Let be the path with edges and be the characteristic polynomial of ; recall that = − where is the adjacency matrix of use properties of determinants of adjacency matrices to show that for ≥ 3, = − −1 − −2 it is acceptable to examine a generic adjacency matrix for a path and expand − along the first row

answer: it is 1: 47 pm

answer: the answer is 110

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)

the correct answer is 1.7