Answer:
y = (1/2)x + 0
Step-by-step explanation:
The equation would be y = mx + b
m is the slope and b is the y-intercept
If the question is y = blank(x) + blank (I can’t see the left of the equation
Then the answer is y = 2x + -4
Let's plug in each coordinate and see what we get:
(2, 0, 0)
-> 2A + 0 + 0 = D
-> 2A = D
-> A = D/2
(0, 6, 0)
-> 0 + 6B + 0 = D
-> 6B = D
-> B = D/6
(0, 0, 5)
-> 0 + 0 + 5C = D
-> 5C = D
-> C = D/5
plugging this back into the equation:
(D/2)x + (D/6)y + (D/5)z = D [then divide through by D]
(1/2)x + (1/6)y + (1/5)z = 1
and since we have to have integer coefficients,
multiply through by 30
so we get
15x + 5y + 6z = 30
Second question
<span>Take a look at the bottom-left point in the picture.
If you move three points in the y-direction, you'll reach to the point A.
If you instead move up 4 points (or in the z-direction), you reach D.
And finally, if you walk back to point F from point E, you'll have moved back 4 points in the x direction. </span>
<span>This gives us our measurements, or dimensions: 3 x 4 x 4.
If this were a rectangular prism, the dimensions would just be each of them multiplied.
But since it's triangular, you need to divide it by two. That gives you a total volume of
(3x4x4)/2 = 24.</span>
The MN matrix is ![\left[\begin{array}{ccc}-2 & 1 & 0 \\17 & 2 & -3\\11 & 12 & -5\end{array}\right]\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%20%26%201%20%26%200%20%5C%5C17%20%26%202%20%26%20-3%5C%5C11%20%26%2012%20%26%20-5%5Cend%7Barray%7D%5Cright%5D%5C%5C)
.
What is matrix?
A matrix is a rectangular array or table with rows and columns of numbers, symbols, or expressions that is used to represent a mathematical object or an attribute of one. is a matrix having two rows and three columns, for instance.
Given ![M=\left[\begin{array}{cc} 1 & 0 \\ -4 & 3 \\ 2 & 5 \end{array}\right]](https://tex.z-dn.net/?f=M%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%201%20%26%200%20%5C%5C%20-4%20%26%203%20%5C%5C%202%20%26%205%20%5Cend%7Barray%7D%5Cright%5D)
![N=\left[\begin{array}{ccc}-2 & 1 & 0 \\3 & 2 & -1\end{array}\right]](https://tex.z-dn.net/?f=N%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%20%26%201%20%26%200%20%5C%5C3%20%26%202%20%26%20-1%5Cend%7Barray%7D%5Cright%5D)
M is a matrix with 3 * 2 dimension and N is a matrix with 2 * 3 dimension.
So finding MN is possible and the dimension will be 3 * 3.
Now,
![MN=\left[\begin{array}{cc}1 & 0 \\-4 & 3 \\2 & 5\end{array}\right] \times \left[\begin{array}{ccc}-2 & 1 & 0 \\3 & 2 & -1\end{array}\right]\\= \left[\begin{array}{ccc}1 \times (-2)+0 \times 3 & 1 \times 1+0 \times 2 & 1 \times 0+0 \times (-1) \\(-2) \times (-4)+3 \times 3 & (-4) \times 1+3 \times 2 & (-4) \times 0+3 \times (-1) \\2 \times (-2)+5 \times 3 & 2 \times 1+5 \times 2 & 2 \times 0+5 \times (-1) \\\end{array}\right]\\](https://tex.z-dn.net/?f=MN%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%20%26%200%20%5C%5C-4%20%26%203%20%5C%5C2%20%26%205%5Cend%7Barray%7D%5Cright%5D%20%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%20%26%201%20%26%200%20%5C%5C3%20%26%202%20%26%20-1%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%20%5Ctimes%20%28-2%29%2B0%20%5Ctimes%203%20%26%201%20%5Ctimes%201%2B0%20%5Ctimes%202%20%26%201%20%5Ctimes%200%2B0%20%5Ctimes%20%28-1%29%20%5C%5C%28-2%29%20%5Ctimes%20%28-4%29%2B3%20%5Ctimes%203%20%26%20%28-4%29%20%5Ctimes%201%2B3%20%5Ctimes%202%20%26%20%28-4%29%20%5Ctimes%200%2B3%20%5Ctimes%20%28-1%29%20%5C%5C2%20%5Ctimes%20%28-2%29%2B5%20%5Ctimes%203%20%26%202%20%5Ctimes%201%2B5%20%5Ctimes%202%20%26%202%20%5Ctimes%200%2B5%20%5Ctimes%20%28-1%29%20%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C)
![=\left[\begin{array}{ccc}-2 & 1 & 0 \\17 & 2 & -3\\11 & 12 & -5\end{array}\right]\\](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%20%26%201%20%26%200%20%5C%5C17%20%26%202%20%26%20-3%5C%5C11%20%26%2012%20%26%20-5%5Cend%7Barray%7D%5Cright%5D%5C%5C)
Therefore the MN matrix is .
To learn more about matrix from the given link
brainly.com/question/94574
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