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3 years ago

Which of the following is an example of a rational function?

Mathematics

1 answer:

Andru [333]3 years ago

3 0

Answer:

the second one is an example of a rational function

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What is an equivalent exponential equation? log5(1/25)=−2

jenyasd209 [6]

$\log_ab=c\iff a^c=b\\\\\log_5\dfrac{1}{25}=-2\iff5^{-2}=\dfrac{1}{25}\\\\5^{-2}=\dfrac{1}{5^2}=\dfrac{1}{25}$

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3 years ago

The hardcover version of a book weighs 7 ounces while its paperback version weighs 5 ounces. Forty-five copies of the book weigh

konstantin123 [22]

Answer:

33 copies were paperback and 12 were hardcover.

Step-by-step explanation:

Let h represent the number of hardcover copies and p represent the number of paperback copies.

We know that the total number of copies was 45; this gives us the equation

h+p = 45

We know that each hardcover copy is 7 ounces; this gives us the expression 7h.

We also know that each paperback copy is 5 ounces; this gives us the expression 5p.

We know that the total weight was 249 ounces; this gives us the equation

7h+5p = 249

Together we have the system

$\left \{ {{h+p=45} \atop {7h+5p=249}} \right.$

We will use elimination to solve this. First we will make the coefficients of the variable p the same; to do this, we will multiply the top equation by 5:

$\left \{ {{5(h+p=45)} \atop {7h+5p=249}} \right. \\\\\left \{ {{5h+5p=225} \atop {7h+5p=249}} \right.$

To eliminate p, we will subtract the equations:

$\left \{ {{5h+5p=225} \atop {-(7h+5p=249)}} \right. \\\\-2h=-24$

Divide both sides by -2:

-2h/-2 = -24/-2

h = 12

There were 12 hardcover copies sold.

Substitute this into our first equation:

12+p=45

Subtract 12 from each side:

12+p-12 = 45-12

p = 33

There were 33 paperback copies sold.

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4 years ago

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Can somebody please help me? (PreCalc

andrew-mc [135]

$\csc\theta=\dfrac1{\sin\theta}=\dfrac{\sqrt{17}}}4\implies\sin\theta=\dfrac4{\sqrt{17}}$

Recall that $\sin^2\theta+\cos^2\theta=1$ , which means

$\cos\theta=\pm\sqrt{1-\sin^2\theta}=\pm\sqrt{1-\dfrac{16}{17}}=\pm\dfrac1{\sqrt{17}}$

Since $\tan\theta=\dfrac{\sin\theta}{\cos\theta}>0$ , and $\sin\theta>0$ , it follows that $\cos\theta>0$ too, so you take the positive root:

$\cos\theta=\dfrac1{\sqrt{17}}$

Therefore

$\cot\theta=\dfrac{\cos\theta}{\sin\theta}=\dfrac{\frac1{\sqrt{17}}}{\frac4{\sqrt{17}}}=\dfrac14$

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4 years ago

Given that f(x) = x2 - 13 and g(x) = 5 - x, find (f-9)(10), if it exists.

rosijanka [135]

Answer:

the value for f-9 (10) doesn't exist

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3 years ago

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Elanso [62]

If x is an which of the following statements adds 5 to the current value of x and stores the new value back in x?If x is an int, which of the following statements adds 5 to the current value

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