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3 years ago

Explain why there can't be a simple graph with the following sequence of vertex degrees: (a) 5,1,1,1

Mathematics

1 answer:

Contact [7]3 years ago

7 0

Answer:

a cant exist because 3 out of the 4 vertices must have only one degree vertex and the remaining one must have 5.

b) This example can be a single graph because of the handshaking lemma. The sum of the odd degrees vertex must be an even number: 3+3+5=11

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My answer is 8, but I'm not completely sure, if I'm wrong could someone please explain how to find the length.

Verdich [7]

By knowing that S is bisected by the line shown, we will conclude that PD = 8

So here we know that PC = 8, we also can see that:

PCS is a right triangle
PDS is a right triangle.

Notice that because the blue line bisects S, the angle at "S" on both of these right triangles is the same, and because both of these are right triangles, both must have a 90° angle.

Finally, if two angles are equal, then the 3 angles must be equal between these two triangles.

And notice that both of these triangles share one side, then:

Triangles we know for sure that triangles PCS and PDS have the same angles and one equal side.

This implies that the triangles are congruent, thus, the measures of the corresponding sides must be the same.

Then the length of the shorter side of both triangles must be the same, in triangle PCS the short leg measures 8 units, then in triangle PDS the short leg, PD, also must measure 8 units.

So you are correct.

If you want to learn more about congruent triangles, you can read:

brainly.com/question/12077512

8 0

2 years ago

Whole numbers are _____ integers. A.always B.sometimes C.never

gulaghasi [49]

The answer to the question is always.

3 0

3 years ago

the inequality |t-57|<7 describes the range of monthly average temperature, T, in Degrees Fahrenheit, for san Francisco, Cali

Y_Kistochka [10]

Solution is: $50\leq T\leq 64$ and it means, the minimum temperature is 50° Fahrenheit and the maximum temperature is 64° Fahrenheit.

Explanation

Given inequality is: $|T-57|\leq 7$

As this is absolute inequality, so we will get two different inequalities-- one for positive and another for negative. So.....

$T-57\leq 7\\ \\ T\leq 7+57\\ \\ T\leq 64$

and

$-(T-57)\leq 7\\ \\ -T+57\leq 7\\ \\ -T\leq 7-57\\ \\ -T\leq -50\\ \\ T\geq 50$

So, the final combined solution will be: $50\leq T\leq 64$

It means that the minimum temperature for San Francisco, California is 50° Fahrenheit and the maximum temperature is 64° Fahrenheit.

7 0

3 years ago

Amy had 23 blocks she gave 7 blocks to isabela and 5 blocks to alexa here are the choices A. (23-7)+5 and B.23-(7+5) and C. 23-7

Semmy [17]

Answer:

C seems right

Step-by-step

seems more work then needs be but 7+5= 12 and she originally had 23. so the equation of adding the 7+5 would just be adding up the ones removed together then adding the -23 to the equation is how many Amy had to begin with. so it would be 23-7+5 = 12. others dont seem right since when you add () to an equation that means your multiplying and you wouldn't be multiplying here and for D to be right it needs to be switched around or you'd end up with a - number and she wouldn't have a - number of blocks. just divide up a problem if need be and break it down to smaller parts to make it easier to deal with.

6 0

3 years ago

Find the area of the figures. lines that appear to be perpendicular are perpendicular

kondor19780726 [428]

You have to use your area equations.like basex height

7 0

3 years ago