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Fynjy0 [20]
2 years ago
8

Before a renovation, a movie theater had 111 seats. after the renovation, the theater has 144 seats. what is the approximate per

centage increase of the number of seats in the theater? if necessary, round to the nearest tenth of a percent.
Mathematics
1 answer:
Blababa [14]2 years ago
3 0
Change in number of seats = 144 - 111 = 33

percentage increase = 33/111 x 100 = 29.8% (nearest tenths)
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5 0
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Which will result in a difference of squares? (–7x + 4)(–7x + 4) (–7x + 4)(4 – 7x) (–7x + 4)(–7x – 4) (–7x + 4)(7x – 4)
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You can simply expand each product and see whether it gives you a difference of squares.


•  \mathsf{(-7x+4)\cdot (-7x+4)}

That's actually  \mathsf{(-7x+4)^2:}

     \mathsf{(-7x+4)^2}\\\\ \mathsf{=(-7x+4)\cdot (-7x+4)}\\\\ \mathsf{=(-7x+4)\cdot (-7x)+(-7x+4)\cdot 4}\\\\ \mathsf{=49x^2-28x-28x+16}

     \mathsf{=49x^2-56x+16}        <span>✖

which is not a difference of squares.

</span>————<span>—

</span>•  \mathsf{(-7x+4)\cdot (4-7x)}

     \mathsf{=(-7x+4)\cdot 4-(-7x+4)\cdot 7x}\\\\ \mathsf{=-28x+16-(-49x^2+28x)}\\\\ \mathsf{=-28x+16+49x^2-28x}

     \mathsf{=49x^2-56x+16}        ✖

which is not a difference of squares.

—————

•  \mathsf{(-7x+4)\cdot (-7x-4)}

     \mathsf{=(-7x+4)\cdot (-7x)-(-7x+4)\cdot 4}\\\\ \mathsf{=49x^2-28x-(-28x+16)}\\\\ \mathsf{=49x^2-\diagup\!\!\!\!\! 28x+\diagup\!\!\!\!\! 28x-16}\\\\ \mathsf{=49x^2-16}

     \mathsf{=(7x)^2-4^2}        <span>✔

That is a difference of two squares.

</span>————<span>—

</span>•  \mathsf{(-7x+4)\cdot (7x-4)}

     \mathsf{=(-7x+4)\cdot 7x-(-7x+4)\cdot 4)}\\\\ \mathsf{=-49x^2+28x-(-28x+16)}\\\\ \mathsf{=-49x^2+28x+28x-16}

     \mathsf{=-49x^2+56x-16}        <span>✖

</span>which is not a difference of squares.

—————

Only the  third option  will result in a difference of squares.


Answer:  (− 7x + 4) · (− 7x − 4).


I hope this helps. =)

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2 years ago
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