1. a polyhedron has 6 vertices and 9 edges. how many faces does it have? a. 3 b. 5 c. 7 d. 9 2. a polyhedron has 25 faces and 36 edges. how many vertices does it have? a. 11 b. 12 c. 13 d. 14 3. what is the cross section formed by a plane that contains a vertical line of symmetry for a tetrahedron? a. triangle b. square c. rectangle d. pentagon 4. what is the cross section formed by a plane that intersects three faces of a cube? a. triangle b. square c. rectangle d. pentagon

Hello Madoudou!

#1

So we have:

F which is the number of faces we are looking for

E which are the numbers of edges

and V the number of vertices

We can use the Euler's polyhedron formula. Which is:

V - E + F = 2

Remember we are solving for F. Thus,

F = E - V + 2

F = 9 - 6 + 2

F = 9 - 4

F = 5

The correct answer is option B

#2

It is almost the same problem. They just want us to find the vertices.

V = E - F + 2

V = 36 - 25 + 2

V = 36 - 23

V = 13

The correct answer is option C

#3

The cross section formed by a plane that contains a vertical line of symmetry for a tetrahedron is a Triangle.

The correct answer is option A

#4

The cross section formed by a plane that intersects three faces of a cube is a Triangle.

The correct answer is option A

Let me know if you have any questions about the answers. As always, it is my pleasure to help students like you.

Polyhedron is three-dimensional solid which consist collection of polygons joint with edges.

The option B is the correct option for problem 1.The option C is the correct option for problem 2.The option A is the correct option for problem 3.The option A is the correct option for problem 4.

Polyhedron

Polyhedron is three-dimensional solid which consist collection of polygons joint with edges.

The Euler's formula between the vertex, edges and faces can be given as,

Here is the number of faces, is the number of the vertex and is the number of edges of the polyhedron.

1) The polyhedron which has 6 vertices and 9 edges,

Use the Euler's formula to find the faces as,

Thus the polyhedron which has 6 vertices and 9 edges has 5 number of faces. The option B is the correct option for problem 1.

2) The polyhedron which has 25 faces and 36 edges,

Use the Euler's formula to find the faces as,

Thus the polyhedron which has 25 faces and 36 edges has 13 number of vertex. The option C is the correct option for problem 2.

3) The cross section formed by a plane that contains a vertical line of symmetry for a tetrahedron-

Tetrahedron is a triangular pyramid with four triangular faces. Thus The cross section formed by vertical line contained plane of symmetry for a tetrahedron is triangle. Thus The option A is the correct option for problem 3.

4) The cross section formed by a plane that intersects three faces of a cube-

When a plane intersect the cube with three of its faces the cross section of that plane is a triangle. Thus The option A is the correct option for problem 4.

Hence,

The option B is the correct option for problem 1.The option C is the correct option for problem 2.The option A is the correct option for problem 3.The option A is the correct option for problem 4.

Learn more about the polyhedron here;

link

f(x) = 36 (1/16)

Step-by-step explanation:

because when its ^2x you multiply the same number for exapmple6*6 is 36 1*1 is 1 and 4*4 is 16 so thats  how i got the answer