Answer: x - 5/x + 1
Step-by-step explanation:
This algebraic fraction
The task to be performed here is factorisation and simplification. Now going by the question,
x² + 4x - 45/x² + 10x + 9, the factorisation of
x² + 4x - 45 = x² + 9x - 5x - 45
= x(x + 9 ) - 5(x + 9 )
= ( x + 9 )(x - 5 ), don't forget this is the algebraic fraction's Numerator
The second part
x² + 10x + 9 = x² + x + 9x + 9
= x(x + 1) + 9( x + 1 )
= ( x + 9 )( x + 1 ), this is the algebraic denominator.
Now place the second expression which is the denominator under the first expression which is the numerator.
( x + 9 )( x - 5 )/( x + 9 )( x + 1 ).
You can see that, ( x + 9 )/( x + 9 ) divide each other , therefore therr then cancelled and left with
x - 5/x + 1
Answer:
a) ∝A ∈ W
so by subspace, W is subspace of 3 × 3 matrix
b) therefore Basis of W is
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}
Step-by-step explanation:
Given the data in the question;
W = { A| Air Skew symmetric matrix}
= {A | A = -A^T }
A ; O⁻ = -O⁻^T O⁻ : Zero mstrix
O⁻ ∈ W
now let A, B ∈ W
A = -A^T B = -B^T
(A+B)^T = A^T + B^T
= -A - B
- ( A + B )
⇒ A + B = -( A + B)^T
∴ A + B ∈ W.
∝ ∈ | R
(∝.A)^T = ∝A^T
= ∝( -A)
= -( ∝A)
(∝A) = -( ∝A)^T
∴ ∝A ∈ W
so by subspace, W is subspace of 3 × 3 matrix
A ∈ W
A = -AT
A = ![\left[\begin{array}{ccc}o&a&b\\-a&o&c\\-b&-c&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Do%26a%26b%5C%5C-a%26o%26c%5C%5C-b%26-c%260%5Cend%7Barray%7D%5Cright%5D)
= ![a\left[\begin{array}{ccc}0&1&0\\-1&0&0\\0&0&0\end{array}\right]](https://tex.z-dn.net/?f=a%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%260%5C%5C-1%260%260%5C%5C0%260%260%5Cend%7Barray%7D%5Cright%5D)
![+b\left[\begin{array}{ccc}0&0&1\\0&0&0\\-1&0&0\end{array}\right]](https://tex.z-dn.net/?f=%2Bb%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%261%5C%5C0%260%260%5C%5C-1%260%260%5Cend%7Barray%7D%5Cright%5D)
![+c\left[\begin{array}{ccc}0&0&0\\0&0&1\\0&-1&0\end{array}\right]](https://tex.z-dn.net/?f=%2Bc%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%260%5C%5C0%260%261%5C%5C0%26-1%260%5Cend%7Barray%7D%5Cright%5D)
therefore Basis of W is
={ }
Answer:
v=2
Step-by-step explanation:
9v-3v=12
6v=12
v=2
You just put the numbers in the formula 3x30 = 90 km
There is 50 which is greater than 10 but no number is less than 15
