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3 years ago

2x − 8 > x + 9. Solve the equation or inequality for the unknown number.

Mathematics

1 answer:

dangina [55]3 years ago

8 0

Answer:

x > 17, any number greater than 17

Step-by-step explanation:

2x − 8 > x + 9

+8 +8

2x > x + 17

-x -x

x > 17

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Through (2,0) slope = -5/3 write the slope intercept of the equation

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For this case we have that the equation of a line of the slope-intersection form is given by:

$y = mx + b$

Where:

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b: It is the cut-off point with the y axis

In this case we have the following data:

$m = - \frac {5} {3}\\(x, y) :( 2,0)$

Then, the equation is of the form:

$y = - \frac {5} {3} x + b$

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$y = - \frac {5} {3} x + \frac {10} {3}$

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3 years ago

The publisher of a recently released nonfiction book expects that over the first 20 months after its release, the monthly profit

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Answer:

(a) $\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}$

(b)P'(5)=-($4.54) Thousand

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(d)The fifth Month

Step-by-step explanation:

Given the monthly profit model:

$P(t)=\frac{240t-40t^2}{t^2+20}$

(a)We want to derive a model that gives the Marginal Profit, P' of the book.

We differentiate

$P(t)=\frac{240t-40t^2}{t^2+20}$ using quotient rule.

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Simplifying

$\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}$

We have derived a model for the marginal profit.

(b) After 5 months, at t=5

Marginal Profit=P'(5)

$\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}$

$P^{'}(5)=\frac{4800-1600(5)-240(5)^2}{(5^2+20)^2}$

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$P^{'}(11)=\frac{4800-1600(11)-240(11)^2}{(11^2+20)^2}$

=-($2.10) Thousand of dollars

(d) Since the marginal profit at t=5 is negative, after the 5th Month, the profit starts to experience a steady decrease.

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