Is the sequence 13, 20, 27, 34 an arithmetic sequence? If so, what is the common difference?

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

What kind of transformation maps a regular pentagon with center (0, 2) onto itself?

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

What figure represents the image of the parallelogram LMNP after reflecting it across the line y = x?

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