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kifflom [539]
3 years ago
9

If f(x) = 2/3x + 9, find f^-1(x)

Mathematics
1 answer:
larisa86 [58]3 years ago
6 0

If f^{-1}(x) is the inverse of

f(x) = \dfrac23x+9

then

f\left(f^{-1}(x)\right) = \dfrac23f^{-1}(x) + 9 = x

Solve for f^{-1}(x) :

\dfrac23f^{-1}(x)+9 = x \\\\ \dfrac23f^{-1}(x) = x-9 \\\\ f^{-1}(x) = \dfrac32(x-9) = \dfrac32x-\dfrac{27}2

which makes D the correct answer.

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The numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

Since a furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week, and each chair produced requires 8 ft of wood and 12 hours of labor, and each table requires 20 ft of wood and 15 hours of labor, to determine, if a chair yields a profit of $ 65 and a table yields a profit of $ 90, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit, the following calculation should be done:

16 chairs; 24 tables

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Time used = 15 x 12 + 18 x 15 = 180 + 270 = 450

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12 chairs; 28 tables

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18 chairs; 20 tables

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Therefore, the only option that meets the requirements of time and wood used is that of 15 chairs and 18 tables, whose economic benefit will be the following:

15 x 65 + 18 x 90 = X

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Therefore, the numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

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Answer:

s = salsa

p = peppers

o = onions

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Step-by-step explanation:

Hope this helps!

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