All categories

2 years ago

Find all roots. 11) x^3 + 6x² + 5x = 0

Mathematics

1 answer:

Dmitrij [34]2 years ago

5 0

Answer:

x=0

x=-1

x=-5

Step-by-step explanation:

To find the roots, we set the equation equal to zero and factor.

x(x²+6x+5)=0 [factor]

x(x+1)(x+5)=0 [set each factor equal to 0]

x=0

x+1=0 [subtract both sides by 1]

x=-1

x+5=0 [subtract both sides by 5]

x=-5

Now, we have found three roots, x=0, x=-1, x=-5.

You might be interested in

6.Suppose the Gallup Organization wants to estimate the population proportion of those who think there should be a law that woul

drek231 [11]

Answer:

A sample of $n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$ is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In a previous study of 1012 randomly chosen respondents, 374 said that there should be such a law.

This means that $n = 1012, \pi = \frac{374}{1012} = 0.3696$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

How large a sample size is needed to be 95% confident with a margin of error of E?

A sample size of n is needed, and n is found when M = E.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$E = 1.96\sqrt{\frac{0.3696*0.6304}{n}}$

$E\sqrt{n} = 1.96\sqrt{0.3696*0.6304}$

$\sqrt{n} = \frac{1.96\sqrt{0.3696*0.6304}}{E}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$

$n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$

A sample of $n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$ is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

4 0

3 years ago

A water park sold 14 child tickets and 6 adult tickets. What percentage of

steposvetlana [31]

Total tickets sold :
14 + 6 = 20

fraction of child tickets sold = 14/20

then, we convert this fraction to %.

14/20 = 70/100
( multiply by 5 )

percentage = 70%

5 0

3 years ago

Read 2 more answers

How to write 30 1/4% as a fraction in simplest formq

ycow [4]

$p\%=\dfrac{p}{100}\\\\30\dfrac{1}{4}=\dfrac{30\cdot4+1}{4}=\dfrac{121}{4}\\\\30\dfrac{1}{4}\%=\dfrac{121}{4}\%=\dfrac{\frac{121}{4}}{100}=\dfrac{121}{4}\cdot\dfrac{1}{100}=\dfrac{121}{400}\\\\Answer:\boxed{30\frac{1}{4}\%=\frac{121}{400}}$

8 0

3 years ago

One ticket to a ride of the merry-go-round at the Sunday Fair costs $2.

sammy [17]

Considering the definition of an inequality, the maximum number of tickets that they can buy is 10.

<h3>Definition of inequality</h3>

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

greater than >.
less than <.
less than or equal to ≤.
greater than or equal to ≥.

An inequality contains one or more unknown values called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.

<h3>Maximum number of tickets that they can buy</h3>

In this case, you know that

One ticket to a ride of the merry-go-round at the Sunday Fair costs $2.
Jenny and her friends have $36 with them.
After buying tickets to the merry-go-round, they want to be left with no less than $15.

So, they want to spend on the purchase of tickets for the merry-go-round a value less than or equal to $36 - $15= $21.

Being "x" the maximum number of tickets that they can buy, the inequality that expresses the previous relationship is

2x≤ 21

Solving:

x≤ 21÷2

Then, the maximum number of tickets that they can buy is 10.

Learn more about inequality:

brainly.com/question/17578702

brainly.com/question/25275758

brainly.com/question/14361489

brainly.com/question/1462764

#SPJ1

7 0

1 year ago

Write a real-world problem that is solved by an equation and then solve (show work).

ololo11 [35]

A company is selling books. It has to pay $500 to start printing the books, and once they have done that, the books sell at $14.99 each. How many books must they sell to make a profit?

First we would model an equation. X will be the amount of books sold, and Y will be profits (in dollars obv). They had to pay $500 before they could start selling, so we must account for that too.

This equation would be $y=14.99x-500$ because for every book sold, X increases by 1, increasing Y by 14.99

The answer would be 34 books sold in order to turn a profit. (500/14.99=

6 0

3 years ago