1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
liberstina [14]
2 years ago
12

Is it possible for a simple, connected graph that has n vertices all of different degrees? Explain why or why not.

Mathematics
1 answer:
ryzh [129]2 years ago
8 0

Answer:

It isn't possible.

Step-by-step explanation:

Let G be a graph with n vertices. There are n possible degrees: 0,1,...,n-1.

Observe that a graph can not contain a vertice with degree n-1 and a vertice with degree 0 because if one of the vertices has degree n-1 means that this vertice is adjacent to all others vertices, then the other vertices has at least degree 1.

Then there are n vertices and n-1 possible degrees. By the pigeon principle there are two vertices that have the same degree.

You might be interested in
Estimate the product. 0.55 x 2.2
ICE Princess25 [194]

Answer:

2

Step-by-step explanation:

0.55 rounded is 1,

2.2 rounded is 2.

1×2=2

have a great day

7 0
3 years ago
What is the equation of the line that passes through (-3,7) and (1,-1)
balandron [24]

Answer: y = -2x + 1  or y +2x - 1 = 0

Step-by-step explanation

Recall, equation of a line passing through two coordinates is

y - y₁ =  y₂ - y₁              ( x - x₁ )

           ₋₋₋₋₋₋₋₋     x  

           x₂ - x₁

note , (x₁ = -3), (x₂ = 1), (y₁ = 7), (y₂ = -1)

Now substitute for those values in the above equation

y - (7) = -1 - 7

            ------         X  ( x - (-3)

            1 - (-3)

y - 7   =  -8/4  X  ( x + 3 )

y - 7   = -2(x + 3 )

y - 7   = -2x - 6

The equation now

y  =  -2x -6 + 7

y = -2x + 1  or

y + 2x - 1 = 0.

6 0
3 years ago
A golfer needs to know how tall a tree is to chip a ball over the tree onto the green in a golf match. his caddie knows that he
Inga [223]
The height of the trre will be given by:
tan θ=(opposite)/(adjacent)

θ=52°
Adjacent= distance of the golfer to the tree= 10 ft
opposite = height, h, of the tree
thus
tan 52=h/10
hence solving for h we get:
h=10tan52
h=12.799~12.8 ft

7 0
3 years ago
Movie A took in $142.44 million on it’s first weekend. This topped the previous opening weekend revenue set by movie B by $4.14
stepladder [879]
Revenue of Movie A on first weekend = $ 142.44 million

According to the given statement, revenue of movie A was $4.14 million more than the revenue of movie B in their first weekends.

So, we can write:

Revenue of movie A = Revenue of movie B + $4.14 million

Revenue of movie B = 142.44 million - 4.14 million = $ 138.30 million.

Thus movie B take in $138.30 million on its opening weekend. 
6 0
3 years ago
PLEASE HELP ASAP!!
Andru [333]

Answer:

x^3+4x^2+x−6

c

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • Which list correctly orders A,B and C from least to greatest when A=-8,B= |-6|, and C=|11|
    8·2 answers
  • Please answer this in two minutes
    7·1 answer
  • Is three fourths equal to five six’s
    6·2 answers
  • Determine the y-intercept of the
    13·1 answer
  • A prism is completely filled with 1120 cubes that have Edge Length of 1/2 inc what is the volume of the prism
    6·1 answer
  • A random sample of cats at the SPCA shows that 25 out of the 40 cats are kittens. There are a total of 800 cats at all the anima
    15·1 answer
  • Part I : Write the type of polynomial next to the terms (monomial, binomial, trinomial)
    6·1 answer
  • Find the value of x. X= ?<br> Chords And Arcs
    12·1 answer
  • A desk drawer is shaped like a rectangular prism. The height of the drawer is 7 inches. The bottom of the drawer has an area of
    12·1 answer
  • Which properties to evaluate 7/5 (1/4 divided by 7/4) (-10)
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!