The expression 1/3x^2-2 can be as 1/3(x-k)(x+k),where k is a positive constant.What is the value of k?

Answers

Answer 1
Final answer:

To find the constant k for rewriting the expression 1/3x^2 - 2 in the form of 1/3(x - k)(x + k), we determine k to be the square root of 6.

Explanation:

The original expression given is 1/3x^2 - 2, and the goal is to rewrite it in the form 1/3(x - k)(x + k), where k is a positive constant. To find k, let's expand the desired form and set it equal to the original expression:

1/3(x^2 - k^2) = 1/3x^2 - 2

Equating the constants, we get:

-1/3 * k^2 = -2

By solving for k^2, we find:

k^2 = 6

Therefore, the value of k is the positive square root of 6, or \(√6\).


Related Questions

what are 3 things that must be present for a internal combustion engine to operate?

Answers

Answer:

Explanation:

Combustion or burning is a high-temperature exothermic redox chemical reaction between a fuel and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion in a fire produces a flame, and the heat produced can make combustion self-sustaining.

A planet has an orbital period of 65.02 years. What is the average distance of the planet from the sun? 2.84 AU 5.14 AU 16.17 AU 39.87 AU

Answers

Answer:16.17 AU is the answer.

Explanation:According to Kepler's Third Law which states that the square of the orbital period of the planets is directly proportional to the cube of the semi-major axis of the orbit of the planet.

      (d-15)^2

T= _______ + 20

         300


The average temperature around the Tropic of Cancer for a particular day in January can be modeled using the equation above, where T is the temperature in degrees Celsius and d is the number of days after January 1 (on January 1, d=0). According to this model, what is the lowest average temperature, in degrees Celsius, for a day in January, which has 31 days?

Answers

Answer:

The expression for temperature is already in vertex form: T=a(d−d subscript 0)^​2​​+T subscript ​0. The vertex of this quadratic function occurs at (15,20).

Perfect competition is mot necessary for the theory of competitive pricing to be practical true or false

Answers

True because not all companies out there have a ton of competition but they still try to stay way ahead of the little competition they have

Kate uses 6.7 pints of white paint and blue paint to paint her bedroom walls. 4 5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?

Answers

6.7 pints = white and blue

-4.5 pints = white

2.2 pints = blue paint

Hope this helps :)

Em que n?o sei se é de outros tempos da sua opini?o sobre geografia dos maiores informaç?es acerca desse departamento pessoal da arte em sua opini?o pública para os Estados americanos em março de uma nova forma mais eficiente de nova espécie na web design inovador de uma forma a Wikipédia em que outros países baixos salários dos refere Wikipédia expandindo de uma

Answers

That's not even a question in Spanish and I understand Spanish

The social worker is responsible for helping clients .

Answers

"Social workers are responsible for helping individuals, families, and groups of people to cope with problems they're facing to improve their patients' lives." https://mswonlineprograms.org/job-duties-and-responsibilities-of-social-workers/

If you use this answer make sure to use quotation marks and include your source.

Answer:

The answer is: Restore their social functioning ability.

Explanation:

I had this question on my assignment, and I got it correct.  :)

According to the conflict theory, which situation is a result of capitalism? A. The rich and poor get an equal share of the power and wealth. B. The poor get an unfair advantage over the rich because they can ask for higher wages. C. The poor benefit from various laws that support their well-being. D. The rich exploit the poor and manipulate the criminal justice system.

Answers

Answer D. The rich exploit the poor and manipulate the criminal justice system. happy to help

Explanation:

According to the conflict theory the following situation takes place the criminal justice system was manipulated by the rich by using poor people.

Option: D

Explanation:  

According to the conflict theory, the one who has both power and wealth try to hold on to power and wealth. They do anything to stay in the powerful position especially by suppressing and exploiting the poor and powerless people of the society. They also tend to take the ‘criminal justice system’ in their hands and manipulate them to enhance their power. This group of people will work to any extent to maintain and gain more power.

The beginning development of a star is marked by a supernova explosion, with the gases present in the nebula being forced .

Answers

Answer:

The beginning development of a star is marked by a supernova explosion, with the gases present in the nebula being forced to scatter. As the star shrinks, radiation of the surface increases and create pressure on the outside shell to push it away and forming a planetary nebula or white dwarf. 5.0. 3 votes.

Monthly incomes of employees at a particular company have a mean of $5954. The distribution of sample means for samples of size 70 is normal with a mean of $5954 and a standard deviation of $259. Suppose you take a sample of size 70 employees from the company and find that they're mean monthly income is $5747. How many standard deviation is the sample mean from the mean of the sample lien distribute distribution

Answers

The sample mean of $5747 is approximately 6.68 standard deviations below the mean of the sampling distribution.

To find out how many standard deviations the sample mean is from the mean of the sampling distribution, you can use the formula for z-score:

[tex]\[ z = \frac{{\text{{sample mean}} - \text{{population mean}}}}{{\text{{standard deviation of sampling distribution}}}} \][/tex]

In this case:

Sample mean [tex](\( \bar{x} \))[/tex] = $5747

Population mean[tex](\( \mu \))[/tex] = $5954

Standard deviation of sampling distribution [tex](\( \sigma_{\bar{x}} \)) = \( \frac{{\text{{population standard deviation}}}}{{\sqrt{\text{{sample size}}}}} \)[/tex]

Given the population standard deviation is $259 and the sample size is 70, you can calculate [tex]\( \sigma_{\bar{x}} \)[/tex]:

[tex]\[ \sigma_{\bar{x}} = \frac{{259}}{{\sqrt{70}}} \][/tex]

Let's calculate:

[tex]$\sigma_{\bar{x}}=\frac{259}{\sqrt{70}} \approx 30.94$[/tex]

Now, plug in the values:

[tex]$\begin{aligned} & z=\frac{5747-5954}{30.94} \\ & z \approx \frac{-207}{30.94} \approx-6.68\end{aligned}$[/tex]

So, the sample mean of $5747 is approximately 6.68 standard deviations below the mean of the sampling distribution.

Last week, janet used 4 cups of flour to make pizza dough. This week, she uses 3 8ths the amount of flour she used last week, which statement is true about the amou

Answers

Answer:

Janet uses less than 4 cups of flour because 3/8 is less than 1.

Explanation:

What types of accidents are among the most common causes of serious work-related injuries and deaths?

Answers

Final answer:

Work-related accidents leading to serious injuries and deaths include falls, head injuries, exposure to hazardous chemicals, and workplace violence.

Explanation:

Work-related accidents are among the most common causes of serious injuries and deaths in the workplace.  These accidents include incidents such as falls, head injuries, exposure to hazardous chemicals, and workplace violence. Fatalities can result from factors like inadequate safety measures, exposure to toxins, and traumatic incidents like assaults.

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