MATHEMATICS HIGH SCHOOL

Which polynomial function f(x) has a leading coefficient of 1, roots –4, 2, and 9 with multiplicity 1, and root –5 with multiplicity 3?f(x) = 3(x + 5)(x + 4)(x – 2)(x – 9)
f(x) = 3(x – 5)(x – 4)(x + 2)(x + 9)
f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x – 2)(x – 9)
f(x) = (x – 5)(x – 5)(x – 5)(x – 4)(x + 2)(x + 9)

Answers

Answer 1

Answer:

The expression for f(x) is:

f(x) = (x+5)(x+5)(x+5)(x+4)(x-2)(x-9)

Step-by-step explanation:

We know that for any polynomial equation with roots:

$a_1,a_2,a_3,...$ with multiplicity:

$m_1,m_2,...$

the equation for the polynomial is given by:

$f(x)=(x-a_1)^(m_1)(x-a_2)^(m_2)......$

if the leading coefficient is negative we may take '-' sign in the starting of the expression.

Here we are given that :

f(x) has a leading coefficient of 1, roots –4, 2, and 9 with multiplicity 1, and root –5 with multiplicity 3

Hence, f(x) is given by:

$f(x)=(x-(-4))^(1)(x-2)^(1)(x-9)^(1)(x-(-5))^(3)\n\n\ni.e.\n\n\nf(x)=(x+4)(x-2)(x-9)(x+5)^3\n\n\nf(x)=(x+5)(x+5)(x+5)(x+4)(x-2)(x-9)$

Hence, the expression for f(x) is:

$f(x)=(x+5)(x+5)(x+5)(x+4)(x-2)(x-9)$

Answer 2

Answer: "polynomial function f(x) has a leading coefficient of 1"

So because of that, we can eliminate A and B.

Now we have "root –5 with multiplicity 3"

That's just product of three factors (x+5)

So D is wrong.

We are left with the only possible correct option C.

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A company offered one half of its employees a bonus if the production of cookies increased by 15%. The other half of the employees was not offered a bonus. As the end of the month, production in the group that did not get the bonus offer increased by a mean of 20 and production in the bonus group increased by a mean of 10. What is the correct order of steps to determine if the results are significant? A. Calculate the probability of a difference of 10. B. Calculate the difference of the means. C. Randomly separate the employees' individual results into two groups. D. Calculate the mean of each group. E. Run the experiment many times.

Answers

Answer:

Company revealed that, One half of employees will get bonus, if the production of cookies increased by 15 %.

And , other half of employees will not get the bonus.

And,

The group who didn't get the bonus, their production increased by mean of 20.

And, the production in the bonus group increased by mean of 10 only.

To check whether results are significant or not,we will follow the following steps

1. C. Randomly separate the employees' individual results into two groups.

2. D.Calculate the mean of each group.

3. B. Calculate the difference of the means

4. E. Run the experiment many times.

5. A .Calculate the probability of a difference of 10

The answer for this question is C, D, B, E, A. I hope that helps!

Please help me, I really need help. I will mark brainliest answer!! A bald eagle can eat 3.85 kilograms of fish in a week. The eagle eats the same amount each day. How many grams of fish will the eagle eat in a day?

Answers

3.85÷7 is =55 grams can be eaten.

well you need to divide 3.85 by 7 which would give you 0.55

What is the midpoint of the segment joining (12,2) and (-5,-7)

Answers

To find midpoint the fomula is
x1+x2/2,y1+y2/2

so the answere would be 12+(-5)/2 , 2+(-7)/2

so mid point would be (x,y) =(3.5,-2.5)

I hope this makes sense :)

Select the equivalent expression

Answers

to my calculations i think it’s c

Marly needs to score 586 points in order to pass a test. Every question is worth 4 points. She already has 58 points. How many more questions does she need in order to pass this test?

Answers

Answer:

Step-by-step explanation:

586 divide by 4 is 146.5 so then i rounded to make it 147 then subtracted the points she already had (58) which led me to 89

Answer:

132 questions

Step-by-step explanation:

First, let’s find how many more points she needs.

To find this, find the difference between the points she needs and the points she has.

points needed- points gained

She needs 586 points and already has 58 points.

586 points-58 points

528 points

Now, we need to find how many questions she needs to answer correctly.

She needs 528 points and every correct question is worth 4 points.

Therefore, we can divide 528 by 4 to find how many questions she must answer correctly.

528/4=132

132 questions

She must answer 132 questions correctly to pass the test.

Due to fire laws no more than 720 people may attend a performance at metro auditorium. the balcony holds 120 people. there are 32 rows on the ground floor, each with the same number of seats. write an inequality to find the numbers of people that can sit in a ground floor row if the balcony is full. indentify what your variable represents WRITE ME A INEQUALITY AND WHAT THE VARIABLE REPRESENTS

Answers

Answer: $x\leq 18.75$ is the inequality and x is the number of seats in each row in the ground floor.

Step-by-step explanation:

Since, The total number of people may attend = People in the balcony + People in the ground floor.

And, According to the question, Number of the people in the balcony = 120

Now, Let x represents the number of the seats in the ground floor,

While y represents total number of people.

And, again according to the question,

There are 32 rows on the ground floor,

Therefore, the number of the people in the ground floor = 32 x

y = 120 + 32 x

But, the total number of the people must be not more than 720.

Therefore, $y \leq 720$

⇒ $120 + 32 x\leq 720$

⇒ $32 x\leq 720-120$

⇒ $x\leq 18.75$

Where x is the number of seats in the ground floor.

32*x < 720-120
32*x < 600
x < 18.75

because of x represents the number of seats in each row, it has to be a natural number -- whole. so x=18 is the max number of seats in each row and x < 18.75 is the desired inequality.

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