Answer:
130
Step-by-step explanation:
You want the determinant of the matrix ...
![\left[\begin{array}{ccc}4&3&2\\-3&1&5\\-1&-4&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%263%262%5C%5C-3%261%265%5C%5C-1%26-4%263%5Cend%7Barray%7D%5Cright%5D)
One way to figure it is as the difference between the sum of products of the down-diagonals and the sum of products of the up-diagonals:
D = (4)(1)(3) +(3)(5)(-1) +(2)(-3)(-4) -(-1)(1)(2) -(-4)(5)(4) -(3)(-3)(3)
= 12 -15 +24 +2 +80 +27
D = 130
The determinant of the coefficient matrix is 130.
_____
Many scientific and graphing calculators and web sites can perform this calculation for you.
The diameter of the plate is 9.24 inches
Step-by-step explanation:
Let us consider the radius to be 'r'
Angle = 120°
Chord length = 8 inches
Chord length = 2rsin(θ/2)
8 = 2r sin(120/2)
8 = 2r sin60°
8/2 = r (√3/2)
4/(√3/2) = r
r = 8/√3
r = 8/1.73
r = 4.62 inches
Diameter of the plate = 2(4.62)
= 9.24 inches
The diameter of the plate is 9.24 inches
Answer:40
Step-by-step explanation:
325 students - 5 going in cars.
320 students left / 8 busses = 40 students per bus
Step-by-step explanation:
Z²=x³
Z²=9³
Z= √9³
Z= 27
Answer:
1/a²⁷
Step-by-step explanation:
Given: 
We know that when the bases are same the powers can be added. i.,e.,
(xᵃ)ᵇ = x ⁽ᵃ ⁺ ᵇ⁾
⇒ 
Also, 
This is nothing but,
.
Note that
cannot be zero here. The condition is provided in the question as well.