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goldfiish [28.3K]
4 years ago
10

Someone please help me with number 6. Also show your work as that will help a lot

Mathematics
1 answer:
adoni [48]4 years ago
7 0

\bf f(x) = x^2+3x+9 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(x+h)^2+3(x+h)+9~~~~-~~~~(x^2+3x+9)}{h} \\\\\\ \cfrac{(x+h)^2+3(x+h)+9~~~~~~-x^2-3x-9}{h} \\\\\\ \cfrac{\stackrel{F~~O~~I~~L}{(x^2+2hx+h^2)}+3x+3h+9~~~~~~-x^2-3x-9}{h}

\bf \cfrac{(2hx+h^2+3h)~~\begin{matrix} +x^2-x^2+3x-3x+9-9 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{h}\implies \cfrac{\stackrel{\textit{common factor}}{~~\begin{matrix} h \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(2x+h+3)}}{~~\begin{matrix} h \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 2x+h+3~\hfill

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A bag contain 10 counters of which 7 are green and 3 are white.A counter is picked at random from the bag and its colour is note
maria [59]

Answer:

See below

Step-by-step explanation:

a) 7/10

b) 7/10 x 3/9 = 21/90 = 7/30

c) Also 7/30

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3 years ago
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Write as a fraction in simplest form %33.5
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Step-by-step explanation:

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Compare the following rational numbers with &gt; or &lt;..<br> -7.56 _____ -5.76
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<

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-7.56 < -5.76

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A leaking pond looses 18 gallons of water in 34 hours , how many gallons will be left after 41 hours
Ann [662]

The amount of water left = 21.3 gallons.

We have a leaking pond which looses 18 gallons of water in 34 hour.

We have to determine how many gallons of water will be left after 41 hours.

<h3>What do you understand by gallon?</h3>

The gallon is a unit of volume in imperial units and United States customary units.

I gallon = 231 cubic inches = 3.785411784 liters.

According to question, we have -

Amount of water lost by the pond in 34 hours = 18 gallons

Therefore -

Amount of water lost by the pond in 1 hour = \frac{18}{34}

So, the amount of water loosed by the pond in 41 hours = \frac{18}{34}\times 41  = 21.3

Hence, the amount of water left = 21.3 gallons.

To solve more questions on Quantity Measurements , visit the link below-

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3 0
2 years ago
The natural resources of an island limit the growth of the population. The population of the island is given by the logistic equ
maksim [4K]

Answer:

The correct option is (a) 3759.

Step-by-step explanation:

The complete question is:

The natural resources of an island limit the growth of the population. The population of the island is given by the logistic equation P(t)=\frac{3759}{1+3.94e^{-0.38t}}where t is the number of years after 1980. What is the limiting value of the population?

(a) 3759

(b) 23

(c) 761

(d) 1017

Solution:

The limiting value is the value of the function P (t) for <em>t</em> → ∞.

As <em>t</em> → ∞, the expression (3.94e^{-0.38t}) → 0.

Thus, making the denominator of P (t) 1.

So, the limiting value of the population is, 3759.

Thus, the correct option is (a) 3759.

5 0
4 years ago
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