If X and Y vary directly, as x decreases, what happens to the value of y?

How many edges must be removed from the wheel graph W6 in order to create a spanning tree for the graph?

sveticcg [70]

Answer:

The correct option is A.

Step-by-step explanation:

If a graph is formed by connecting a single universal vertex to all vertices of a cycle, then it is known as wheel graph.

W₆ means wheel graph having 6 vertices as shown in the below figure.

Total number of edges in a wheel graph is 2(n-1), where n is number of vertices. So, the number of edges in W₆ is

$2(6-1)=10$

In a spanning tree all the vertices covered with minimum possible number of edges. Total number of edges in a spanning tree is (n-1).

Total number of edges in a spanning tree which has 6 vertices is

$6-1=5$

The number of edges we need to remove is

$10-5=5$

Therefore the correct option is A.

5 0

3 years ago

A polygon has vertices whose coordinates are A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1). Use the midpoint formula to determine w

Alenkinab [10]

Answer:

The diagonals of the polygon ABCD bisect each other

Step-by-step explanation:

The given vertices of the polygon are;

A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1)

Given that the vertices of the polygon in clockwise order from the top left corner are ABCD, we have the diagonals as AC and DB

By the midpoint formula, we have;

$(x_m , \ y_m) = \left (\dfrac{x_1 + x_2}{2} , \ \dfrac{y_1 + y_2}{2} \right )$

Where;

$(x_m , \ y_m)$ = The midpoint coordinates

Therefore, the midpoint of diagonal AC = $\left (\dfrac{1 + (-1)}{2} , \ \dfrac{4 + (-4)}{2} \right ) = (0, 0)$

The midpoint of diagonal DB = $\left (\dfrac{(-4) +4}{2} , \ \dfrac{1 + (-1)}{2} \right ) = (0, 0)$

Therefore, given that the coordinates of the location of the midpoint of the diagonals AC and DB is the same, the diagonals bisect each other

Each diagonal passes through the midpoint of the other diagonal.

3 0

3 years ago

Please help ! Desperate here !<br><br> Evaluate the expression :<br><br> 2{5[12+5(500-100)+399]}

-Dominant- [34]

Answer:

hope this will help

Step-by-step explanation:

3 0

3 years ago

The graph of f(x) is shown below. where is f(x) < 0? write your answer in interval notation.

Bad White [126]

Answer:

The graph of f(x) passes through (1,1) , (2,1.4...), (3,1.7....),(4,2)......

As, this curve is not linear.

To find the graph of a inverse function if a function is given

As we can see that ,

√1=1

√2=1.414..

√3=1.732..

√4=2

it means, √x=y is f(x).

So, to find the inverse of f(x), follow the procedure

Squaring both sides

Replace x by y and y by x to get inverse of f(x)

So,there will be two inverses of f(x)

1. x=√y

2. x= -√y

Domain of g(x)∈[0,∞], means y≥0.

Option A, 2nd graph below. and Option B. 3 rd Graph below is true regarding graph of g(x).

3 0

3 years ago

Multiply your answer in the first question (the number of

Kisachek [45]

The lines on a basketball form a half circle at the free throw line. Use the picture to determine the area of the half circle. Round your answer to the nearest tenth.

7 0

3 years ago