Which three-dimensional figure has half the number of vertices as the rectangular prism?
2 answers:
1. The rectangular prism is a right prism with rectangular bases (check the picture)
2. It has 8 vertices, so we are looking for 3d figures with 4 vertices.
3. A face can have at least 3 vertices, and the 4th must be outside of the plane determined by the first 3 vertices. This makes 4 vertices in total.
4. The 3d figure described in step 3 is a pyramid.
2. It has 8 vertices, so we are looking for 3d figures with 4 vertices.
3. A face can have at least 3 vertices, and the 4th must be outside of the plane determined by the first 3 vertices. This makes 4 vertices in total.
4. The 3d figure described in step 3 is a pyramid.
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<h3>Answer: A) infinite solutions</h3>
Explanation:
Despite there only being one line shown, there are actually two lines here. One just happens to be directly on top of the other.
We can see this by noting that 2y = 3x-1 turns into 4y = 6x-2 when we multiply both sides by 2. Multiplying both sides by the same number keeps the same equation, so that's why we have identical graphs.
The two identical graphs intersect each other infinitely many times, leading to infinitely many solutions. All solutions are (x,y) points on the blue line. Two such solutions are (1,1) and (3,4). All solutions are of the form