1. Prove the below statements: A. K7 has 21 edges. Use the theorem. B. C6 is bipartite, but C5 is not. C. K2,3 has 6 edges and 5 vertexes. Use the theorem.

Q: What is the number of edges and the degree of each vertex in a graph a) 4-regular of order n = 15?…

A:

Q: Consider a convex polyhedon P with 3 square faces and 6 regular pentagon faces such that each vertex…

A: Solution :- Euler's Formula for convex polyhedron is given as :- V-E+F = 2 Where, E = No. of edges V…

Q: Prove that quadrilateral PLUS with the vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle.

A: 1) Opposite sides are equal , 2) The diagonals of a rectangle are equal.  Distance formula of point…

Q: Alper is the owner of Cube-XYZ, a perfect cube-shaped planet, and builds a mansion on one vertex of…

A: According to given conditions and labeling. 1. Alper  is at Mension (M). 2. Wes is diagonally…

Q: When K100 and C47 share exactly 20 vertices, all of which are consecutive in C47, how many edges…

A: Total number of edges in K100 = (100*99)/2          =  4950 Total number of edges in C47  = 47 If…

Q: Consider the two rows of points on the grid below. Count the number of triangles that can be formed…

A: The two rows grid is given as: In both rows, there are 8 points in each. Therefore there are total…

Q: Prove that quadrilateral PLUS with the vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle.…

A:

Q: Consider the two rOws of polnts on the grid below. (a) Count the number of quadrilaterals that can…

A: PART B To form rectangles first join subsequent 2 dots, No. of rectangles = 8 To form rectangles by…

Q: 3- Compute the following equation by using a) Single loop b) No-loop 19 Mn] EMA[n +k]

A: h = 1:19 % create a vector h x = 12:30 % create a vector x

Q: 1. Use Euler's formula to find the missing number Vertices: 15 Edges: 24 Faces: ? 09 10 O11 O12

A: If in a rigid solid F represent the number of facesE represent the number of edgesV represent the…

Q: Find the area of a parallelogram having the vertices P(1, 1, -1), Q(4, 2, 1), and R(6,3,1) O √13 O…

A: To find the area of a parallelogram having the vertices P1, 1, -1, Q4, 2, 1 and R6, 3, 1.

Q: Given the following isometric drawing, how many edges will be drawn in true lengths and visible in…

A: Given problem:-

Q: 5. Suppose AABC is a triangle and l is a line such that none of the vertices A, B, or C lies on l.…

A: Find your answer below

Q: he figure shows the net of the three-dimensional package for a board game. TI et is made of four…

A: Introduction: The most well-known and simplest formula, which almost everyone remembers from school,…

Q: What point divides the directed line segment AB into a 2 : 3 ratio? A B. 4. 2 3 6789 10 11 12 13 14…

A: Our Aim is to tell the point which divides the directed line segmentAB⇀ into a 2:3.

Q: Let K_(n,m) be a complete bipartite graph, then the edges of K_(n,m) equal to * (d) nxm. O (a) nxn.…

A:

Q: How many polygons can be possibly formed from 8 distinct points in which no three of which are…

A:

Q: A polygon is graphed on a coordinate grid with (x,y) representing the location of a certain on a…

A: solve the following

Q: A solid in the formof a cube of edge 12 cm. is melted and formed into three smaller cubes of…

A:

Q: Find the perimeter of ADEF wit vertices D(3, 2), E(4, 2), and F(3,-2). 61 4- 3. 2 6-5-4-3 -1 1 234…

A:

Q: . Solve the travelling problem for the given graph by finding the total weight of all Hamilton…

A:

Q: Q1. Let AABC be a triangle having a defect 10 and let BCFE be the corresponding Saccheri…

A:

Q: 53. Suppose that A, B, and C are vertices of a triangle and that a, b, and c are, respectively, the…

A:

Q: If x, y, and z are lengths of the edges of a rectangular box, the common length of the box's…

A: Length of rectangular box =x Breadth of rectangular box =y Height of rectangular box =z

Q: The segment addition postulate only works when the segments in question are collinear. O True O…

A: Let's find.

Q: The parent of vertex y in K, is K1 a b u

A:

Q: Find b and c so that y = la? + bx + c has vertex (3, – 6). %3D

A:

Q: Consider the tree diagram. Path number 0.4 D 1 0.6 2 0.5 D 3 4 A2. 0.5 D 4 2 0.7 D A3 0.3 D…

A: The tree diagram is given.

Q: Q, has how many edges ? k

A: Let us determine the number of edges does Qk has.

Q: Show that, If M and N are nbds. of a point p, then M∩N is also a nbd. of p.

A:

Q: Use Euler's Formula to find the missing number. Edges: 29 Faces: 17 Vertices: ? O a 17 O b 14 13 O d…

A: According to Euler's formula. in any closed 3-dimensional figure, the sum of the faces (F) and the…

Q: a. Draw any two segments, AC and BD, that bisect each other at O. Whatappears to be true of quad.…

A: a) Consider the obtained quadrilateral ABCD, Where AC and BD bisect each other at O. So the…

Q: 8 (Refer to the drawing in #7) Find all vertices adjacent to v5. O V3 and vi V2 V1, V2, and v3

A:

Q: In triangle ABC, line t is drawn through vertex A in such a way that t BC. a) Which pairs of Zs are…

A: Given data:     The first given condition is: AB ∥ DE. The given measure of the first angle is:…

Q: Solve the traveling salesman problem for this graph by finding the total weight of all Hamilton…

A:

Q: Suppose G has V vertices and E edges. Let M and m denote, respectively, the maximum and minimum of…

A:

Q: What additional information is needed to prove that the triangles are similar by SAS-? * 12 8. 18 12

A:

Q: Use Euler's Formula to find the missing number. Vertices: 11 Edges: 34 Faces: 2 O a 24 O b 28 O c 25…

A: For any polyhedron that doesn't intersect itself, the. Number of Faces F plus the Number of…

Q: 5) Identify the segment bisector of S a) x+ 12 Bx-2

A:

Q: Prove that quadrilateral DAVE with the vertices D(2,1), A(6,-2), V(10,1), and E(6,4) is a mbus. Yt…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Use Euler’s Formula to find the missing number of faces, edges, and vertices a) Faces = ?, Edges =…

A: Euler's formula is: F + V = E + 2, where F=the number of faces, V =the number of vertices, and E =…

Q: Solve the traveling salesman problem for this graph by finding the total weight of all Hamilton…

A: We pick any point to start at and select all possible combinations of the other 3 points.Let's start…

Q: The following Graph shows the regions of feasible Solutions. Find the siinimure values of the…

A: Given that a graph and the graph shows the feasible solutions. We have to find the minimum values of…

Q: Which of the following vertices are adjacent to vertex B? * E D O AC AEDC

A: We have to find adjacent vertices to B

Q: In the complete bipartite graph K21,7 there are vertices and edges.

A:

Q: Let z1, z2 and z3 are the vertices of a AABC respectively. If D is the mid point of BC, ZADB = 45°…

A: Given z1, z2 and z3 are the vertices of a triangle ABC and D is the midpoint of BC

Q: Which of the following vertices are adjacent to vertex D? A B F E ID O AC O AEDC O AEFC O AEDFC O…

A:

Q: The number of edges in a complete bi-partite graph Km.n is equal to n2 whenever а. m>n O b. m< n. O…

A: Since we know that "The number of edges in a complete bi-partite graph Km,n is equal to mn ".

Q: Prove that if two pairs of opposite edges of a tetrahedron are perpendicular, then the third pair is…

A: Consider the tetrahedron  ABCD and let two pairs of opposite sides are perpendicular. Consider the…