Answer:
The height is 6 inches.
Step-by-step explanation:
Area of the square = length of a side squared.
This square has area 6^2 = 36 in^2.
Area of the parallelogram = base * height
= 6h.
As the areas are equal:
6h = 36
h = 36/6 = 6 inches.
Answer:
y = -5/3 * x - 40/3
Step-by-step explanation:
A perpendicular line has an opposite and a reciprocal of the slope.
Your equation should be:
-5y = -3x +6
Divide all parts by -5.
y = 3/5x - 6/5
Since the perpendicular line has an opposite and a reciprocal of the slope, the slope will be -5/3.
Now you must make an equation in point-slope form. This is an example of that form. You will need at least one point to make this equation work. In this case we have (-8,0).
In put the y and x coordinates like this:
y - 0 = -5/3(x - (-8)
Start solving the equation.
y - 0 = -5/3(x + 8)
y - 0 = -5/3 * x - 40/3
y = -5/3 * x - 40/3
This is your equation.
y = -5/3 * x - 40/3
(You can make it -5/3x in your answer but it looks weird online. You may think that it is -5 divided by 3 times x, but it actually is 5/3 times x. That's why I wrote it as y = -5/3 * x - 40/3)
Answer:
3
Step-by-step explanation:
3 is a possible number of distinct real roots for a cubic function.
The maximum possible number of distinct roots are equal to the degree of any polynomial function.
Hence quadratic function has 2 roots
Cubic has 3
Linear has 1
Answer:
1/2
Step-by-step explanation:
(y2-y1)/(x2-x1) is the equation for finding slope with two given points
-5-(-2) over 3-9 equals
-3/-6=-1/-2=1/2
Answer:
a) ∝A ∈ W
so by subspace, W is subspace of 3 × 3 matrix
b) therefore Basis of W is
={ ![{\left[\begin{array}{ccc}0&1&0\\-1&0&0\\0&0&0\end{array}\right]](https://tex.z-dn.net/?f=%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%260%5C%5C-1%260%260%5C%5C0%260%260%5Cend%7Barray%7D%5Cright%5D)
![,\left[\begin{array}{ccc}0&0&1\\0&0&0\\-1&0&0\end{array}\right]](https://tex.z-dn.net/?f=%2C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%261%5C%5C0%260%260%5C%5C-1%260%260%5Cend%7Barray%7D%5Cright%5D)
![,\left[\begin{array}{ccc}0&0&0\\0&0&1\\0&-1&0\end{array}\right]](https://tex.z-dn.net/?f=%2C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%260%5C%5C0%260%261%5C%5C0%26-1%260%5Cend%7Barray%7D%5Cright%5D)
}
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
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