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3 years ago

Sketch the graph of each rational function showing all the key features. Verify your graph by graphing the function on

Mathematics

1 answer:

xenn [34]3 years ago

8 0

Answer:

Rational Function

Step-by-step explanation:

Gives the function:

$f(x) = \frac{x}{x^2-9}$

It has the following,

Domain

x∈ $\mathbb{R}$ : $x\neq 3, x\neq -3$

Range

$\mathbb{R}$ (All real numbers)

End behaviour

As x $x \rightarrow \infty, y \rightarrow 0$

Horizontal and Vertical Asymptote

Vertical $x = 3, x=-3$

Horizontal $y = 0$

x-intercept: (0,0)

y-intercept: (0,0)

**The Graph is in the annex

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In 2000, the population of a county was 25,300,987. The population decreased at a rate of 2% each year. What was the population

EastWind [94]

Answer: In 2008 the population was 21,525,144

Step-by-step explanation:

You need to use the following formula for Exponential decay:

$P=P_0(1-r)^t$

Where $P_0$ is the initial population in the year 0, $r$ is the rate of decay and $t$ is the time.

In this case, you can identify that:

$P_0=25,300,987\\\\r=2\%\\\\t=8$

Therefore, substituting these values into the formula for Exponential decay, you get:

$P=P_0(1-r)^t\\\\P=(25,300,987)(1-\frac{2}{100})^8\\\\P=21,525,144$

Then, in 2008 the population was 21,525,144

6 0

3 years ago

A principal of $1,000 is invested in an account paying an annual interest rate of 6%.

Evgesh-ka [11]

A(t) = P(1+(r/n))^(nt)

A(5) = 1000(1+0.12/2)^(2*5)

A(5) = 1000(1.06)^(10)

A(5) = $1790.85

6 0

3 years ago

Read 2 more answers

Consider the sequence 1, –3, 9, –27, 81, … Which statement describes the sequence?

ludmilkaskok [199]

Answer:

There is a similar problem with the same numbers except with no negatives so it goes 1 , 3 , 9 , 27, 81 for this question the answer is that it diverges.

Step-by-step explanation:

It was on the unit test review for edge and the answer was that it diverges.

8 0

3 years ago

Read 2 more answers

What is the solution to this equation 1/2n^2+18=0

ololo11 [35]

Answer:

n = ±6 .

Step-by-step explanation:

A quadratic equation is given to us and we need to find out the solution of the given equation . The given equation is ,

$\rm\implies -\dfrac{1}{2}n^2+18=0$

Subtracting 18 both sides ,

$\rm\implies -\dfrac{1}{2}n^2 = -18$

Multiplying both sides by -2 ,

$\rm\implies -2\times\dfrac{1}{2}n^2 = -2\times -18$

On simplyfing , we get ,

$\rm\implies n^2= 36$

Putting squareroot both sides ,

$\rm\implies n= \sqrt{36}$

This equals to ,

$\rm\implies \boxed{\quad\blue{\rm n =\pm 6 }}$

Hence the value of n is ±6 .

6 0

3 years ago

Very buys a basket of mangoes that is priced $14 before tax. The sales tax is 6%. What is the total price Avery pays for t

igor_vitrenko [27]

Answer:

Avery needs to pay $14.84

Step-by-step explanation:

When there's a tax we need to sum the original value of the product with the tax's value. To find the amount of money Avery needs to pay in taxes we can apply a rule of three as shown below:

$\frac{14}{x} = \frac{100}{6} \frac{\%}{\%}$

Where "x" is the tax value, and $14 represents 100%, since it's the value used to calculate the tax. We have:

$x = \frac{14*6}{100}\\x = \frac{84}{100}\\x = 0.84$

The value to be paid is the product value plus the tax, therefore:

$\text{paid} = 14 + 0.84 = 14.84$

Avery needs to pay $14.84

6 0

3 years ago