My teacher didn't go over this and we have to show work Find three consecutive even integers such that the sum of twice the smallest number and three times the largest is 42.

The three consecutive even integers are 6, 8, 10

Step-by-step explanation:

∵ The three consecutive even numbers are x, x + 2, x + 4

∵ The smallest number is x

∴ Twice the smallest number = 2x ⇒ (1)

∵ The largest number is x + 4

∴ Three times the largest number = 3(x + 4) = 3(x) + 3(4)

∴ Three times the largest number = 3x + 12 ⇒ (2)

∵ The sum of twice the smallest number and three times the largest is 42

→ Add (1), (2) and equate the sum by 42

∴ 2x + 3x + 12 = 42

→ Add the like terms

∴ 5x + 12 = 42

→ Subtract 12 from both sides

∴ 5x + 12 - 12 = 42 - 12

∴ 5x = 30

→ Divide both sides by 5

∵

∴ x = 6

∴ The smallest integer is 6

∴ The middle integer is 6 + 2 = 8

∴ The largest integer is 6 + 4 = 10

∴ The three consecutive even integers are 6, 8, 10

i believe the answer is the polygon, heptagon.

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3