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

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

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,

Learn more about the polyhedron here;

link

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this