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crimeas [40]
3 years ago
15

Hot dogs come in packages of 8. hot dog buns come in packages of 12. if grace wants to have enough to serve 24 people and have n

one left over, how many packages of hot dogs and hot dog buns should she purchase?
Mathematics
1 answer:
OLga [1]3 years ago
5 0
She would by 3 packages of hot dogs and 2 packages of hot dog buns. This is because 3*8 would be 24 and 12*2 is also 24. These would both be the minimum amount of packages.
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Based on the polynomial remainder theorem, what is the value of the function when x=−6 ?
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f( - 6) =  10


EXPLANATION

The given function is
f(x) =  {x}^{4}  + 8 {x}^{3}  + 10 {x}^{2}  - 7x + 40

According to the remainder theorem,

f( - 6) = R
where R is the remainder when
f(x)

is divided by
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We therefore substitute the value of x and evaluate to obtain,

f( - 6) =  { (- 6)}^{4}  + 8 {( - 6)}^{3}  + 10 { (- 6)}^{2}  - 7( - 6)+ 40




f( - 6) =  1296 + 8 ( - 216) + 10 (36) - 7( - 6)+ 40




f( - 6) =  1296  - 1728 + 360  + 42+ 40



This will evaluate to,


f( - 6) =  10


Hence the value of the function when
x =  - 6

is
10



According to the remainder theorem,
10
is the remainder when

f(x) =  {x}^{4}  + 8 {x}^{3}  + 10 {x}^{2}  - 7x + 40
is divided by
x + 6
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