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To understand how to derive 35 from the expression 27 – 8, we first need to clarify the identity involved. There’s a fundamental polynomial identity known as the subtracting a constant identity, which states that: f(x) = ax^2 + bx + c where the constants replace the values present in the expression. However, in this … Read more

Yes, the sequence 13, 20, 27, 34 is indeed an arithmetic sequence. An arithmetic sequence is defined as a sequence of numbers in which the difference between consecutive terms is constant. This constant difference is known as the common difference. To find the common difference, we can subtract each term from the term that follows … Read more

To understand the transformation that maps a regular pentagon onto itself, particularly one centered at the point (0, 2), we need to explore the geometric properties of regular polygons. A regular pentagon has rotational and reflectional symmetries. For a pentagon, the notable transformations include: Rotations: The pentagon can be rotated about its center. In our … Read more

To find the slope of the tangent line to the function y = x² + 2x + 3 at the point x = 1, we first need to calculate the derivative of the function. The derivative represents the slope of the tangent line at any given point on the curve. The first step is to … Read more

To find the equation of the plane consisting of all points that are equidistant from the points A(1, 0, 2) and B(3, 4, 0), we start by recalling that a plane can be determined by a point and a normal vector or can be defined as all the points that satisfy a specific distance condition. … Read more

To determine whether the product of two even functions, f and g, is also an even function, let’s start by recalling the definition of an even function. A function h(x) is considered even if it satisfies the following condition for all x in its domain: h(-x) = h(x) Now, since both f and g are … Read more

To find the slope of a line that passes through two points, you can use the slope formula: Slope (m) = (y2 – y1) / (x2 – x1) In this case, you have the points (1, 3) and (3, 5). Here: (x1, y1) = (1, 3) (x2, y2) = (3, 5) Now, plug the coordinates … Read more

To solve the system of linear equations given by: Equation 1: 3y + x = 6 Equation 2: y + x = 3 We can use the substitution or elimination method. Here, let’s use the substitution method for clarity. Step 1: Solve one equation for one variable We can start with Equation 2: y + … Read more

To determine the image of the parallelogram LMNP after reflection across the line y = x, we need to follow a systematic approach: Understand the reflection process: When a point (x, y) is reflected across the line y = x, its coordinates are swapped. Therefore, the new coordinates become (y, x). Identify the original vertices: … Read more

To determine whether a geometric series is convergent or divergent, we first need to identify the common ratio (r) between subsequent terms. A geometric series converges if the absolute value of the common ratio is less than 1 (< |r| < 1) and diverges otherwise. Let’s analyze the series: First term (a) = 8 Second ... Read more