Express the inverse of the following matrix (assuming it exists) as a matrix containing expressions in terms of k. [-25 -25 -25]^-1 [0 0 0]
[ k 0 3] = [0 0 0]
[-5 -5 -3] [0 0 0]

the Inverse of the matrix is; A⁻¹

Step-by-step explanation:

Given the data in the question;

Matrix A =

To find the Inverse of matrix A

A⁻¹ = Adj.A / det.A

so

Determinant of the matrix A will be

|A| = -25( 0 + 15) + 25( -3K + 15 ) - 13( -15K + 0 )

= -375 - 75K + 375 + 65K

= -10K

Now, the adjoin of matrix A will be

Adj.A =

The Inverse of the matrix is;

A⁻¹ = Adj.A / det.A

Therefore the Inverse of the matrix is; A⁻¹

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.