find three consecutive odd integers such that the sum of the first, two times the second and three times the third is 82.

choose the mathematical translation for the given situation.

a.

6 x plus 16 equals 82

6x+16=82

b.

6 x plus 8 equals 82

6x+8=82

c.

3 x plus 3 equals 82

3x+3=82

d.

3 x plus 6 equals 82

3x+6=82

A

Step-by-step explanation:

Let the first odd integer = x

Let the second odd integer = (x+2)

This is because adding 2 to x makes it an odd integer. If 1 is added, it would become an even integer.

Let the third odd integer = (x+2)+2

= (x+4)

The sum of the first, two times the second and three times the third is written as

x + 2(x+2) + 3(x+4) = 82 (open the bracket)

x + 2x+ 4+ 3x + 12 = 82 (collect like terms)

x + 2x + 3x + 4 +12 = 82

6x + 16 =82 (this is the mathematical translation)

6x = 82 - 16

6x = 66

Divide both sides by 6

6x/6 = 66/6

x = 11

The first odd integer= 11

The second odd integer = x + 2

= 11 + 2

= 13

The third odd integer = x + 4

= 11+4

= 15

The consequtive odd integers are 11, 13 and 15

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.