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ioda
2 years ago
11

find the formula for a rational function that satisfies all of the following. its x-intercept is (-3,0). it has a vertical asymp

totes, namely x=-1 and x=0. it has one horizontal asymptote, namely y=3
Mathematics
1 answer:
Norma-Jean [14]2 years ago
4 0

Let that be

\\ \rm\Rightarrow y=\dfrac{a(f(x))}{g(x)}

Two vertical asymptotes at -1 and 0

\\ \rm\Rightarrow y=\dfrac{a(f(x)}{x(x+1)}

If we simply

\\ \rm\Rightarrow y=\dfrac{a(f(x)}{x^2+1}

  • Denominator has degree 2
  • Numerator should have degree as 2 and coefficient as 3 inorder to get horizontal asymptote y=3 means the quadratic equation should contain 3x²
  • But there should be a x intercept at -3 so one zeros should be -3

Find a equation

  • 3x²+9x

Find zeros

  • 3x²+9x=0
  • 3x(x+3)=0
  • x=0,-3

Horizontal asymptote

  • 3x²/x²
  • 3

So our equation is

\\ \rm\Rightarrow y=\dfrac{3x^2+9x}{x(x+1)}

Graph attached

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natali 33 [55]

9514 1404 393

Answer:

  • 4% fund: $39,000
  • 52% fund: $1000

Step-by-step explanation:

Let x represent the amount invested at 52%. Then (40000-x) is the amount invested at 4%. The total annual interest is ...

  0.52x +0.04(40000-x) = 2080

  0.48x = 480 . . . . . . . . . subtract 1600, simplify

  x = 1000 . . . . . . . . . divide by 0.48

Then the amounts invested in each fund are ...

  4% fund: $39,000

  52% fund: $1000

6 0
2 years ago
Can someone help me with #s 16 18 19 20 I WILL GIVE BRAINLIEST
Masteriza [31]

Answers & Step-by-step explanation:

<h2>PEMDAS (Parenthesis, exponents, multiplication, division, addition, subtraction)</h2>

Now let's solve your problems!

<h2>___________________________________________________</h2><h2>16.</h2>

First, we see if there are any parentheses. Since there are no parentheses, we will evaluate the exponent 3² first.

After this, our problem now looks like this:

<h2>\frac{41 - 9}{6 * 3 -26}</h2>

Next, since multiplication (not subtraction) is next on the list, we will evaluate 6 × 3, which equals 18.

After that, we will subtract:

41 - 9 = 32

18 - 26 = -8

We now have 32/-8 or 4/-1 or simply -4.

<h2>The answer is: -4</h2><h2>___________________________________________________</h2><h2>17.</h2>

With this, one, note the parentheses. This means that we will do these operations first.

(21 - 4²) = 5

(3 + 1) = 4

The problem now looks like this:

\frac{5 * 4}{8^{2}-44}

Next, we do the exponents:

8² = 64

After that, we do the multiplication of 5 x 4, which equals 20.

We now have 20/64 - 44, which simplifies to 20/20 or 1/1 or 1.

<h2>The answer is: 1</h2><h2>___________________________________________________</h2><h2>18.</h2>

Again, we see parentheses, so that means we need to do these operations first.

(6² - 20) = 16

We now have:

48 ÷ 16 + 5

48/16 = 3 and 3 + 5 = 8

<h2>The answer is: 8</h2><h2>___________________________________________________</h2><h2>19.</h2>

Here, we see an exponent 3³, so we'll need to evaluate this first.

3³ = 27

We now have:

4 × 27 ÷ 18 + 14

4 × 27 = 108

108/18 = 6

And finally:

6 + 14 = 20

<h2>The answer is: 20</h2><h2>___________________________________________________</h2><h2>20.</h2>

Here we again see the parentheses, which means we need to evaluate the subtraction first.

3 - 8 = -5

We now have:

11 + 2 (-5)

2 × -5 = -10

11 + -10 (same as 11 - 10) = 1

<h2>The answer is: 1</h2><h2>___________________________________________________</h2><h2><em>I AM ALWAYS HAPPY TO HELP :)</em></h2>
7 0
3 years ago
Combine like terms to create an equivalent expression: -n + (-4) - (-4n) + 6
Taya2010 [7]

Answer:

3n + 2

Step-by-step explanation:

-n + 4n -4 + 6

3n + 2

6 0
3 years ago
You spin the spinner and flip a coin. Find the probability of the compound event.
zimovet [89]

Answer:

the compound probability is 1/8.

Step-by-step explanation:

1/4 for the spinner x 1/2 for the coin

4 0
3 years ago
An animal shelter has 9 puppies. If the puppies are 36% of the total dog and cat population, how many dogs and cats are in the a
Luda [366]

Answer:

Let total number of dog and cat population in animal shelter be x.

As per the statement:

An animal shelter has 9 puppies.

⇒ Total number of puppies = 9

It is also given that if the puppies are 36% of the total dog and cat population.

⇒ 9 = 36\% \text{of}{\text{total number of dogs and Cat}

or

9 = \frac{36}{100} \times x

By cross multiply we get;

900 = 36 x

Divide both sides by 36 we get;

25 = x

Therefore, total number of dogs and cat population in animal shelter are 25


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3 years ago
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