To find the nth degree of polynomial function f(x) = x^4 - 4x^3 + 27x^2 -46x +60

**What is Function?**

Each element of X receives exactly one element of Y when a **function **from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

For polynomial with real coefficients, the complex zeros come with conjugates so 2+4i must come with 2-4i , then for 4th degree polynomial

f(x) =a (x+1)(x-3)(x-2-4i)(x-2+4i). With given f(1)=-68

a(1+1)(1-3)(1-2-4i)(1-2+4i)= -68.

By this we can find a

a (2)(-2)(-1-4i)(-1+4i) = -68

a(-4)(1+4i-4i-16i^2) = -68

a(-4)(1+16) = -68

a(-4)(17) = -68

a(-68) = -68

a = 1

Now, solving

f(x) =(x+1)(x-3)(x-2-4i)(x-2+4i)

f(x) = (x+1)(x-3)(x^2 - 2x + 20)

f(x) = (x^2 - 2x - 3)(x^2 - 2x + 20)

f(x) = x^4 - 2x^3 + 20x^2 - 2x^3 + 4x^2 - 40x + 3x - 6x + 60

f(x) = x^4 - 4x^3 + 27x^2 -46x +60

Hence, the for 4th degree polynomial is f(x) = x^4 - 4x^3 + 27x^2 -46x +60

To learn more about **Function **click on the link

https://brainly.com/question/10439235

#SPJ9

convert these measurements to centimeters : (a)73.1 cm and (b) 0,0012km

**Answer:**

(a) 73.1 cm (b) 120 cm

**Step-by-step explanation:**

**Step-by-step explanation:**

**Part (a)**

**73.1 cm** [It remains the same as it is already given in cms]

**Part (b) **

To convert 0.0012km to cm we multiply x 100000

=> 0.0012 x 100000

=> **120 cm**

Rajan climbed to a height of 15 ft from the bottom of a climbing wall. He then climbed up an additional 10 ft.

What must he do to return to the bottom of the climbing wall?

In the first blank, say whether Rajan must climb up or down. In the second blank, state the number of feet Rajan must travel up or down.

Rajan must climb_____ft to return to the bottom of the climbing wall.

**Rajan** must climb **down **25** **ft to return to the bottom of the climbing **wall**

Height **climbed** from the bottom of the wall = 15ft

**Height**: The measurement of an object's height from the base to the top is known as height. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.

Additional height climbed = 10ft

Total height climbed = 25ft

He should climb down the distance, as climbing up will further move him away from the **bottom** of the wall

Distance to climb down to the bottom of the wall = 25ft

Learn more about **height:**

https://brainly.com/question/21836055

#SPJ1

How many times larger is 8.1 than 2.7

8.1 is 5.4 more times larger than 2.7

Four of the twelve members of the panel were late for

the meeting. What fraction of the members were on

time?

**Answer:**

2/3

**Step-by-step explanation:**

If 4 were late, then 8 were on time.

8/12 Divide the top and bottom by 4

2/3

I just need to know how to work it out for future problems. (Business Calc)

Find the price elasticity of the demand function as a function of p.

1. q=D(p)=600-3p

A)E(p)= p/p-200

B)E(p)= p/600-3p

C)E(p)= p/200-p

D)E(p)= p(200-p)

The price **elasticity** of the **demand** function as a function of p is C. E(p)= p/200-p

It should be noted that the price **elasticity** of **demand** simply means the ratio of the percentage change in quantity demanded to the percentage change in price.

In this case, the **function** is given as:

q = D(p) = 600-3p

Differentiate with respect to p

D'(p) = 3

The **elasticity** of demand will be:

= (P / 600 - 3p) × (-3)

= P / (200 - P)

In conclusion, the correct option is C.

Learn more about **demand** on:

brainly.com/question/1245771

#SPJ1

What is the exact decimal equivalent of 7/12

Answer:

0.58333333333

If f (x) = x

2 − 2 x , g (x) = x − 2

1) prove that : f(2) = g(2)

2) If g (K) = 7 , find : the value of k

1. The **value **of f(2) = 0 and g(2) = 0

2. The **value**** **of k is 9

A **function** can simply be described as a law, rule, theorem or expression that explains the **relationship** between two terms.

These terms are known as;

The dependent variableThe independent variableGiven the functions;

f(x) = x^2 - 2xg(x) = x - 21To prove that f(2) = g(2)

Substitute the value of x as 2 in the functions, we have;

f(2) = 2^2 - 2(2)

expand the bracket

f(2) = 4 - 4

f(2) = 0

Then for g(2), we have;

g(2) = 2 - 2

g(2) = 0

Then, f(2) = g(2) = 0

If g(k) = 7

Then, we have;

k - 2 = 7

collect like terms to determine the value of k

k = 7 + 2

k = 9

Hence, the **value** is 9

Learn more about **funct****ions**** **here:

https://brainly.com/question/25638609

#SPJ1

The number of hours it takes for ice to melt varies inversely with the air temperature. A block of ice melts in 2.5 hours whenthe temperature is 54 degrees.How long would it take for the same block of ice to melt if the temperature was 45 degrees?

Let **t** be the time in hours it takes a block of ice to melt at **T** degrees.

Since both variables have an **inverse relation**, we can say that:

Where alpha is a constant value.

Since we know that a block of ice melts in 2.5 hours when the temperature is 54 degrees, we can plug in such data and find alpha as following:

[tex]\begin{gathered} 2.5=\alpha\cdot\frac{1}{54}\rightarrow2.5\cdot54=\alpha \\ \Rightarrow\alpha=135 \end{gathered}[/tex]Therefore, our expression would be:

[tex]t=\frac{135}{T}[/tex]For **T = 45**,

**We can conclude that it would take 3 hours for the block of ice to melt.**

Find sinθ, tanθ, and secθ, where θ is the angle shown in the figure. Give exact values, not decimal approximations.sinθ=tanθ=secθ=

[tex]undefined[/tex]

1) We have here a right triangle, so we can use the Pythagorean Theorem to find the adjacent leg. Note that the hypotenuse is leg opposite to the right angle. In this case, a=4.

a²=b²+c²

4²=b²+3²

16=b²+9

16-9=b²

b=√7

2) Let's find the trigonometric functions. The first one is the sine (θ), which relates the opposite side and the hypotenuse:

[tex]\sin (\theta)\text{ =}\frac{3}{4}[/tex]2.2)Moving on, we can deal with the tangent of theta, relating the opposite side over the adjacent, for this one we have to rationalize it:

[tex]\begin{gathered} \tan (\theta)\text{ =}\frac{3}{\sqrt[]{7}} \\ \tan (\theta)=\frac{3\sqrt[]{7}}{7} \end{gathered}[/tex]Finally, let's find the reciprocal function of the cosine function by setting this as the reciprocal of the cosine, and then calculating it:

[tex]\begin{gathered} \sec \text{ (}\theta)=\frac{1}{\cos(\theta)}\Rightarrow\sec (\theta)=\frac{1}{\frac{\sqrt[]{7}}{4}}\Rightarrow\sec (\theta)\text{ =}\frac{4}{\sqrt[]{7}} \\ \sec (\theta)\text{ =}\frac{4\sqrt[]{7}}{7} \end{gathered}[/tex]it says on top that the image is not drawn to scale.

**D; Both statements are correct**

Here, we want to check the correct statement

Basically from the diagram, it is confirmed that what we have is a 30-60-90 triangle

Now, for a 30-60-90 degrees triangle, the side lengths are in a particular ratio

From the diagram, MO faces the right angle and thus, it is the longest side and the hypotenuse

Now, let us take a look at the ratio of the sides in both submissions

For a 30-60-90 degrees triangle, the ratio of the sides is;

[tex]1\colon\sqrt[]{3}\text{ :2}[/tex]Hence, one side must be twice the length of the other

From Kellie's statement we can see MO is twice NO

From Eddie's statement, we can also see that MO is twice NO

Lastly, we can also see in both that dividing MN by NO yields the root of 3 in both statemets which confirms the existence of the theoretical ratio

So the conclusion here is that;

**Both students are correct**

If you spend 1 hours a week studying for English and 3.5 hours studying for math what is the ratio of time spent studying in math to studying for English?

The **ratio** of time spent studying math to studying English is 7:2.

According to the question,

We have the following information:

One spends 1 hour a week to study English and 3.5 hours to study math.

Now, we know that the ratio can be simply understood as the division.

So, we will divide the number of hours devoted to** math** by the number of hours devoted to English.

Ratio of time spent studying math to studying **English** = 3.5/1

Ratio of time spent studying math to studying English = 35/10

(Now, we will convert this fraction into the simplest form by dividing both the numerator and **denominator** of the fraction by 5.)

Ratio of time spent studying math to studying English = 7/2

Ratio of time spent studying math to studying English = 7:2

Hence, the ratio of time spent studying math to studying English is 7:2.

To know more about** ratio** here

https://brainly.com/question/13419413

#SPJ1

can you help me factor the expression x^2+4x-21

To factor this expression we need to find two numbers which sum is 4 and the product is -21.

Now, 21 has only 2 factors (besides 1 and 21), 7 and 3, se we need to write them in a way such that they sum 4, so

[tex]x^2+4x-21=(x+7)(x-3)[/tex]we see that 7-3=4 and 7(-3)=-21, so the factorization is correct.

5 tons of rocks cost $7,000.00. What is the price per pound ??

Answer: Per rock or pound?

In the distribution shown, state the mean and the standard deviation. Hint: The vertical lines are 1 standard deviation apart.

We are given a distribution graph.

The mean of the distribution is the center that is **125.**

The **standard deviation** is given by

**Therefore, the mean of the distribution is 125 and the standard deviation is 28.**

Write the inequality shown by the shaded region in the graph with the boundary line y = -3x +5

Inequality is an inequality comparison of numbers or expressions.

Given inequality:

y < -3x+5, y < x+2, y < -1

Graph the above inequality using Geogebra's online graphing calculator.

**Answer:**

...................... Hoffe er u

on a map where each unit represents one kilometer two marinas are located at p(4,2) and q(8,12). if a boat travels in a straight line from one marina to the other how far does the boat travel. Answer choices: 14 kilometers 2sqrt296 kilometer 2sqrt5 kilometers

Solution:

Given the points below

[tex]p\left(4,2\right)and\text{ }q\left(8,12\right)[/tex]To find the distance between two points, the formula is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where point p represents coordinates 1 and point q represents coordinates 2

Substitute the coordinates into the formula above

[tex]\begin{gathered} d=\sqrt{(8-4)^2+(12-2)^2} \\ d=\sqrt{4^2+10^2} \\ d=\sqrt{16+100} \\ d=\sqrt{116} \\ d=\sqrt{4\times29} \\ d=2\sqrt{29}\text{ units} \end{gathered}[/tex]Since, 1 unit represents 1 kilometer on the map,

**Hence, the answer is**

Question 10The table below shows the amount of water that is in a bathtub that is being filled.Minutes1234Gallons ofWater12172227Which of the following functions could model the amount of gallons of water, f(x), that the bathtub will contain after x minutes of being filled?Аf(x) = 5x + 7Bf(x) = 5x + 12сf(x) = 7x + 5Df%) = 12x + 5No

[tex]\begin{gathered} x=\text{ number of minutes} \\ f(x)=\text{amount of gallons of water the bathtub will contain} \\ \text{The function that fit the table is } \\ f(x)=5x+7 \end{gathered}[/tex]

Can you please help me solve this questions. I want a clear explanation thank you.

**Given:**

The z-score for 90 percent is 1.64.

To find the 90 percent confidence interval,

[tex]\begin{gathered} \mu+(\frac{\sigma}{\sqrt[]{n}}\times1.64)=21.4+(\frac{5}{\sqrt[]{66}}\times1.64) \\ =21.4+1.0094 \\ =22.4094\ldots\ldots(\text{ upper limit)} \\ \text{And} \\ \mu-(\frac{\sigma}{\sqrt[]{n}}\times1.64)=21.4-(\frac{5}{\sqrt[]{66}}\times1.64) \\ =21.4-1.0094 \\ =20.3906\ldots\ldots\ldots(\text{lower limit)} \end{gathered}[/tex]**Answer: The 90 % confidence interval is ( 20.3906 , 22.4094 )**

Jolie is redesigning a water bottle to fit better in her cup holder. The diameter will have to be no larger 2.5 in. The water bottle is straight up and down. What would the height of the bottle be if she wants it to have a 99.34 in3 volume. (Round to nearest whole number)

Answer:

20in

Explanations:The water bottle in question is known to be **cylindrical in shape.** The formula for calculating the** volume of a cylinder** is expressed as:

where;

r is the **radius**

h is the **height**

**Given the following** parameters

diameter = 2.5in

radius = 2.5/2 = 1.25in

volume = 99.34 in^3

**Required**

Height of the water bottle

**Substitute the given parameters** intothe formula

The **height** of the water bottle will be** 20in**

To rent a certain meeting room, a college charges a reservation fee of $46 and an additional fee of $6.70 per hour. The math club wants to spend less than$106.30 on renting the meeting room.What are the possible amounts of time for which they could rent the meeting room?Use t for the number of hours the meeting room is rented, and solve your inequality for t.

As given by the question

There are given that the college charges a reservation fee of $46.

Now,

According to the question, the inequality is:

[tex]46+6.70t<106.30[/tex]Then,

To solve the above inequality, collect the constant terms on the right side

So,

[tex]\begin{gathered} 46+6.70t<106.30 \\ 6.70t<106.30-46 \\ 6.70t<60.3 \\ t<\frac{60.3}{6.70} \\ t<9 \end{gathered}[/tex]Hence, t**he room could be rented for up to 9 hours less than the stated amount.**

HELP ASAP HELP ASAP PLEASEEEEE

The **distance **between the **parallel lines **measured in the **y direction** is **3 units.**

given data

y = - 3x + 4

y = - 3x + 1

let line 1 be y = - 3x + 4 and line two be y = -3x + 1

Analyzing the two lines show that the **slope **is equal hence parallel

slope = -3

The **y intercept** of the line or just the intercept is what varied

The **difference **between these two pints represents the distance between them measured in the** y direction.**

The difference is solved as

4 - 1 = 3 units

The distance is **3 units**

Read more on **straight lines** here: https://brainly.com/question/25969846

#SPJ1

Helping my son with homework.. I have no clue what this is

**Answer:**

45 times

**Step-by-step explanation:**

it is 45 times because it can land on blue or green 5 out of 8 times so u do 72 divided by 8 and u get 9 so I do 9 times 5 and u get 45

2. A membership to the theme park is $48 per year. Marcos cancelled his membership early and is only required to pay for 0.25 of a year. How much will he need to pay?

**Marcos** needs to pay $12 for 0.25 of a year due to **cancelling** the **membership**

Membership cost to the **theme** park per year = $48

**Payment** required to be made by Marcos = 0.25 of a year

When we divide a whole into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a **decimal** number has the same decimal place value system as the complete number. However, as we proceed to the right following the decimal point, we obtain the fractional portion of the decimal number.

Converting the decimal into a fraction we get:

=0.25

= 25/100

= 1/4 of a year

So, Marcos needs to pay the membership fees for only 1/4 of a year

According to which we get: 48*1/4 = $12

Learn more about **decimals:**

https://brainly.com/question/548650

**#SPJ1**

PLS HELP WILL MARK YOU BRAINLIEST!!

Point B is the midpoint of AC. AB=2x and AC=3x+20.

What is the value of x?

x=-20

x=20

x=4

x=6

**Answer:**

X=4

**Step-by-step explanation:**

i got the answer on a different app

**Answer: The correct answer is 20 or -20**

**Step-by-step explanation:**

its between 20 and -20 since i selected x=6 and x=4 and they were both wrong lol

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Find the difference. Write your answer in simplest form.

The **mixed fraction** 11 [tex]\frac{7}{16}[/tex] - 4[tex]\frac{7}{12}[/tex] is equivalent to the **fraction **to 6 41/48

An **equation **shows the relationship between two or more numbers and variables.The mixed fraction 11 7/16 is equivalent to the **fraction **(11 * 16 + 7)/16 = 183/16

The **mixed fraction** 4 7/12 is equivalent to the **fraction** (4 * 12 + 7)/12 = 55/12

Substituting:= 18 [tex]\frac{3}{16}[/tex] - 5 [tex]\frac{5}{12}[/tex]

Simplifying:= 329/48

= 6 41/48

11 [tex]\frac{7}{16}[/tex] - 4 [tex]\frac{7}{12}[/tex] is equal to 6 [tex]\frac{41}{48}[/tex]

Find out more on **equation **at:

https://brainly.com/question/2972832

#SPJ1

Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?

As per the given **percentage**, there are **147** **students **are not take French their freshman year.

**Students**:

The students are the person formally engaged in **learning**, especially one enrolled in a **school or college.**

Given,

Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students.

Here we need to find the number of students who are not take French as their freshman year.

Let x be the total number of students in the **freshman **year.

So according to the given question, we know that,

72% of x = 378

Therefore, we have to find the value of x, so we have to move the others,

Then we get,

x = 378/72%

x = 378 x 100/72

x = 525

So, the total number of students are 525.

Then the students who are not taken French is,

=> 525 - 378 = 147

Therefore, the students who are not taken French is 147.

To know more about **Percentage **here.

https://brainly.com/question/8324374

#SPJ1

(3ax - n) ÷ 5

Solve for X.

**Answer:**

x = 10/a; restrictions a ± 0

**Answer:**

=============================

Given **expression**

**Solve it for x **in steps below:

Find X.

Cirucumscribed angles

**Answer:**

x = 64

**Step-by-step explanation:**

to find x add make an equation to solve for x. the equation is 90+90+44+2x+8=360. after solving for x, x will equal 64.

A person tosses a coin 14 times. In how many ways can he get 10 heads?

probability 50% for each side

14 times 14 =196 divided by 2 = 98

10 times 10 = 100 divided by 2 = 50

He can get 10 heads 50 different ways

14 times 14 =196 divided by 2 = 98

10 times 10 = 100 divided by 2 = 50

He can get 10 heads 50 different ways

which number is the closest approximation to the value of 3/94?

**Answer:**

[tex] \frac{1}{3} [/tex]

**Step-by-step explanation:**

[tex] \frac{3}{94} = 0.31 \\ \\ \frac{1}{3} = 0.33[/tex]

Please help asap!! Thanks
If the first two terms of a fibonacci sequence are 5, 25 then what us the next term ?
hurry plssssssssssssss
Describe how the economic system would affect entrepreneurs in the country.
NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!
In the story about Jim and Della, one reason the narrator calls them the magi is because they understand that there are more valuable things than moneyTrueFalse
our teacher often tell us a story to _ the meaning of a lesson A. bring in B. bring out C. bring up D. bring in
The word advocacy contains the root poc, which is from the Latin word var, meaning voice. How does the word voice relate to the meaning of the term advocacy?
Something Is DIFFERENT about this problem..I'm not sure what..991 + 2 = ?
Write the system of equations associated with the given augmented matrix. Do not solve
By 1680, Virginia had written laws to restrict the rights of people of African descent. Which of the following was an example of one of these laws? A. It was illegal for people of African descent to marry white colonists. B. It was illegal for people of African descent to speak English. C. It was illegal for people of African descent to operate machinery. D. It was illegal for people of African descent to own businesses. PREVIOUS SUBMIT
Isotope: 239PuHalf-life(years): 24,100InitialQuantity: Amount After4000 Years: 3.7g
please help, this is due by today
the irreversible elementary reaction a b takes place in the gas phase of an isothermal, isobaric pfr. reactant a and a diluent c are fed in equimolar ratio. if the molar feed rate of c is doubled and the conversion is kept constant, by how much does the reactor size change?
Estimate.45.86 + 54.14A.90B.99C.100D.110
what is the value of 10-
What is the definition of these terms? short storyconflictclimaxthemerealistic storycharacter studygenre story
A store sells 12 cans of fruitcocktail for $21.How much would it cost you to buy 7 cans of fruit cocktail?
suppose we use a hash function hto hash n distinct keys into an array t of length m. assuming simple uniform hashing, what is the expected number of collisions?
Find the slope between these two points:(-19, 12), (-9, 1)