Answer:
z = 15
Step-by-step explanation:
The sum S of the interior angles of a regular polygon is given by the formula
S = (n-2) x 180 where n is the number sides
Here n = 9
So S = (9-2) x 180 = 7 x 180 = 1,260
There are 9 interior angles and each angle is (5z + 65)
So the sum of all 9 interior angles = 9 (5z + 65)
= 45z + 585
Set these equal to each other and solve for z
45z + 585 = 1260
45z = 675
z = 675/45 = 15
Step-by-step explanation:
It would be 9/8
Hope this helps!
surface area (S) of a right rectangular solid is:
S = 2*L*W + 2*L*H + 2*W*H (equation 1)
where:
L = length
W = width
H = height
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you have:
L = 7
W = a
H = 4
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formula becomes:
S = 2*7*a + 2*7*4 + 2*a*4
simplify:
S = 14*a + 56 + 8*a
combine like terms:
S = 22*a + 56
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answer is:
S = 22*a + 56 (equation 2)
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to prove, substitute any value for a in equation 2:
let a = 15
S = 22*a + 56 (equation 2)
S = 22*15 + 56
S = 330 + 56
S = 386
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since a = 15, then W = 15 because W = a
go back to equation 1 and substitute 15 for W:
S = 2*L*W + 2*L*H + 2*W*H (equation 1)
where:
L = length
W = width
H = height
-----
you have:
L = 7
W = 15
H = 4
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equation 1 becomes:
S = 2*7*15 + 2*7*4 + 2*15*4
perform indicated operations:
S = 210 + 56 + 120
S = 386
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surface area is the same using both equations so:
equations are good.
formula for surface area of right rectangle in terms of a is:
S = 22*a + 56
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