SOLUTION: Arianna needed 140x²+60x square inches of paper to make
a book jacket 10x inches tall. In figuring the area she
needed, she allowed for a front and back flap. If the spine
of
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-> SOLUTION: Arianna needed 140x²+60x square inches of paper to make
a book jacket 10x inches tall. In figuring the area she
needed, she allowed for a front and back flap. If the spine
of
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Question 1035655: Arianna needed 140x²+60x square inches of paper to make
a book jacket 10x inches tall. In figuring the area she
needed, she allowed for a front and back flap. If the spine
of the book jacket is 2x inches, and the front and back of
the book jacket are 6x inches, how wide are the front and
back flaps? A quotient of polynomials can be used to identify
the answer.
Hello, what is the formula of geometry that applies in this
situation? How can the division of polynomials be used to
find the width?
Problem: http://postimg.org/image/bxw1rg4p7/
ty! Answer by Edwin McCravy(20055) (Show Source):
Arianna needed 140x²+60x square inches of paper to make a book
jacket 10x inches tall. In figuring the area she needed, she
allowed for a front and back flap. If the spine of the book
jacket is 2x inches, and the front and back of the book jacket
are 6x inches, how wide are the front and back flaps? A quotient
of polynomials can be used to identify the answer.
(Area) = (length)(width)
(Area) = (140x²+60x)
(length) = the horizontal (left-to-right) dimension
= (f+6x+2x+6x+f) =
= (combine like terms) = (2f+14x)
width = the vertical (top to bottom) dimension = (10x)
Substitute in
Area = (length)(width)
(140x²+60x) = (2f+14x)(10x)
Reverse the factors on the right to make it easier to
distribute:
(140x²+60x) = 10x(2f+14x)
140x²+60x = 20xf+140x²
Subtract 140x² from both sides
60x = 20xf
Divide both sides by 20x
divide by canceling:
The front and back flaps must be 3 inches wide.
[Not much division of polynomials is required. Just division
by canceling terms in numerator and denominator.]
Edwin
Arianna needed 140x²+60x square inches of paper to make a book
jacket 10x inches tall. In figuring the area she needed, she
allowed for a front and back flap. If the spine of the book
jacket is 2x inches, and the front and back of the book jacket
are 6x inches, how wide are the front and back flaps? A quotient
of polynomials can be used to identify the answer.
(Area) = (length)(width)
(Area) = (140x²+60x)
(length) = the horizontal (left-to-right) dimension
= (f+6x+2x+6x+f) =
= (combine like terms) = (2f+14x)
width = the vertical (top to bottom) dimension = (10x)
Substitute in
Area = (length)(width)
(140x²+60x) = (2f+14x)(10x)
Reverse the factors on the right to make it easier to
distribute:
(140x²+60x) = 10x(2f+14x)
140x²+60x = 20xf+140x²
Subtract 140x² from both sides
60x = 20xf
Divide both sides by 20x
