Answer:
Option C
Step-by-step explanation:
- For the matrix A of order
to be invertible, its determinant must not be equal to zero, |A| 
0, 
exists if- AC = CA = I, where I is identity matrix.
- The homogeneous equation with coefficient matrix A has a unique solution:
AB = 0, B = 
Thus, B = (0, 0, 0......., 0) is a unique solution
2. The non - homogeneous equation system with coefficient matrix A has a unique solution:
For an equation- AY = D
Y = 
is a unique solution
3. Every non homogeneous equation with coefficient matrix A is not consistent as:
For an equation- AY = D, has a solution.l Thus coefficient matrix is inconsistent whereas augmented matrix is.
4. Rank of matrix A = n, Thus the column space of A is 
5. Since, column space of A = , thus x→xA is one-to-one
Answer:
141
Step-by-step explanation:
CD = | 4-(-2)| = 6
DB = |3-(-7)| = 10
area of a right triangle
A = (leg 1 x leg2)/2 = (6 x 10)/2 = 30
EB = |3-(-3)| = 6
EF = |-8-(-2)| = 6
area of a square = side^2
A = 6^2 = 36
segment G(and a point with same x coordinate of H)
|8-3| = 5
segment H(and the same point)
|-10-(-8)| = 2
A = (5x2)/2 = 5
segment I(and the same point)
|-8-6| = 14
Area of a rectangle
A = base x width
A = (5 x 14) = 70
total area = 70 + 5 + 36 + 30 = 141
Write the ratio as a fraction in the fourth column of the table.
Given: In the given figure, there are two equilateral triangles having side 50 yards each and two sectors of radius (r) = 50 yards each with the sector angle θ = 120°
To Find: The length of the park's boundary to the nearest yard.
Calculation:
The length of the park's boundary (P) = 2× side of equilateral triangle + 2 × length of the arc
or, (P) = 2× 50 yards + 2× (2πr) ( θ ÷360°)
or, (P) = 2× 50 yards + 2× (2×3.14× 50 yards) ( 120° ÷360°)
or, (P) = 100 yards + 2× (2×3.14× 50 yards) ( 120° ÷360°)
or, (P) = 100 yards + 209.33 yards
or, (P) = 309.33 yards ≈309 yards
Hence, the option D:309 yards is the correct option.
If you want to know the concept of square roots and cube roots ?
the square root of a number is that number which when multiplied by itself two times gives us that number
e.g.
√64 = x , so that (x)(x) = 64
and from our multiplication table we know that
(8)(8) = 64 , so that
√64 = 8
the cube root of a number is that number which when multiplied by itself three times gives us that number
e.g.
∛64 = x , so that (x)(x)(x) = 64 , and thus x = 4 because 4x4x4 = 64
so ∛64 = 4
