Answer:
We know that the sum of the degrees of the vertices of the graph is twice the number of edges of the graph.
Let 
be a graph with vertices 
Then 
where 
is the number of edges of the graph. Since the graph is regular of degree r then all vertices have degree r. Thus,
Answer:
118
Step-by-step explanation:
E = 41
Colin is 10 years older than Emily. C = E + 10 = 41 + 10 = 51, C = 51
Dan is 15 years younger than Emily. D = E - 15 = 41 - 15 = 26, D = 26
E + C + D = 41 + 51 + 26 = 118
Hope this helps you out :D
It’s 2 equations so in order to solve the previous system, you can use different methods, as for example substitution or addition of equations. In this case, you use the second one, due to the fact you have 7x in one equation and -7x in the other equation. In this way you can easily eliminate variable x and then solve for y. With the value of y you can replace in any of the two equations and solve for x.
7x-y=-1
-7x+3y=-25
Summarizing, you proceed as follow:
- add up the given equations
7x - y = -1
-7x+3y=-25
——————
0 +2y=-26
- solve for y in the previous equation
2y=-26
y=-26/2
y=-13
- replace the obtained value of y in one of the given equations, and solve for x
7x-(-13)=-1
7x+13=-1
7x=-1-13
7x=-14
x=-14
x=-14/7
x=-2
Hence, the solution of the given systems of equation is:
X=-2
Y=-13
What are the answer choices
X + y = 9 Subtract x from both sides.
y = 9 - x
x^2 + y^2 = 53
x^2 + (9 - x)^2 = 53 Remove the brackets.
x^2 + 81 - 18x + x^2 = 53 Collect the like terms on the left.
2x^2 - 18x + 81 = 53 Subtract 53 from both sides.
2x^2 - 18x + 81 - 53 = 0
2x^2 - 18x + 28 = 0 This factors, but you can see it much easier if you pull out 2 as a common factor.
2(x^2 - 9x + 14) = 0
2(x - 2)(x - 7) =0 You could divide by 2 on both sides. But you can also leave it.
x - 2 = 0
x = 2
x - 7 = 0
x = 7
If x = 2 then y = 7
If x = 7 then y = 2
