Geometry

The shape in the question consists of several geometric components that need to be arranged to form the desired shape. The components in the given shape are a combination of triangles, rectangles, and other geometric figures. We need to analyze the available groups to determine which one can be assembled to form the target shape. Let’s break down the solution step-by-step: Step 1: Understanding the given shape.
The shape consists of two large triangular sections with a smaller triangular section at the top and a rectangular section in between. It is crucial to notice the relative positioning of the shapes and the angles, which suggest the need for specific rotations and translations to arrange the parts in the desired way. Step 2: Evaluating the options.
Let’s now analyze each option: - Option (A) Group 1: This group contains two triangles and a rectangle. If we attempt to assemble these shapes, we can notice that while the group has the right shapes, the positioning does not align properly to form the desired structure. The arrangement of the triangles does not match the required shape. - Option (B) Group 2: This group contains a combination of shapes that exactly match the structure of the given shape. By rotating and translating the pieces, we can assemble them into the desired configuration. The triangles can be rotated to fit into the correct positions, and the rectangle fits perfectly in between the two triangles, forming the exact shape shown in the question. - Option (C) Group 3: This group contains a similar set of shapes but with additional extra components that do not fit the structure. The extra pieces create a mismatch and cannot be used to form the target shape. - Option (D) Group 4: This group also has the necessary shapes, but the arrangement and the size of the components do not fit correctly. Even after rotation and translation, the pieces do not align properly to match the given shape. Step 3: Conclusion.
After carefully evaluating all the options, it is clear that Group 2 (Option B) is the correct choice. This group can be assembled into the exact shape shown in the question by rotating and translating each piece appropriately. Thus, the correct answer is (B) Group 2.

Let us first evaluate and .
Step 1: Evaluate
From the given formula for : Step 2: Evaluate
From the given formula for : Step 3: Compare the results.
Since and , we conclude that . Therefore, the correct answer is (A).

First, let's solve the inequality: Multiply both sides by 3 to eliminate the denominator: Expanding both sides: Now, move the terms involving to one side: Simplifying: Now, divide by 9: Thus, the solution is , which corresponds to a closed circle on and extending to the right. The representation that matches this solution is option (C).