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fgiga [73]
2 years ago
7

In rectangle ABCD, point E lies halfway between sides AB and CD and halfway between sides AD and BC. If AB=6 and BC=9, what is t

he area of the shaded region? Write your answer as a decimal, if necessary. Do not include units in your answer.
Mathematics
1 answer:
zloy xaker [14]2 years ago
4 0

Answer:

Height=9/2=4.5

A=1/2*b*h

A=1/2*6*4.5

A=13.5

13.5*2=27

The area of the shaded region is 27.

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For the system of equations that follows, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in
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Answer:

\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}

Step-by-step explanation:

From the question we are told that

System of equations given as

x₁ + 3x₂ + x₃ + x₄ = 3;

2x₁ - 2x₂ + x₃ + 2x₄ = 8;

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Matrix form

\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}  \begin{Vmatrix}x_1\\x_2\\x_3\\x_4\end{Vmatrix}

Generally the echelon reduction is mathematically applied as

\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}

Add -2 times the 1st row to the 2nd row

\begin{Vmatrix}1 & 3 & 1&1&3\\0 & -8 & -1&0&2\\0&1 & -5 & 1& 5\end{Vmatrix}

Multiply the 2nd row by -1/8  

\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&1 & -5 & 1& 5\end{Vmatrix}

Add -1 times the 2nd row to the 3rd row

\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & -41/8 & 1& 21/4\end{Vmatrix}

Multiply the 3rd row by -8/41

\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}

Add -1/8 times the 3rd row to the 2nd row

Add -1 times the 3rd row to the 1st row

\begin{Vmatrix}1 & 3 & 0&49/41&165/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}

Add -3 times the 2nd row to the 1st row

\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}

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3 years ago
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Prime factorization

11340 | 2
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  567  | 3
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We observ that the possible length of the side is 18( we have 35 small squares ).
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