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3 months ago

Which of the following rational functions is graphed below?

Mathematics

2 answers:

Svet_ta [12.7K]3 months ago

6 0

Answer:

The rational function depicted on the graph is B.

zzz [12.3K]3 months ago

5 0

Answer:

The graphed rational function corresponds to:

Option: B

B. $F(x)=\dfrac{x}{(x-1)(x+1)}$

Detailed explanation:

Examining the graph indicates vertical asymptotes at x=1 and x= -1.

The vertical asymptotes occur where the denominator equals zero.

If the numerator’s degree is lower than the denominator’s, y=0 acts as the horizontal asymptote.

Only function B meets both criteria:

B. $F(x)=\dfrac{x}{(x-1)(x+1)}$

(For option A, denominator zeros are at x=0 and -1, so vertical asymptotes lie there.

Option C has vertical asymptotes at x=0 and 1.

Option D has a single vertical asymptote at x=0, which doesn’t match the graph.)

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Detailed explanation:

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3 months ago

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Zina [12379]

Response:

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2 months ago

Read 2 more answers

Yolanda invests $30,000 in an account that offers a compound interest rate of 7.9% per year. Which of the following is the corre

Zina [12379]

To find the solution, we will utilize the compound interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where
$A$ represents the total amount after $t$ years
tex]P[/tex] indicates the original investment
$r$ signifies the interest rate expressed in decimal
$n$ shows the frequency of compounding per year
$t$ indicates the duration in years

According to our problem, the initial investment is $30,000 with a duration of ten years, thus $P=30000$ and $t=10$ . Interest is compounded annually, so $n=1$ . To convert the percentage interest rate into decimal, we divide it by 100%
$r= \frac{7.9}{100}$
$r=0.079$
Now, we can insert these values into our formula:
$A=P(1+ \frac{r}{n} )^{nt}$
$A=30000(1+ \frac{0.079}{1} )^{(1)(10)}$
$A=3000(1+0.079)^{10}$
Substituting $A$ with $P_{10}$ :
$P_{10}=3000(1+0.079)^{10}$

Consequently, we find that the correct answer is D. $P_{10}=3000(1+0.079)^{10}$

Finally, to determine the total amount Yolanda will have after ten years, we just need to carry out the operations in our equation:
 $P_{10}=3000(1+0.079)^{10}$
$P_{10}=30000(1.079)^{10}$
$P_{10}=64170.54$

Thus, we conclude that Yolanda will end up with $64,170.54 in her account after a decade of earning at a compound interest rate of 7.9% yearly.

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3 months ago