A an election, a total of 240 votes were cast for four candidates. The winner won by a margin of 8, 13, and 15 votes over the other three candidates. What was the lowest number of votes received by a candidate?

54

Step-by-step explanation:

Total votes: 240

Votes for the winner: x

Votes for candidate 1: x - 8

Votes for candidate 2: x - 13

Votes for candidate 3: x - 15

Equation to find the amount of votes of the winner (x) is:

240 = x +  x - 8 + x - 13 + x - 15

Combine x and x to get 2x.

240=2x−8+x−13+x−15

Combine 2x and x to get 3x.

240=3x−8−13+x−15

Subtract 13 from −8 to get −21.

240=3x−21+x−15

Combine 3x and x to get 4x.

240=4x−21−15

Subtract 15 from −21 to get −36.

240=4x−36

Swap sides so that all variable terms are on the left hand side.

4x−36=240

Add 36 to both sides.

4x=240+36

Add 240 and 36 to get 276.

4x=276

Divide both sides by 4.

x= 4/276  

Divide 276 by 4 to get 69.

x=69

Votes for the winner: 69

Votes for candidate 1: 69 - 8 = 61

Votes for candidate 2: 69 - 13 = 56

Votes for candidate 3: 69 - 15 = 54

The candidate that had the lowest number of votes received 54 votes.

1. 34

2. 268

3. x=14.4

step-by-step explanation:

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.