Let us recall that the famous fibonacci sequence: 0; 1; 1; 2; 3; 5; 8; 13; 21; : : : is de ned as follows: we put '0 = 0, '1 = 1 and de ne 'n+2 = 'n+1 + 'n: we want to nd a formula for 'n. to do this a) find a 2 2 matrix a such that 'n+2 'n+1 = a 'n+1 'n hint: combine the trivial equation 'n+1 = 'n+1 with the fibonacci relation 'n+2 = 'n+1 + 'n. b) diagonalize a and nd a formula for an. c) noticing that 'n+1 'n = an '1 '0 = an 1 0 nd a formula for 'n. (you will need to compute an inverse and perform multiplication here). d) show that the vector ('n+1='n; 1)t converges to an eigenvector of a. what do you think, is it a coincidence?

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

if im not mistaking its

step-by-step explanation:  

i would love   to but there is no graph shown

step-by-step explanation:

i am so sorry

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.