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3 years ago

Find the zeros of the polynomial function: f(x) = 9x^3 - 27x^2 - 4x + 12.

Mathematics

1 answer:

hichkok12 [17]3 years ago

3 0

Answer:

{-2/3, 2/3, 3}

Step-by-step explanation:

The equation can be factored by grouping.

f(x) = (9x^3 -27x^2) +(-4x +12)

f(x) = 9x^2(x -3) -4(x -3)

f(x) = (9x^2 -4)(x -3)

We recognize the first factor as the difference of squares, so know it can be further factored to give ...

f(x) = (3x -2)(3x +2)(x -3)

The zeros are the values of x that make these factors be zero:

3x -2 = 0 ⇒ x = 2/3

3x +2 = 0 ⇒ x = -2/3

x -3 = 0 ⇒ x = 3

The zeros of the polynomial are x = -2/3, 2/3, 3.

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How in the world do I answer this problem??

galben [10]

Answer:

Step-by-step explanation:

ST is y and SU is 2y-4.

Note that SU = ST + TU = y + 18

So we have 2y - 4 = y + 18

2y - 4 = y + 18

2y = y + 22

y = 22

So ST is 22.

4 0

3 years ago

There are 482 studemts in the school and there are two Grade 4 classes: Ms.Ashley's and Mr.Ben's classes. Mrs. Aheley's class ha

Paraphin [41]

Answer:

1. 45/482 of the students are in grade 4.

2. 5/9 of the students of the grade 4 are boys.

3. 7/15 of the grade 4 students are in Ms. Ashley's class

4. 3/4 of the students in Mr. Ben's class do not have siblings in the same school.

5. There are 14 students with glasses and 7 without glasses.

Step-by-step explanation:

1. Let's review the information given to us for solving the questions:

Number of students in the school = 482

Ms. Ashley's Grade 4 class = 21 students

Ms. Ashley's Grade 4 class boys = 15 students

Ms. Ashley's Grade 4 class girls = 6 students

Ms. Ashley's Grade 4 class with glasses = 2/3 * 21 = 42/3 = 14 students

Mr. Ben's Grade 4 class = 24 students

Mr. Ben's Grade 4 class boys = 10 students

Mr. Ben's Grade 4 class girls = 14 students

Mr. Ben's Grade 4 class with siblings in the school = 1/4 * 24 = 24/4 = 6 students

2. Let's answer all the questions:

1. What fraction of the students in the school are in grade 4?

(Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)/ Number of students in the school

21 + 24 / 482 = 45/482

2. What fraction of the grade 4 students are boys?

(Ms. Ashley's Grade 4 boys + Mr. Ben's Grade 4 boys)/ (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)

15 + 10 / 21 + 24

25 / 45 = 5/9

3. What fraction of the grade 4 students are in Ms. Ashley's class?

Ms. Ashley's Grade 4 class / (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)

21 / 21 + 24

21 / 45 = 7/15

4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?

(Mr. Ben's Grade 4 class - Mr. Ben's Grade 4 class with siblings in the school)/ Mr. Ben's Grade 4 class

24 - 6 / 24

18 / 24 = 3/4

5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?

There are 14 students with glasses and 7 without glasses.

4 0

3 years ago

I didn’t pay attention in class help

Alona [7]

Answer:

The 1/4th power means the 4th root of a number.

Therefore for the first question, the answer should be 4th root of 1296 -4th root of 625. or \sqrt[4]{1296}

1296

-\sqrt[4]{625}

625

For the second question just calculate? what to the 4th power is 1296 and what to the 4th power is 625?

They should respectively be 6 and 5. So the final answers we get is 6-5=1

If you have any questions about this just ask me in the comment and I will get to it as soon as I could.

hopecthis helps

4 0

3 years ago

8 ten thousands 4 hundreds =

zhenek [66]

8,400 is your answer.

7 0

3 years ago

Read 2 more answers

An engineer in charge of water rationing for the U.S. Army wants to determine if the average male soldier spends less time in th

lina2011 [118]

Answer:

a) H0: μm = μf versus Ha: μm < μf

b) $t=\frac{(2.68-2.7)-0}{\sqrt{\frac{0.65^2}{66}+\frac{0.5^2}{69}}}}=-0.200$

c) $p_v =P(t_{133}$

d) Fail to reject the claim that the average shower times are the same for male and female soldiers because the P-value is greater than 0.1.

Step-by-step explanation:

Data given and notation

$\bar X_{m}=2.68$ represent the mean for the sample male

$\bar X_{f}=2.7$ represent the mean for the sample female

$s_{m}=0.65$ represent the sample standard deviation for the males

$s_{f}=0.5$ represent the sample standard deviation for the females

$n_{m}=66$ sample size for the group male

$n_{f}=69$ sample size for the group female

t would represent the statistic (variable of interest)

Part a

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the average male soldier spends less time in the shower than the average female soldier, the system of hypothesis would be:

Null hypothesis: $\mu_{m}-\mu_{f}\geq 0$

Alternative hypothesis: $\mu_{m} - \mu_{f}< 0$

Or equivalently:

Null hypothesis: $\mu_{m}-\mu_{f}= 0$

Alternative hypothesis: $\mu_{m} - \mu_{f}< 0$

And the best option is:

H0: μm = μf versus Ha: μm < μf

Part b

We don't have the population standard deviation, so for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{(\bar X_{m}-\bar X_{f})-\Delta}{\sqrt{\frac{s^2_{m}}{n_{m}}+\frac{s^2_{f}}{n_{f}}}}$ (1)

And the degrees of freedom are given by $df=n_m +n_f -2=66+69-2=133$

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

What is the test statistic?

With the info given we can replace in formula (1) like this:

$t=\frac{(2.68-2.7)-0}{\sqrt{\frac{0.65^2}{66}+\frac{0.5^2}{69}}}}=-0.200$

Part c What is the p-value?

Since is a left tailed test the p value would be:

$p_v =P(t_{133}$

Part d

The significance level given is $\alpha =0.1$ since the p value is higher than the significance level we can conclude:

Fail to reject the claim that the average shower times are the same for male and female soldiers because the P-value is greater than 0.1.

4 0

3 years ago