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Finding the Quotient of a Polynomial Division To divide the polynomial 2x³ – 13x² + 16x – 5 by x – 5, we can use polynomial long division. Step-by-Step Solution: Set Up the Division: Write the expression in long division format: Divide 2x³ – 13x² + 16x – 5 by x – 5. First Division … Read more

To solve the problem, let’s break it down step by step. First, we need to determine the cost of one pen. If 100 pens cost x dollars, we can find the price of a single pen by dividing the total cost by the number of pens: Cost of one pen = x dollars / 100 … Read more

The additive inverse of a complex number is found by negating both its real and imaginary parts. For the complex number 12 + 4i, the real part is 12 and the imaginary part is 4i. To find the additive inverse, we simply change the signs of these parts. Thus, the additive inverse of 12 + … Read more

To find the zeros of the polynomial function f(x) = x³ + x² – 20x, we need to solve the equation f(x) = 0. This means we want to find the values of x for which the function equals zero. First, we start by factoring the polynomial. We can rearrange the function as follows: f(x) … Read more

Finding the Diagonal of a Square To determine the length of the diagonal of a square when you know its area, you can follow a series of straightforward steps. Here’s how to do it: Step 1: Understanding the Area of a Square The area of a square is calculated using the formula: Area = side … Read more

The equations you provided are: 3x + 2y = 4 2x + y = 5 To determine the solutions, we can solve this system of linear equations using either the substitution method or the elimination method. Let’s use the substitution method for clarity. Step 1: Solve one equation for one variable We can solve the … Read more

To solve the equation x + 4x + 4 = 9, we first need to combine like terms and simplify it. Here’s how to do that step by step: Combine the terms with x

In triangle BDC, which is noted to be isosceles, we need to determine which angle is congruent to angle BAD. In an isosceles triangle, two sides are of equal length, which means the angles opposite those sides are also equal. Assuming triangle BDC has two equal sides, we can deduce the following: let’s say sides … Read more

To find the approximate solutions to the equation 2x + 8 = 025x, we first need to understand the equation better by simplifying and analyzing it. 1. **Rearranging the equation**: We can rewrite the equation in a more manageable form by subtracting 2x from both sides: 8 = 025x – 2x 2. **Combining like terms**: … Read more

To find all polar coordinates of the point P given in the form of the ordered pair (1, π/3), we need to understand the concept of polar coordinates. Polar coordinates are represented as (r, θ), where: r: The distance from the origin to the point. θ: The angle measured from the positive x-axis to the … Read more