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3 years ago

. Given ABCD 2 EFGH, what is the value of X? H Н 6 m 7 m 5 m А D 9 m

Mathematics

1 answer:

Nookie1986 [14]3 years ago

5 0

Answer:

x=6 cm

Step-by-step explanation:

As given in the question that ABCD is congruent to EFGH.

We can say that,

AD <-----> EH {Corresponding Parts Of Congruent Polygons}

AD=EH

We are given that,

$AD=9\\EH=(2x-3)\\Hence,\\As\ AD=EH\\9=2x-3\\9+3=2x\\12=2x\\x=6$

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Use a matrix to solve the system:

Romashka-Z-Leto [24]

Answer:

(2.83 , 1 , 4)

Step-by-step explanation:

$2x+2y-z=4\\4x-2y-2z=2\\3x+3y-4z=-4\\$

Rewrite these equations in matrix form

$\left[\begin{array}{ccc}2&2&-1\\4&-2&-2\\3&3&-4\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\$

we can write it like this,

$AX=B\\X=A^{-1}B$

so to solve it we need to take the inverse of the 3 x 3 matrix A then multiply it by B.

We get the inverse of matrix A,

$A^{-1}=\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right] \\$

now multiply the matrix with B

$X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right]\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}2.83\\1\\4\end{array}\right] \\$

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3 years ago