetic division, the coefficients of the polynomial are aligned with the value being used as the divisor, which in this case … Read more

The perimeter of a triangle is simply the sum of the lengths of all its sides. For triangle LMN, you would need to know the lengths of sides LM, LN, and MN. To calculate the perimeter, you can use the following formula: Perimeter (P) = LM + LN + MN Here’s a step-by-step guide on … Read more

A polygon is a flat shape consisting of straight lines that are joined to form a closed chain or circuit. Let’s examine the potential candidates to determine whether they are polygons: Triangle: Yes, a triangle has three straight sides and is a polygon. Rectangle: Yes, a rectangle has four straight sides and is a polygon. … Read more

To simplify the expression 7x + 34x² + 3x + 6, we start by identifying like terms. The expression can be broken down as follows: Terms with x²

To solve the equation described, we can break down the problem step by step. The statement says that four times the difference of a number (let’s call it x) and 7 is equal to 12. We can express this mathematically as: 4(x – 7) = 12 Now, let’s solve for x: First, divide both sides … Read more

To solve the absolute value inequality |2x – 4| < 14, we start by breaking it down into two separate inequalities. The absolute value inequality |a| < b means that -b < a < b. In this case, a is 2x – 4 and b is 14. So, we can rewrite the inequality as: -14 ... Read more

To solve the equation 28y + 6 = 02y + 5y + 14, let’s first simplify both sides of the equation. 1. Simplifying the right side: 02y + 5y can be simplified as follows: 02y = 2y, so we have 2y + 5y = 7y. This means that the equation now looks like this: 28y … Read more

To find the value of ‘c’ in the quadratic equation given in the standard form ax² + bx + c = 0, we need to identify the coefficients from the equation 3x² + 5x + 7 = 0. In this equation: a (the coefficient of x²) = 3 b (the coefficient of x) = 5 … Read more

To find the solutions to the quadratic equation 4x² + 3x – 24 = 0, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a) Here, the coefficients are: a = 4 b = 3 c = -24 Now, we need to calculate the discriminant, which is the part under … Read more

To find the area of a regular hexagon when you know the length of the apothem, you can use the following formula: Area = (Perimeter x Apothem) / 2 First, let’s break it down: Find the side length: A regular hexagon can be divided into 6 equilateral triangles. The relationship between the apothem (a) and … Read more