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nignag [31]
3 years ago
13

A rectangle with an area of 120 in squared has a length of 8 inches longer then two times its width what is the width of the rec

tangle
Mathematics
1 answer:
Vaselesa [24]3 years ago
6 0

Answer:  \\The\: width\: is \: 6 \:  {in}^{2}  \\ \\  Step\: by\: step\: explanation: \\ Let \:  x  \: be \:  the  \: width  \: of  \: the \:  rectangle,\: x > 0\Rightarrow the \: length:2x + 8 \\ We  \: have  \: an \:  equation:x(2x + 8) = 120 \\ \Leftrightarrow 2 {x}^{2}  + 8x  + 8= 128 \\ \Leftrightarrow  {x}^{2}  + 4x   + 4 = 64 \\ \Leftrightarrow {(x + 2)}^{2}  = 64 \\ \Leftrightarrow x + 2 =  \pm8 \\ \Leftrightarrow x = 6 \:  \vee \: x =  - 10 \\ \Rightarrow x = 6 \: (x > 0)

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Which of the below descriptions shows a possible HAMILTON PATH?
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Option B: FECBAD represents the Hamilton path

Explanation:

The vertices in the given graph are A,B,C,D,E and F

We need to determine the Hamilton path of the given graph.

By definition, we know that a Hamilton path touches each and every vertex in a graph exactly once.

Hence, we need to connect the vertices in such a way that the graph touches each and every vertex exactly once.

Option A: EFADECBA

From this description, we can see that the path starts from the vertex E and connects all the vertices but some of the vertices are repeated twice.

Hence, the path EFADECBA is not a Hamilton path.

Therefore, Option A is not the correct answer.

Option B: FECBAD

From this description, we can see that the path starts from the vertex F and connects all the vertices exactly once.

Hence, the path FECBAD is the Hamilton path.

Therefore, Option B is the correct answer.

Option C: ADEFBC

From this description, we can see that the path starts from the vertex A and connects all the vertices but the path from F to B has to touch the vertex A. Thus, the vertices are repeated twice.

Hence, the path ADEFBC is not a Hamilton path.

Therefore, Option C is not the correct answer.

Option D: ADECBAFE

From this description, we can see that the path starts from the vertex A and connects all the vertices but some of the vertices are repeated twice.

Hence, the path ADECBAFE is not a Hamilton path.

Therefore, Option D is not the correct answer.

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