Question

State whether the following statements are true or false.

(a) A polyhedron can have 12 faces, 22 edges and 17 vertices.

(b)All square are rectangles.

(c) x 2 + (a + b) x + ab = (x 2 + a) (bx + ab).

(d)If 21a327 is divisible by 3, then the value of a can be 0.

(e) The sum of the measures of the external angles of a hexagon is 360º.​

Answer 1

Answer:

Heya!!

Here's your answer..

(a) False

(b) True

(c) False

(d) True

(e) True

Step-by-step explanation:

(a) According to Euler's Formula for polyhedrons

F+V= E+2

12+17 = 22+2

29 is not equal to 24.

(b) Every square is a rectangle because it is a quadrilateral with all four angles right angles.

(c) x 2 + (a + b) x + ab = (x 2 + a) (bx + ab)

x 2 + ax + bx +ab = bx 2 + x 2 ab+ abx+a2b

(d) Divisibility by 3= sum of digits must be divisible by 3.

21a327 where a=0

2+1+0+3+2+7= 15

(e) Each exterior angle of a regular polygon of n sides = 360° / n

360°/6

= 60°

Number of exterior angles of a hexagon= 6

60°×6

=360°

Hope It Helps You  :)

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