Answers
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
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]
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!)
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 :)
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
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}
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)
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. :)
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
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.
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
Write 3.24 x 10-4 in standard notation.
Answers
Write the improper fraction 33/10 as a mixed number
Answers
the answer is 3 3/10
hope this helps
there’s 33 take away the ones that go to ten.
10 10 and 10 is 30. Therefore it’s 3 and 3/10
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
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
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
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.
Is 8/5
an irrational number?
Answers
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.
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
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:
please help me i'm confused
(grade 7-8)
Answers
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 .
- 3c = - 5 — 4с
I want to know the answer
Answers
Answer:
c=-5
Step-by-step explanation:
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:
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.
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.
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
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
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 .