Parallel graphs have the same slope. perpendicular has opposite reciprocal slopes. These equations have slopes of -2/5 and 25 so they are neither.
Four children average is 15.25 so ages must add to 61
61-12-16=33
11 and 22 go into 33
Youngest is 11
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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9,2.5,-4,-10.5,-17
Let's find the difference between two consecutive terms
2.5 - 9 = -6.5
-4 - 2.5 = -6.5
-10.5 - (-4) = -6.5
-17 -(-10.5) = -6.5
We can see that the common difference is -6.5
-6.5 is the common difference between successive terms in the sequence 9,2.5,-4,-10.5,-17
the common difference is negative because we subtract 6.5 to get the next term.
