Please help me! This is for my math homework and if i get it wrong I will have to start over

PLEASE HELP I AM ON A TIME LIMIT

Alinara [238K]

Answer:

(a) even: J, K, M, O; odd: L, N

(b) L and O are connected to J

(c) N is of degree 3

Step-by-step explanation:

Count the edge ends that intersect each vertex. You get ...

J-2, K-2, L-3, M-2, N-3, O-4

These numbers are the degree of the vertex.

a) Vertices with even degree are J, K, M, O, since these have degrees of 2, 2, 2, and 4, respectively--all even numbers.

Vertices with odd degree are L and N, since these both have degree 3, an odd number.

__

b) The vertices that are adjacent to J are the ones at the other ends of the edges that intersect vertex J. One of those two edges connects to vertex L; the other to vertex O. J is adjacent to L and O.

__

c) When we counted edges in part (a), we found vertex N to be of degree 3.

5 0

2 years ago

A school wishes to enclose its rectangular playground using 480 meters of fencing.

Harlamova29_29 [7]

Answer:

Part a) $A(x)=(-x^2+240x)\ m^2$

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

$P=2(L+W)$

we have

$P=480\ m\\L=x\ m$

substitute

$480=2(x+W)$

solve for W

$240=x+W\\W=(240-x)\ m$

Find the area of the rectangular playground

The area is given by

$A=LW$

we have

$L=x\ m\\W=(240-x)\ m$

substitute

$A=x(240-x)\\A=-x^2+240x$

Convert to function notation

$A(x)=(-x^2+240x)\ m^2$

Part b) What side length x gives the maximum area that the playground can have?

we have

$A(x)=-x^2+240x$

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

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

$A(x)=-x^2+240x$

Factor -1

$A(x)=-(x^2-240x)$

Complete the square

$A(x)=-(x^2-240x+120^2)+120^2$

$A(x)=-(x^2-240x+14,400)+14,400$

$A(x)=-(x-120)^2+14,400$

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

$x=120\ m$

$W=(240-120)=120\ m$

The playground is a square

$A=120^2=14,400\ m^2$

8 0

3 years ago

What expression can be used to determine the total cost of buying c pounds of cashews for $3.85

Anna [14]

Answer:

B

Step-by-step explanation:

8 0

3 years ago

(72-y)+(26-X) when x=9,y=51

disa [49]

Answer:

38

Step-by-step explanation:

(72-51)+(26-9)

21+17

38

7 0

3 years ago

What is the result when the number 20 is decreased by 75%?\

Viefleur [7K]

Answer:

5

Step-by-step explanation:

If 20 is decreased by 75%, you would have to do 20×0.25 because 1.00-0.75= 0.25. Therefore, the answer to your question would be 5.

Hope this was helpful!!!

8 0

3 years ago