What is the solution of 9x – 8 = 34x – 12?

Step-by-step explanation:

Let  

V

be the number of vertices of a polyhedron,  

F

the number of faces of that polyhedron, and  

E

be the number of edges. The quantity  

χ

=

V

−

E

+

F

is called the Euler characteristic (of a polyhedron). In the case of convex polyhedra,  

χ

=

2

.

Consider, for example, a tetrahedron (which is the simplest solid). It has 4 faces,  

1

2

(

4

)

(

3

)

=

6

edges, and  

1

3

(

4

)

(

3

)

=

4

vertices. Thus we have  

V

−

E

+

F

=

4

−

6

+

4

=

2

.

Euler's formula holds for all Platonic solids (tetrahedron, cube, octahedron, dodecahedron, and icosahedron). Since a cube and an octahedron are dual polyhedra (each is formed by connecting the centers of the faces of the other), their  

V

and  

F

values are equal to the  

F

an  

V

values of the other. (The same is true for the dodecahedron and icosahedron).

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.