i am confused in this can someone help?

I Am Confused In This Can Someone Help?

Answers

Answer 1

Answer:

[tex]\huge\boxed{\sf a = -12 , b = 8}[/tex]

Step-by-step explanation:

Given polynomial is:

[tex]f(x) = ax^3+ b^2 + 3x + 4[/tex]

[tex]\rule[225]{225}{2}[/tex]

First factor is (x-1)

Let x - 1 = 0  => x = 1

Putting this in the above polynomial

[tex]f(1) = a(1)^3 + b(1)^2 + 3(1) + 4[/tex]

Given that it's remainder is 3

[tex]3 = a + b + 3 + 4[/tex]

[tex]3 = a + b + 7[/tex]

Subtracting 7 to both sides

[tex]-4 = a + b\\OR \\[/tex]

a + b = -4 -------------------------- (1)

[tex]\rule[225]{225}{2}[/tex]

Second Factor is 2x + 1

Let 2x + 1 = 0 => x = - 1 / 2

Putting in the above polynomial

[tex]f(-\frac{1}{2} ) = a (-\frac{1}{2} )^3 + b (-\frac{1}{2} )^2 + 3 (-\frac{1}{2} ) + 4[/tex]

The remainder is 6

[tex]6 = -\frac{a}{8} + \frac{b}{4} - \frac{3}{2} + 4\\6 - 4 = -\frac{a}{8} + \frac{b}{4} - \frac{3}{2}\\2 = \frac{-a + 2b -12 }{8} \\-a + 2b - 12 = 16\\-a + 2b = 16 + 12\\[/tex]

-a + 2b = 28  --------------------------------(2)

[tex]\rule[225]{225}{2}[/tex]

Adding both equations

a + b -  a + 2b = -4 + 28

3b = 24

Dividing both sides by 3

b = 8

[tex]\rule[225]{225}{2}[/tex]

Putting b = 8 in Equation (1)

a + 8 = -4

a = - 4 - 8

a = -12

[tex]\rule[225]{225}{2}[/tex]


Related Questions

I need help finding the Function notation

Answers

Answer:

  1.5, -8, 0, 2f, 2/3

Step-by-step explanation:

j(x) = 2x means the function name is j, and it is a function of the variable x. To evaluate the function, you put the given value everywhere you see x, and do the arithmetic.

  j(0.75) = 2(0.75) = 1.5

  j(-4) = 2(-4) = -8

  j(0) = 2(0) = 0

  j(f) = 2f

  j(1/3) = 2(1/3) = 2/3

Let sin(45°)=0.7071.Enter the angle measure (μ), in degrees for cos(μ)=−0.7071.
any value equivalent to 360n +
, wheren is an integer

Answers

Given :

Let sin(45°)=0.7071.

To Find :

The angle measure (μ), in degrees for cos(μ)=−0.7071 and value equivalent to 360n + , where n is an integer .

Solution :

We know , value of sin x and cos x is same at x = 45° .

Now , cos (-x) = cos(90°+x)

Therefore , μ in given question is :

μ =90°+45°

μ=135°

So , for angle of type 360°n + :

μ = 360°n + 135° .

Hence , this is the required solution .

Write the improper fraction 33/10 as a mixed number

Answers

the answer is 3 3/10

hope this helps

Answer = 3 3/10

there’s 33 take away the ones that go to ten.

10 10 and 10 is 30. Therefore it’s 3 and 3/10

Susie and Peggy arrive at the fair with $32.50. The entrance fee per person is $7.50 and each ride costs $2.50 per person. What is the total number of rides they can go on if they each pay the entrance fee? Write and solve an equation for this situation

Answers

32.50 - (7.50*2) = 17.50

17.50 / 2.50 = 7

vienna earns $53 per week working part time at a bookstore. She makes $1 more for each book that she sells. The amount, A (in dollars), that vienna earns in a week if she sells b books is given by the following function.
A(b)=53+b
how much does Vienna earn in a week if she sells 35 books?​

Answers

Answer:

$88 or $298

Step-by-step explanation:

take viennas $53 per week and add the extra $35 she makes for selling books and you get $88

or

take viennas $53 per week and add the extra $245 she makes for selling books and you get $298

the first is if she sells 35 books for the whole week, and i wrote the second one for if you mean she sells 35 books a day

(im not sure if this is right, but its the closest thing i can think of)

Answer:

88 or 298!

Step-by-step explanation:

take viennas $53 per week and add the extra $35 she makes for selling books and you get $88

or

take viennas $53 per week and add the extra $245 she makes for selling books and you get $298

the first is if she sells 35 books for the whole week, and i wrote the second one for if you mean she sells 35 books a day

(im not sure if this is right, but its the closest thing i can think of)

Evaluate the following function over the domain {0,1,2,3}. What is the range? g (x) = -2x^{2} + 2

Answers

Answer:

the range= {-16, -6, 0, 2}

Step-by-step explanation:

domain={0,1,2,3}

g(x)= -2x^{2} + 2

g(0)= -2(0)^{2} + 2 =2

g(1)= -2(1)^{2} + 2 =0

g(2)= -2(2)^{2} + 2= -6

g(3)= -2(3)^{2}+ 2= -16

the range = {-16, -6, 0, 2}

If 26 out of 100 high school students plays high school sports, what fraction
and what percentage of high school students do not play sports?
Check all that apply

Answers

Answer:

26%, 26/100

Step-by-step explanation

The total students will your denominator, and the number "out of" the total will be your numerator, so the fraction is 26/100. Next, convert the fraction into a decimal by dividing 26 by 100, making it 0.26. To convert a decimal into a percent, move the decimal two places to the right, ie, 0.26 becomes 26%.

Answer:

74/100 and 74%

Step-by-step explanation:

JUST ANSWER ME PLEASE

Do the ratios 20/10 and 1/2 form a proportion?

Answers

Answer:

no

Step-by-step explanation:

they do not form a proportion because they are not equivalent to each other.

The given box plots show the number of text messages Paul and Sally received each day on their cell phones. Select the true statement. * Captionless Image Paul's data has a larger overall spread than Sally's data. The median of Paul's data is equal to the median of Sally's data. The median of Paul's data is greater than the median of Sally's data. The interquartile range of Paul's data is less than the interquartile range of Sally's data.

Answers

Answer:

Its pauls data has a larger  overall spread than sally.

Step-by-step explanation:

I just took the test and I got a 100. :)

How do I simplify -11+5+6(-6+13)^2

Answers

Answer:

288

Step-by-step explanation:

To simplify use the mnemonic device PEMDAS (parenthesis, exponent, multiplication, division, addition, subtraction)

First simply -6 and 13 (since they are in the parenthesis)

-11+5+6(7)^2

Now find out what 7^2 is

-11 + 5 + 6(49)

Next multiply 6 and 49 (294)

Lastly add 5 then subtract 11 from it

299-11

288

Answer:

Hello! :) I hope I am correct!

Step-by-step explanation:

(The answer should be 288)

Below is the steps!!

Steps:

⇒-6+6(-6+13)^2

⇒-6+6(7^2)

⇒-6+(6)(49)

The answer would be 288 if you solve this equation.

The last step:

⇒-6+294

Which equals 288

Therefore your answer would be 288.

Hope this helps!

By:BrainlyAnime! ^-^

(Just in case you didn’t understand, I attached a picture!)

An up-and-coming artist has 85 followers on Twitter and this number doubles every week. In what week will the artist first reach 1,000 followers? Use at least two different methods to come up with your answer.

Answers

Answer:

5.8 , which approximately is 6 weeks.

Step-by-step explanation:

the first method is the short one since u just have to double the 85 then divide to 1000.

1000 ÷ ( 85 × 2)

1000 ÷ 170 = 5.882,,,,,. round off to whole number to get 6.

the second method is the addition method.

we start by 85 then keep doubling 85 for every week........inshort.......we add 170 to each weeks number to get the number of followers for the following week.

85 ⇒ 170 ⇒ 340 ⇒ 510 ⇒ 680 ⇒ 850 ⇒ 1020.

     1st      2nd      3rd     4th      5th         6th     week.

u notice that we add (85×2), 170, to get the following week's number of followers..

in 5 weeks..... the number of followers is yet to get to 1000.

when u divide, u get 5.8.....,and it is not logic to say 5.8823....weeks

since she reaches 1000 followers in the 6th week.......though there is an addition,,,, it is the most appropriate answer.

It will take [tex]6[/tex] week to reach [tex]1000[/tex] followers.

First, we are using two step to find the answers.

  Division   Addition

Division:

   By given, A artist has [tex]85[/tex] followers.

Every week  the no. of. followers is doubled .

Now, find how many week the artist reach [tex]1000[/tex] followers.

Since week followers is doubled,

So ,[tex]85*2[/tex]

Thus,

 [tex]1000\div(85*2)\\\\=1000\div170\\\\=5.883[/tex]

Which is not possible .

Then, it take [tex]6[/tex]  week to reach the  [tex]1000[/tex] followers.

Addition:

    By given, A artist has [tex]85[/tex] followers.

Every week  the no. of. followers is doubled .

To find how many week the artist reach [tex]1000[/tex] followers.

Now, the first week has [tex]85[/tex] followers.

[tex]85[/tex] followers doubled.

[tex]85+85=170[/tex] followers doubled in every week .

Then,

Second week has   [tex]85+85=170[/tex] followers.Third week has    [tex]170+170=340[/tex] followers.Fourth week has  [tex]340+170=680[/tex] followers.Fifth week has      [tex]680+170= 850[/tex] followers.Sixth week has     [tex]850+170= 1020[/tex] followers.

Hence, the artist reach [tex]1000[/tex] followers in mid week of [tex]5[/tex] to [tex]6[/tex] week .

so, it approximately take  [tex]5.88[/tex] week to reach [tex]1000[/tex] followers but which is impossible to take decimal in week .

Thus, the artist take [tex]6[/tex] week to reach the [tex]1000[/tex] followers.

For more information:

https://brainly.com/question/17367033

what is 18 less than the quotient of a number and 3 as an expression

Answers

Answer:

n/3 - 18

Step-by-step explanation:

"quotient of a number and 3" is n/3, and so

"18 less than the quotient of a number and 3" as an expression is:

   n/3 - 18

You have money in your wallet, but you don't know the exact amount. When a friend asks you, you say that you have 100 dollars give or take 25. Write an inequality to describe the amount of money in your wallet.

Answers

Answer: 75 < x < 125.

Step-by-step explanation:

Let x be the amount of money in your wallet.  

The phrase "100 dollars give or take 25" means wallet can have money between (100-25) dollars and (100+25) dollars.

i.e. 100-25 < x < 100+25

⇒ 75 < x < 125.

That means the amount of money in your wallet lies between 75 dollars and 125 dollars.

Hence, the inequality to describe the amount of money in your wallet is 75 < x < 125.

Which number line have a point that is equal to point p? Check all that apply

Answers

A and C is the answer

Answer: A and C

Step-by-step explanation:

An adults heart beats about 2100 times every 30 minutes.A baby beats about 2600 times every 20 minutes. How many more heart beat i 60 minutes than an adults hearts?

Answers

Given :

An adults heart beats about 2100 times every 30 minutes.

A baby beats about 2600 times every 20 minutes.

To Find :

How many more heart beat baby have than adult in 60 min .

Solution :

Now , total number of heart beats of adult in 60 min , [tex]T_a=2100\times 2=4200[/tex]

Also , total number of heart beats of adult in 60 min , [tex]T_b=2600\times 3=7800[/tex]

Difference between them , [tex]7800-4200=3600[/tex] beats .

So , baby have 3600 more heart beats than adult .

Hence , this the required solution .

1. 6(8+7)=6∙8+6∙7 (this is an example of which property?)


A) Associative (addition)

B) Associative (multiplication)

C) Commutative

D) Distributive


Answers

Answer:

d: distributive

Step-by-step explanation:

8 ( 8 + 7 ) = 6 x 8 + 6 x 7, it may seem like commutative, except it pulls the parentheses  out making it distributive.

solve this please
[tex]5x - 2(4x + 11) = 14[/tex]

Answers

Answer:

Step-by-step explanation:

5x - 8x - 22 = 14

-3x - 22 = 14

-3x = 36

x = -12

Answer:

x = -12

Step-by-step explanation:

5x - 2(4x+11) = 14

5x - 2*4x -2*11 = 14

5x - 8x - 22 = 14

-3x = 14 + 22

-3x = 36

x = 36/-3

x = -12

Check:

5*-12 -2(4*-12 + 11) = 14

-60 -2(-48+11) = 14

-60 -2(-37) = 14

-60 + 74 = 14

- 3c = - 5 — 4с
I want to know the answer

Answers

Answer:

c=-5

Step-by-step explanation:

Last month, Jim ate 4 strawberries. Finn ate 1/8 as many strawberries as Jim did. How many strawberries did Finn eat?

Answers

Answer:

He ate 0.5 strawberry

Step-by-step explanation:

4÷8 or 4×(1/8) =0.5 strawberry

Edit 1: Typo

Answer:

1/2 or half a strawberry

Step-by-step explanation:

1/8*4

Question /
Alice is three more than twice Emma's age. The sum of their ages is 48. How old is Alice?

Answers

Answer:

Alice is 33 years old.

Step-by-step explanation:

Alice is 3 more than twice Emma's age:

E = Emma

A = Alice

A = 3 + 2E

Sum = 48 years

So,

A + E = 48

(3+ 2E) + E = 48

3 + 2E + E = 48

3 + 3E = 48 (-3 both sides)

3E = 45

E = 45/3

E = 15

Emma is 15 years old.

A = 3 + 2E

A = 3 + 2(15)

A = 3 + 30

A = 33

Alice is 33 years old.

Write 3.24 x 10-4 in standard notation.

Answers

3.24 x 10-4 in standard notation is 0.000324

Can someone please help me I need help

Answers

Answer:

C and B.

Step-by-step explanation:

f(x) = 4 - x^2.

The degree of f(x) is 2, which means it is a quadratic graph. The coefficient of x^2 is negative, which means the curve is pointing downwards. The only curve that satisfies this is Graph C.

f(x) = 2^x + 5.

Notice that 2^x is positive for all real values of x. Therefore the answer is Graph B.

The first one is graph c. The second is graph b.

If a/\2+1/a/\2=11, then a+1/a=?

Answers

Answer:

[tex] \pm \sqrt{13} [/tex]

Step-by-step explanation:

[tex] \bigg(a + \frac{1}{a} \bigg)^{2} = {a}^{2} + \frac{1}{ {a}^{2} } + 2 \times a \times \frac{1}{a} \\ \\ \bigg(a + \frac{1}{a} \bigg)^{2} = 11 + 2 \\ \\ \bigg(a + \frac{1}{a} \bigg)^{2} = 13 \\ \\ \bigg(a + \frac{1}{a} \bigg) = \pm \sqrt{13} [/tex]

Frank has a sample of steel that weighs 80 grams. If the density of his sample of steel is 8 g/cm3, what is the sample’s volume?

Answers

Answer:

volume of the sample is 10 cm³

Step-by-step explanation:

volume = 80 g / 8 g/cm³

volume = 10 cm³

I hope this helps you :)

-KeairaDickson

please help me i'm confused
(grade 7-8)

Answers

Best of my understanding, it would be 5+5, then 10+10, , 20+20 and so on, just add the numbers.

Is 8/5
an irrational number?

Answers

No, it’s not. It’s a rational number

the difference of a number x and 5

Answers

Answer:

x-5

Step-by-step explanation:

"difference" means subtraction. since there isn't a specific number given then we can use x. "and" indicates where the symbols goes.

What is the distance from M(-1, 6) to N(11, 1)?

Please show all work and not just the answers.

Answers

Distance = sqrt(x1-x2^2 + y1-y2^2)

Distance = sqrt((-1-11)^2 +(6-1)^2)

Distance = sqrt(12^2 + 5^2)

Distance = sqrt(144 + 25)

Distance = sqrt(169)

Distance = 13

Evaluate the expression when g=3 and h=39.
h-5g

Answers

Answer:

29

Step-by-step explanation:

g=3 h=39

h-5g

Substitute the values in for the variables :

39-5(3)

Order of operations: multiply first

39-15

=24

Hope this helps :)

Mr. Smith set aside 5/6 of an hour for homework after school each day. How many hours of homework does he do in 5 days?

4 1/6 hours
3 1/2 hours
4 1/2 hours
50 minutes

Answers

The answer is 1/2 hours
Other Questions
Identify if the following sequence is arithmetic or geometric.-5, 0, 5, 10, 15, 20, ...ArithmeticGeometric If r = 5 units and h = 7 units, what is the volume of the cylinder shown above? Use 3.14 for . Which of the following refers not only to a dish but also to the pot it is cooked in?A. Poutine (Canada)B. Smorgasbord (sweden)C. Tagine (Northwestern Africa)D. Goulash (Hungary) Gorgi found a shoe pair for $35. She had a 30% discount. What is the price now? Kyle is searching for the solver function but cannot seem to find it anywhere, not even under the Data tab in theribbon Lieutenant Commander Data is planning to make his monthly (every 30 days) trek to Gamma Hydra City to pick up a supply of isolinear chips. The trip will take Data about four days. Before he leaves, he calls in the order to the GHC Supply Store. He uses chips at an average rate of seven per day (seven days per week) with a standard deviation of demand of three per day. He needs a 95 percent service probability.a. If he currently has 40 chips in inventory, how many should he order? (Use Excel's NORMSINV() function to find the correct critical value for the given a-level.)Number of chips _____b. What is the most he will ever have to order? (Use Excel's NORMSINV() function to find the correct critical value for the given a-level. )Maximum order quantity _____ to what extent is the government responsible for it's citizens/members of society? explain. 4. Anything that has mass and takes up space is anexample ofA. energyB. chemical changeC. matterD. temperature Who is at the trail start at 9:00 a.m.? Solve the system of linear equations for x and y.(cos )x + (sin )y=1(sin )x + (cos )y = 0x=y= 1/7x + 3= 15 what is x? Describe the reasons for the growth of the cattle industry on the Great Plains. #4: Which property could be used to solve the equation below? *15 = x + 13 -3(4x+3)+4(6x+1)=43 Which is the general setting of "Sea Life"? How did the Renaissance affect England and English culture in 1907, Duncan preformed a series experiments in which he attempted to measure the weight of a soul as it left a dying person in his experiment McDowell cool place a dying person on a scale and measure their weight immediately prior to the following death. McDowell determined the change and weighed approximately 21 grams for the experiments he concluded the soul exists and has mass what is the fundamental scientific flaw in his conclusions find equation of the line shown Atomic Structure and Bonding_quiz Q12 Points The principal, angular momentum, magnetic and spin quantum numbers for an atomic system are designated as nn, ll, m_lm l , and m_sm s , respectively. Which of the following statements is true? a. nn represents the shape of the electron cloud b. m_lm l represents the orientation of the electron spin an electron at n=1c. n=1 classifies as a "free electron" ll represents the shape of an orbital Which organelle breaks down materials and releases energy into the cell?