is f(x)=5x^2+6x^3 a polynomial function​

Answers

Answer 1
Polynomials are expressions whose exponents are non-negative integers and the coefficients are real numbers. The leading term is the term with the highest power. The coefficient of the leading term is the leading coefficient. The power of x in the leading term is called the degree of the polynomial! Here are some examples of polynomials:
Degree Name Example
0 constant 11
1 linear 4x + 7
2 quadratic 3x2 + 4x + 5
3 cubic 4x3 + 3x + 7
4 quartic 3x4 + 2x2 + 4
5 quintic x5 + 3x + 1
Any value of x such that P(x) = 0 is a root of the equation and a zero of the function.
Review of synthetic substitution
To use synthetic substitution, do the following:
1) Write the polynomial in descending order.
2) Make sure any missing terms are replaced with zero!
3) Bring down the leading coefficient.
4) Multiply by the divisor and add to the next term.
5) Repeat the process until the last coefficient is reached.

Example
Use synthetic division to find P(2) for P(x) = 2x3 - 9x2 + 27
2| 2 -9 0 27
4 -10 -20
2 -5 -10 7 The value of P(2) = 7, the last number!!
Sample Problems
1) State whether each is a polynomial function. If yes, find the degree and the zeros.
Problem Polynomial? Degree zeros
a) f(x) = 5 - 4x yes 1 5/4
b) f(x) = 3x2 - 6x yes 2 0, 2
c) f(x) = x - 3/x no
d) f(x) = 18 yes 0 none
e) f(x) = (x-3)/(x+2) no
2) Use synthetic substitution to find P(3) for each function:
a) P(x) = 4x3 - 5x2 + 3
3| 4 -5 0 3
12 21 63
4 7 21 66
Therefore, P(3) = 66

b) P(x) = 3x4 + 2x3 - 5x - 2

3| 3 2 0 -5 -2
9 33 99 282
3 11 33 94 280
Therefore, P(3) = 280


3) If 4 is a zero of f(x) = 3x3 + kx - 2, find the value of k.
Since 4 is a zero, the value of f(4) = 0. Use synthetic substitution.
4| 3 0 k -2
12 48 192 + 4k
3 12 48 + k 190 + 4k
Now 190 + 4k = 0, solve for k
4k = -190
k = -190/4 = -47.5

Related Questions

Pete grabbed 18 mixed nuts, StartFraction 2 Over 9 EndFraction of which were almonds. Which equation shows how to determine the number of almonds Pete grabbed? 18 divided by StartFraction 2 Over 9 EndFraction = 81 18 times StartFraction 2 Over 9 EndFraction = 4 StartFraction 2 Over 9 EndFraction divided by 18 = StartFraction 1 Over 81 EndFraction StartFraction 9 Over 2 EndFraction divided by 18 = one-fourth

Answers

Answer:

1/4

Step-by-step explanation:

9 divide by 18= 1/4

Need answer asap please help

Answers

Answer:

5(-3)^2+7

Step-by-step explanation:

Answer:

5(-3)^2+7

Step-by-step explanation:

please this is my true answer dont judge me please..thank...

you want new jeans and there is a sale this week where they are marked down 30%. what is your final cost if the original price is $50?

Answers

Answer: 15 dollars

Step-by-step explanation:

0.3 * 50

Question 1 (2 points)

(03.04)

For the function f(x) = -(x + 1)2 + 4, identify the vertex, domain, and range. (2 points)

A-The vertex is (-1,4), the domain is all real numbers, and the range is y greater than4.

B-The vertex is (-1, 4), the domain is all real numbers, and the range is y less than4.

C-The vertex is (1,4), the domain is all real numbers, and the range is y greater than 4.

D-The vertex is (1.4), the domain is all real numbers, and the range is y less than4.

Answers

Answer:

The vertex is (-1, 4), the domain is all real numbers, and the range is y less than 4

Step-by-step explanation:

Given

[tex]f(x) = -(x+1)^2 + 4[/tex]

Solving (a): The vertex;

Assume the general form of a function is

[tex]f(x) = a(x-h)^2+k[/tex]

The vertex is determined by [tex](h,k)[/tex]

By comparison, we have:

[tex]-h = 1[/tex]

Solve for h, we have:

[tex]h = -1[/tex]

[tex]k = 4[/tex]

So, the vertex is:

[tex](h,k) = (-1,4)[/tex]

The domain; x is all real numbers

From the function;

[tex]f(x) = -(x+1)^2 + 4[/tex]

This can be rewritten as:

[tex]f(x) = 4 - (x+1)^2[/tex]

This implies that:

Whatever the value of [tex](x + 1)^2[/tex] is, it will be subtracted from 4 to give y or f(x);

Hence:

y is less than 4

Option B answers the question

Select the values that correctly complete the problem. a = b = c = d = e =​

Answers

Answer:  2/3 = b/ac = d/e

Step-by-step explanation:

This is all I got if I got it right. Is this one of your answers?

Answer:

a= 2

b=4

c=3

d=2

e=3

Step-by-step explanation:

i hope this helps.

Find the set of solutions for the linear system Use s1, s2, etc. for the free variables if necessary. ,

Answers

Answer and explanation:

Please find attached

To win a trivia game you must score 90 points each correct answer is worth 1 3/4 points, each incorrect point is worth -1/4 points if he gets 58 questions correct and 22 questions incorrect, what is his score?

Answers

96 because make 1 3/4 an improper fraction and turn into a decimal it will be 1.75 then multiple by 55(how many you got right) it’ll be 101.5 then 1/4= .25 in decimal form so multiple that by 22(how many you got incorrect) and it’ll be 5.5 so you’ll do 101.5 - 5.5 and it’ll be 96 hope it helps!!

HELP!!!!!!!! I LOVE YOU AND ILL EVEN GIVE BRAIN

Answers

Answer It’s the last choice

Scientists examined data on mean summer sea‑surface temperatures (in degrees Celsius) and mean coral growth (in millimeters per year) over a several‑year period at locations in the Red Sea.

Temperature (∘C) 29.55 29.96 30.04 30.28 30.34 30.47 30.81
Growth (mm/y) 2.64 2.37 2 .74 2.52 2.34 2.46 2.31

Required:
Use your calculator to find the mean and standard deviation of both sea surface temperature x and growth y and the correlation r between x and y . Then use these basic measures to find the slope and intercept of the least‑squares line for predicting y from x .

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Temperature (∘C) 29.55 29.96 30.04 30.28 30.34 30.47 30.81

Growth (mm/y) 2.64 2.37 2.74 2.52 2.34 2.46 2.31

Using calculator and treating temperature and growth data as samples :

Temperature :

Mean : ΣX/n

n = sample size

Mean temperature (m) = 211.45 / 7

Mean temperature = 30.21°C

Standard deviation (s) :

Sqrt(Σ(X - m)²/n - 1)

s = 0.403

Growth:

Mean : ΣX/n

n = sample size

Mean growth (m) = 17.38 / 7

Mean growth = 2.483 mm/yr

Standard deviation (s) :

Sqrt(Σ(X - m)²/n - 1)

s = 0.161

Using the correlation Coefficient a calculator : the correlation Coefficient is - 0.6278, This shows that a negative relationship exists between both variables.

The intercept of the graph = 17.812

The slope of the relationship : -0.504

PLEASE HELP :’( last one

Answers

Answer:

A.3

Step-by-step explanation:

PLZZZZ HELPPPP I WILL MAKE YOU BRAINLIEST ANSWER PLZZZZZ THANKYOUUU!!!!!!!

Answers

1-corresponding
2-alt exterior
3-same side interior
4-corresponding
5-alt interior
6-alt exterior
I agree with them up here ^

Round to the nearest hundredth 13.459

Answers

Answer:

13.46

Step-by-step explanation:

The correct response is 13.46.

Since 9 is greater than 5, we replace the 5 in the hundreths place with a 6.

find the 13 term
7 la For the sequence 11,13,15,17​

Answers

well i don’t understand your question but the pattern is infinitely (+2) the next 3 terms are 19,21,23

How many different combinations of pennies, nickels, dimes, quarters, and half dollars can a piggy bank contain if it has 23 coins in it

Answers

Answer:

C ( 27, 4 )  number of ways

Step-by-step explanation:

number of coins in piggy bank = 23

x1 = number of pennies

x2 = number of nickels

x3 = number of dimes

x4 = number of quarters

x5 = number of half dollars

The required condition = 23

The required different combinations can be represented as

=  C ( 5 + 23 - 1 , 23 ) = C ( 27 , 23 )

                                  = C ( 27, 4 )

This is because :( C ( n, r ) = C (n, n-r ))

         

The Law of Large Numbers states that as an experiment is repeated, the relative frequency of an event tends toward the real probability.
a. if the probability of a specific observed event is very small, it is unlikely that the assumption about the probability is correct.
b. the probability of obtaining a favorable outcome increases as the number of trials increases.
c. the sampling distribution of the sample mean will be approximately normally distributed as long as the sample size is sufficiently large.
d. the probability that an event will occur is derived from one's increasing knowledge of relevant circumstances.

Answers

Answer:

c. the sampling distribution of the sample mean will be approximately normally distributed as long as the sample size is sufficiently large

Step-by-step explanation:

The law of large numbers is a statistical law, that states : As sample size grows, the sample mean tends to go closer to whole population mean.

So, the sampling distribution of the sample mean will be approximately normally distributed as long as the sample size is sufficiently large

List all subsets of the given set.
B = {Lennon, McCartney}
O {}, {Lennon}, {McCartney}
O {}, {Lennon}, {McCartney}, {Lennon, McCartney}
{}, {McCartney}, {Lennon, McCartney}
{ }, {Lennon}, {Lennon, McCartney}
{Lennon}, {McCartney}, {Lennon, McCartney}

please help!

Answers

Answer:

O {}, {Lennon}, {McCartney}, {Lennon, McCartney}

Step-by-step explanation:

Both the empty set and the total set are subsets of the given set.

Hence there are 4 subsets.

Answer:

O {}, {Lennon}, {McCartney}, {Lennon, McCartney}

Step-by-step explanation:

Two students missed a lot of school. One student missed every 4 days and the other students missed every 6 days. In 60 days how many times will they miss school at the same time?

LCM

Answers

The answer might be 2

Which one is right i need this fast

Answers

Answer:

The answer for the question is A, D and E

Answer:

a.

Step-by-step explanation:

is b because is answer is b thank you


Which expression is equivalent to (5x3)(2x)3
O 10x6
O 30X6
O 40x6
O 1,000x12

Answers

Answer:

10[tex]x^{6[/tex]

Step-by-step explanation:

I really hope 5x3 is 5x cubed and 2x3 is 2x cubed.

First multiply the coefficients (5*2)=10

then multiply the variables [tex]x^{3}[/tex]x[tex]x^{3}[/tex]=[tex]x^{6}[/tex]

then multiply them both

10[tex]x^{6[/tex] or option 1

The answer is C: 40x6


HELP PLEASE! I WILL GIVE BRAINILEST!
The graph of the function B is shown below. Find B(1).
O-1
01
02

Answers

Answer:

id say -1 though not enough details

Step-by-step explanation:

State whether each equation is true or false. For each equation that is true, write the number property shown by the equation.


a. 0 + 17 = 17. True or False?

false

Property:

communitive


b. 15 ÷ 3 = 3 ÷ 15. True or False?

true

Property:

comunitive


c. 2 + (4 + 9) = (2 + 4) + 9. True or False?

true

Property:

asociotive


d. 14 • 0 = 14. True or False?

false

Property:

Multiplication Property of Zero

fix the wrong answers

Answers

Step-by-step explanation:

a. true

property: identity

b. false

property: communitive

c. true

associative

d. false

property: multiplication property of zero

Evaluate the expression 12- x when x=8​

Answers

[tex]given \: that \ :[/tex]

[tex]x = 8[/tex]

[tex]then \:12 - x \: will \: be \: :[/tex]

[tex]12 - 8[/tex]

[tex] = 4[/tex]

[tex]∴ \: 12 - 8= 4 [/tex]

Answer:

The result of 12-x when x=8, is 4

Step-by-step explanation:

Numerical Evaluation

Evaluate an algebraic expression means substituting the variables present in the expression by their respective numerical values, operate and report the result.

The given expression is

12 - x

Substituting x = 8, we get:

12 - 8 = 4

The result of 12-x when x=8, is 4

Use the product rule to answer each of the questions below. Throughout, be sure to carefully label any derivative you find by name. It is not necessary to algebraically simplify any of the derivatives you compute.

a. Let m (w) = 3 w^17 4^w. Find m ′(w) .
b. Let h (t) = ( sin (t) + cos (t)) t 4. Find h ′(t).
c. Determine the slope of the tangent line to the curve y = f (x) at the point where a = 1 if f is given by the rule f(x) = e^x sin (x).
d. Find the tangent line approximation L(x) to the function y = g (x) at the point where a = − 1 if g is given by the rule g (x) = ( x^2 + x ) 2^x .

Answers

Answer:

A)  M'(w) = w^16 * 4^w [ 51 + 3w In4 ]

B) h'(t) = [ cos (t) - sin (t) ] t^4  + [ sin(t) + cos (t) ] 4t^3

C)  f'(1) = e' [sin(1) + cos(1) ]

D) g'(a) = 0 - 1/2

L(x) = - 1/2 ( x + 1 )

Step-by-step explanation:

Attached below is the detailed solution of the problem

A) m(w) = 3w^17 * 4^w

M'(w) = w^16 * 4^w [ 51 + 3w In4 ]

B) h(t) = [sin(t) + cos(t) ] t^4

h'(t) = [ cos (t) - sin (t) ] t^4  + [ sin(t) + cos (t) ] 4t^3

C)  f(x) = e^x sin (x).  at a = -1

f'(1) = e' [sin(1) + cos(1) ]

D) g (x) = ( x^2 + x ) 2^x .

g'(a) = 0 - 1/2

L(x) = - 1/2 ( x + 1 )

Yoko made $306 for 18 hours of work.
At the same rate, how much would she make for 8 hours of work?
What’s the answer I need help

Answers

Answer:

$136.

Step-by-step explanation:

Divide how much they made by the # of hours. 306/18=17. Multiply the amount per hour 17 by the 8 hours of work. 17x8=136.

What does the value of the LCM represent? How many packs of red sticks and blue sticks should Harold purchase?

Answers

Answer:

LCM mean least common multiple

Step-by-step explanation:

The red sticks in a pack of 8 so, to get 24 red sticks, Harold needs = 3 packs. The blue sticks come in a pack of 12 to get 24 blue sticks, Harold need = 2 pack

Answer:

the LCM represents the minimum number of sticks of each color that Harold would have to buy to have the same number of blue sticks and red sticks.

The red sticks come in packs of 8. So, to get 24 red sticks Harold need 3 packs.

The blue sticks come in packs of 12, so to get to 12 blue sticks Harold needs 2 packs.

in conclusion Harold should purchase 3 packs of red sticks and 2 packs of blue sticks.

hope this helped ^^

Help APSPP!!!!!!!!!!

Answers

Answer:

c is the answer young flyyy

Step-by-step explanation:

Answer:

hhaaaaaaaaaaaahhhhhhhhaaaaaaaaaaaaaaas

Step-by-step explanation:

According to a survey, 74% of households said that they have never purchased organic fruits or vegetables. Suppose that this result is true for the current population of households. a. Let x be a binomial random variable that denotes the number of households in a random sample of 10 who have never purchased organic fruits or vegetables. What are the possible values that x can assume

Answers

Complete Question

According to a survey, 74% of households said that they have never purchased organic fruits or vegetables. Suppose that this result is true for the current population of households. a. Let x be a binomial random variable that denotes the number of households in a random sample of 10 who have never purchased organic fruits or vegetables. What are the possible values that x can assume? Integers to . b. Find to 3 decimal places the probability that exactly 6 households in a random sample of 10 will say that they have never purchased organic fruits or vegetables. Use the binomial probability distribution formula. Probability

Answer:

a

The possible value of x is 0, 1 ,2,3,4,5,6,7,8,9,10

b

[tex]P(X = 6) =   0.158 [/tex]

Step-by-step explanation:

From the question we are told that

 The proportion that stated that they have not purchased organic fruits or vegetables is [tex]p =0.74[/tex]

   The sample size is  n = 10

The possible value x can take is  0, 1 ,2,3,4,5,6,7,8,9,10

Generally the probability that exactly 6  households in a random sample of 10 will say that they have never purchased organic fruits or vegetables is mathematically represented as

      [tex]P(X = 6) =  ^nC_6 * p^{6}* (1-p)^{n-6}[/tex]

Here C denotes combination

So

        [tex]P(X = 6) =  ^{10}6 * (0.74)^{6}* (1-0.74)^{10-6}[/tex]

=>    [tex]P(X = 6) =   0.158 [/tex]

2. What is the measure of the missing angle? *
C-120
B-95
A-85
What is D?

Answers

Answer:

60

Step-by-step explanation:

it is because 360-(120+85+95)

Which equation has exactly one solution?
А
3(x +1) =3x+ 2
B
3x =r +2.c
C
3x =T +2
3(x +1) =3x +3

Please answer fast

Answers

I’m pretty sure that it’s b

2r(2.59 + 10) - 3(r + 4) + s(r - 1)?
equivalent?

Answers

Answer:

2.30 is going to be your anwer

Step-by-step explanation:

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