A bag contains 4 red marbles, 2 blue marbles, 1 purple marble, and 3 green marbles.If a single marble is pulled out of the bag,
2 answers:
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Answer:
see explanation
Step-by-step explanation:
Given
y = x² - 2x - 8
To find the x- intercepts let y = 0 , that is
x² - 2x - 8 = 0 ← in standard form
(x - 4)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 2 = 0 ⇒ x = - 2
x- intercepts : x = - 2, x = 4
The x- coordinate of the vertex is mid way between the x- intercepts, that is
=
=
= 1
Substitute x = 1 into the equation for corresponding y- coordinate
y = 1² - 2(1) - 8 = 1 - 2 - 8 = - 9
vertex = (1, - 9 )
inproper fraction form:
Decimal form:
Mixed number form:
Hope this helps :)
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