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3 years ago

Let G be a connnectde graph with n vertices and m edges. supposed also that m = n. prove that G contains exactly one cycle

Mathematics

1 answer:

ElenaW [278]3 years ago

7 0

Answer:

Contradiction

Step-by-step explanation:

Suppose that G has more than one cycle and let C be one of the cycles of G, if we remove one of the edges of C from G, then by our supposition the new graph G' would have a cycle. However, the number of edges of G' is equal to m-1=n-1 and G' has the same vertices of G, which means that n is the number of vertices of G. Therefore, the number of edges of G' is equal to the number of vertices of G' minus 1, which tells us that G' is a tree (it has no cycles), and so we get a contradiction.

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Which statement is true about the extreme value of the given quadratic equation?

ICE Princess25 [194]

Answer:

Option B. The equation has a maximum value with a y-coordinate of -21.

Step-by-step explanation:

The correct quadratic equation is

$y=-3x^{2}+12x-33$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

Convert to vertex form

Factor -3

$y=-3(x^{2}-4x)-33$

Complete the square

$y=-3(x^{2}-4x+2^2)-33+12$

$y=-3(x^{2}-4x+4)-21$

Rewrite as perfect squares

$y=-3(x-2)^{2}-21$

The vertex is the point (2,-21)

therefore

The equation has a maximum value with a y-coordinate of -21

3 0

3 years ago

Alex drove 135 miles in 3 hours at a constant speed

Dominik [7]

Speed = distance / time
speed = 135/3 = 45 miles per hr <==

7 0

3 years ago

Two cars leave the same parking lot, with one heading north and the other heading east.

Otrada [13]

Answer:

wouldn't it be 3 kilometers because 3 this way plus 3 that way = 6 away from each other?

8 0

3 years ago

Matt E. Matic was applying for a job. To determine whether he could handle the job, the personnel manager sent him out to poll 1

Rom4ik [11]

Answer:

No; he did the survey incorrectly.

He surveyed 107 people, not 100.

Step-by-step explanation:

Draw a Venn diagram, when you are presented with information like this;

Presenting it in a Venn diagram would look like what is shown in the pic.

P.S. when drawing a Venn diagram, start with the information regarding individuals who fit in all categories and then work your way to the individuals who fit in just in one category.

8 0

3 years ago

What's the solution and answer? And explain please

Advocard [28]

The solution is subtract4.7x on both sides. Then you get -2.2x=7.7. Divide 7.7 by -2.2 and you get x= -3.5

7 0

3 years ago