Which shape has 5 faces, 8 edges and 5 vertices? A. triangular pyramid B. rectangular pyramid C. rectangular prism D. triangular
2 answers:
Answer:
C. Rectangular Pyramid
Step-by-step explanation:
Faces:
A rectangular pyramid has a rectangle as its base. So from it's pinnacle to each of the rectangle's edges, there is a triangular face. As the base has 4 sides, it should have 4 such faces. And the base rectangle is also a face. So it has a total of 5 faces.
So, the number of faces = 5
Edges:
And from its pinnacle to 4 base vertice there are 4 edges. And the base rectangle has four edges. So there are a total of 8 edges
So, the number of edges = 5
Vertice:
The number of vertices must be 5. Becaue we know by Euler's formula
which holds for any shape that doesn't have any hole within it. And 5 is the only value for
that satisfies the equation.
So we can conclude that, the shape must have to be rectangular pyramid.
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Answer:
See attached photo
Step-by-step explanation:
6x-5y>35
- Vertex/General Form: y = a(x - h)^2 + k, with (h,k) as the vertex
- (x + y)^2 = x^2 + 2xy + y^2
- Standard Form: y = ax^2 + bx + c
So before I put the equation into standard form, I'm first going to be putting it into vertex form. Since the vertex appears to be (-1,7), plug that into the vertex form formula:
Next, we need to solve for a. Looking at this graph, another point that is in this line is the y-intercept (0,5). Plug (0,5) into the x and y placeholders and solve for a as such:
Now we know that <u>our vertex form equation is y = -2(x + 1)^2 + 7.</u>
However, we need to convert this into standard form still, and we can do it as such:
Firstly, solve the exponent:
Next, foil -2(x^2+2x+1):
Next, combine like terms and <u>your final answer will be: </u>
Answer:
1).
2).
Step-by-step explanation:
For multiplication of the rational expressions,
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For division of the rational expressions,
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[When the divisor is a rational expression or a rational number, we change the sign from division to multiplication and reciprocate or flip the fraction.
This is applicable for division of the rational expressions only].