A sports conference has 13 teams. It was proposed that each team play precisely one game against each of exactly seven other conference teams. Prove that this proposal is impossible to implement.

Step-by-step explanation:

Number of team = 13

Let us consider a graph with 13 vertices, each edge represents a match of two teams.

Total number of edges = 13(13-1)/2 =78 edge

Given conditions:

Each component plays 7 match with 7 other teams.

Total edges in the case = 7(6)/2 =21

Therefore edges in the graph are not equal to edges in the condition.

Therefore impossible to implement

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

5/20 so 25%

step-by-step explanation: