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To find the other factor of the polynomial 3x² + 10x + 8, given that one factor is 3x + 4, we can use polynomial long division. 1. **Set up the division**: We will divide 3x² + 10x + 8 by 3x + 4. 2. **Divide the leading terms**: Take the leading term of the … Read more

Identifying Similar Polygons When we talk about similar polygons, we are referring to shapes that have the same form but may vary in size. This means that their corresponding angles are equal, and the lengths of their corresponding sides are proportional. Key Characteristics of Similar Polygons Equal corresponding angles: All the angles in one polygon … Read more

To find the number of sides (n) in a polygon when given the sum of its angle measures, we can use the following formula: Sum of interior angles = (n – 2) × 180 In this case, we’re told that the sum of the angle measures is 2880 degrees. So we can set up the … Read more

To find two unit vectors that are orthogonal to both vectors (3, 2, 1) and (1, 1, 0), we can follow these steps: Step 1: Find the Cross Product The first step is to find a vector that is orthogonal to both given vectors. This can be done using the cross product. For two vectors … Read more

In geometry, adjacent angles are defined as two angles that share a common side and a common vertex, yet do not overlap. To determine which pairs of angles are adjacent, you need to look closely at their positions and relationships. Consider the following pairs of angles: Angle A and Angle B Angle C and Angle … Read more

To solve the quadratic equation x² + 4x – 18 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a In our equation, we can identify the coefficients as follows: a = 1 (the coefficient of x²) b = 4 (the coefficient of x) … Read more

To solve the equations for x and y, we start with the given equation: 7y + 3 = 2x^2 + 14 + 4y – 2 + 3x. First, we need to simplify the equation. Reorganizing terms, we get: 1. Move all terms involving y to one side and those involving x to the other side: … Read more

To find the greatest number that can be formed using the digits 5, 3, 1, 4, and 7, we need to arrange these digits in descending order. The descending order means we start with the largest digit and proceed to the smallest. Here are the digits in the set: 5 3 1 4 7 Arranging … Read more

To solve the equation x2 + 4x + 5 = 0 by graphing, you’ll first need to understand the process of converting the quadratic equation into a function that can be plotted. Here’s a step-by-step guide: Define the function: Rewrite the equation in the standard quadratic function format. In this case, you can express it … Read more

The quadratic formula is a useful tool for finding the solutions to any quadratic equation of the form ax² + bx + c = 0. The formula is: x = (-b ± √(b² – 4ac)) / (2a) In this case, your equation is: x² – 2x – 20 = 0 Here, we can identify the … Read more