Answer:n= 1/3d - 2/3m
Step-by-step explanation:
d=2m+3n
Step 1: Flip the equation.
2m+3n=d
Step 2: Add -2m to both sides.
2m+3n+−2m=d+−2m
3n=d−2m
Step 3: Divide both sides by 3.
3n/3 = d-2m/3
Therefore
n= 1/3d - 2/3m
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Answer:
n = d - 2m
3*
Step-by-step explanation:
First we want to get n alone on one side, so we should subtract 2m from both side;
d = 2m + 3n
3n = d - 2m
Now to get n by itself, we need to divide by 3 from both sides;
3n = d - 2m
n = d - 2m
3*
*Pretend there is a fraction bar between d - 2m and 3
Step-by-step explanation:
Option D. D has the matrix of constants [[12], [11], [4]].
Step-by-step explanation:
Step 1:
With the given equations, we can form matrices to represent them.
The coefficients of x, y, and z form a matrix of order 3 ×3, the variables x, y, and z form a matrix of order 1 ×3 and the constants form a matrix of order 1 ×3.
Step 2:
The linear system A is represented as
![\left[\begin{array}{ccc}12&1&1\\1&-11&0\\1&-1&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D12%261%261%5C%5C1%26-11%260%5C%5C1%26-1%264%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}x\\y\\z\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D)
![= \left[\begin{array}{ccc}26\\17\\23\end{array}\right]](https://tex.z-dn.net/?f=%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D26%5C%5C17%5C%5C23%5Cend%7Barray%7D%5Cright%5D)
.
Step 3:
The linear system B is represented as
![\left[\begin{array}{ccc}4&1&1\\1&-11&0\\1&-1&12\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%261%261%5C%5C1%26-11%260%5C%5C1%26-1%2612%5Cend%7Barray%7D%5Cright%5D)
![= \left[\begin{array}{ccc}23\\17\\26\end{array}\right]](https://tex.z-dn.net/?f=%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D23%5C%5C17%5C%5C26%5Cend%7Barray%7D%5Cright%5D)
.
Step 4:
The linear system C is represented as
![\left[\begin{array}{ccc}1&1&1\\1&-1&0\\1&-1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%261%5C%5C1%26-1%260%5C%5C1%26-1%261%5Cend%7Barray%7D%5Cright%5D)
![= \left[\begin{array}{ccc}4\\11\\12\end{array}\right]](https://tex.z-dn.net/?f=%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C11%5C%5C12%5Cend%7Barray%7D%5Cright%5D)
.
Step 5:
The linear system D is represented as
![= \left[\begin{array}{ccc}12\\11\\4\end{array}\right]](https://tex.z-dn.net/?f=%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D12%5C%5C11%5C%5C4%5Cend%7Barray%7D%5Cright%5D)
.
Step 6:
Of the four options, the linear system D has the matrix of constants [[12], [11], [4]]. So the answer is option D. D.
Answer:
Formula for area of a circle;
<u>A = πr^2</u>
where pi is 3.14 in this case, and r is the radius squared
Plug in the actual values;
A = 3.14 x 11^2
A = 3.14 x 121
A = 379.94 square feet
Answer:
The possible lengths and widths of the prism will be all those positive ordered pairs whose multiplication is equal to
Step-by-step explanation:
we know that
The volume of a rectangular prism is equal to
where
B is the area of the rectangular base
h is the height of the prism
In this problem we have
substitute and solve for B
-----> area of the rectangular base
therefore
The possible lengths and widths of the prism will be all those positive ordered pairs whose multiplication is equal to
Step-by-step explanation:
Answer:
7.429 cents
Step-by-step explanation:
Given that:
Price change = $1.51 to $2.03
Period of time = 7 years
Therefore, the annual inflation rate :
Difference in price / number of years
($2.03 - $1.51) / 7
$0.52 / 7
= 0.0742857 per year
= 0.0742857 * 100 (about 7.429 cents per year)
