x^5 + ax^3 + bx^2 - 3 = (x^2 - 1)Q(x) - x - 2
find the value of a and b?
Answers
9514 1404 393
Answer:
a = -2b = 1Step-by-step explanation:
Subtracting the remainder from the original polynomial gives a polynomial that has (x^2 -1) as a factor. Dividing, we find the quotient and remainder to be ...
(x^5 +ax^3 +bx^2 +x -1)/(x^2 -1) = (x^3 +(1+a)x +b) remainder (2+a)x +(b -1)
Since we want the remainder to be zero, we require ...
2+a = 0 ⇒ a = -2
b -1 = 0 ⇒ b = 1
_____
The attachment shows the division as given in the problem statement (with the given remainder expression).
Related Questions
Help due asap
Show workings
Answers
Answer:
P' = (-4,2)
Q' = (-2,5)
R' = (-1,-4)
S' = (-6,-1)
Step-by-step explanation:
our friends are going to the movies. The cost of one ticket is $9.50, and the cost of one large popcorn is $4.50. The expression Syntax error from line 1 column 49 to line 1 column 73. Unexpected 'mathsize'. shows the total cost for the four friends. Which of these is equivalent to the given expression?
Answers
Answer:
No clue not even close to a clue
Answer:
I'm pretty sure I know the question they're talking about. The answer would be 4(4.5) + (9.5)
Step-by-step explanation:
Help plz anyone who’s good with slope?
Answers
Answer:
-3
Step-by-step explanation:
you go down from the dot left most and you count towards the line that the second dot falls on and count over too it
Answer:
slope = - 3
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line
m = [tex]\frac{-1-2}{2-1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3
expand - 4x(x^2 - y)
Answers
Answer:
-4x³ + 4xy
Step-by-step explanation:
distribute -4x by 'x²' and '-y'
-4x(x²) = -4x³
-4x(-y) = 4xy
Answer:
-4x^3+4xy
Step-by-step explanation:
Distribute the -4xy
1)Identify the conjugate for 6 – 7√3 and explain your reasoning.
2)Multiply the radical expression 6 – 7√3 and its conjugate and write in simplified form. Show all your steps
3) Explain why we always get an integer when multiplying a radical expression by its conjugate? Provide your own appropriate example with supporting work that matches your explanation..
Answers
Answer:
1) The conjugate for [tex]6-7\cdot \sqrt{3}[/tex] is [tex]6+7\cdot \sqrt{3}[/tex].
2) -111
3) It is because number and its conjugate have the same numbers but their second components are opposite to each other.
Step-by-step explanation:
1) A radical number of the form [tex]r = a + b\sqrt{c}[/tex], [tex]\forall \,a,b,c\in \mathbb{R}[/tex], where the first component is a non-radical real number which acts as a "pivot" and the second component is the radical component, which generates a "displacement" from pivot.
The conjugate of [tex]r[/tex] is a real number [tex]s = a - b\sqrt{c}[/tex], [tex]\forall \,a,b,c\in \mathbb{R}[/tex], which that is "pivot" plus "displacement" in the direction opposite to that of [tex]r[/tex]. We proceed to complement this explanation with the image attached below.
Then, the conjugate for [tex]6-7\cdot \sqrt{3}[/tex] is [tex]6+7\cdot \sqrt{3}[/tex].
2) We proceed to performed all the need algebraic operation until result is found:
1) [tex](6+7\sqrt{3})\cdot (6-7\sqrt{3})[/tex] Given
2) [tex]6\cdot (6-7\sqrt{3})+7\sqrt{3}\cdot (6-7\sqrt{3})[/tex] Distributive property
3) [tex]6\cdot [6+(-7)\cdot \sqrt{3}]+7\cdot \sqrt{3}\cdot [6+(-7)\cdot \sqrt{3}][/tex] Definition of subtraction/ [tex]-a\cdot b = (-a)\cdot b[/tex]
4) [tex]6\cdot 6 +[6\cdot (-7)]\cdot \sqrt{3}+(6\cdot 7)\cdot \sqrt{3}+[7\cdot (-7)]\cdot (\sqrt{3}\cdot \sqrt{3})[/tex] Distributive, associative and commutative properties
5) [tex]36 +(-42)\cdot \sqrt{3}+42\cdot \sqrt{3}+(-49)\cdot 3[/tex] Definition of multiplication/[tex]-a\cdot b = (-a)\cdot b[/tex]/Definition of square root
6) [tex][36 +(-147)]+\sqrt{3}\cdot [42+(-42)][/tex] Commutative, associative and distributive properties/[tex]-a\cdot b = (-a)\cdot b[/tex]
7) [tex]-111+\sqrt{3}\cdot 0[/tex] Definition of subtraction/Existence of additive inverse
8) [tex]-111+0[/tex] [tex]a\cdot 0 = 0[/tex]
9) [tex]-111[/tex] Modulative property/Result
3) It is because number and its conjugate have the same numbers but their second components are opposite to each other.
The table below shows the height and the hand span of five students.
Which pattern of association best describes the relationship between the height and the hand span?
Answers
Answer:
positive linear association
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
please help due soon
Answers
Answer:
5z^2-8z+3
-5×-3=15
-5+-3=-8
so...
5z^2-5z-3z+3
5z(z-1)-3(z-1)
therefore the answer is...
(5z-3) (z-1)
Can you plz help me the first answer that is right gets brainliest
Answers
Answer:
slope = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 1) ← 2 points on the line
m = [tex]\frac{1-0}{0-(-2)}[/tex] = [tex]\frac{1}{0+2}[/tex] = [tex]\frac{1}{2}[/tex]
What is the least prime number that is a divisor N? N = (13 X 17) + (19 X 23)
Answers
Answer:
2
Step-by-step explanation:
13 x 17=221
19 x 23=437
437+221=658
658 divided by 2= 329
2 is prime and the least
Solve 5(y - 10) = -5
Answers
Answer:
y = 9
Step-by-step explanation:
Trying to get the variable alone is the main goal in solving these
to get the variable alone here we can divide both sides by 5, which gets us
y - 10 = -1
now we can add 10 to both sides to get y = 9
Pleaseeeeee help this is due today and I don’t know how to do thissss! Tug of War Activity
DIRECTIONS: Use the information provided about the first two rounds to figure out who will win the remaining rounds of the Tug of War.
Round 1:
On one side of the rope, there are four acrobats who all have equal strength. On the other side are five grandmas who each have equal strength as well. The result of the tug of war is dead even-- it’s a perfect tie.
Round 2:
On one side is Ivan the dog. On the other side are two grandmas and one acrobat. Again, it is dead even-- a perfect tie.
Round 3:
Three grandmas and Ivan are pulling against four acrobats. Which team wins? Justify your answer with at least 2 sentences.
Round 4:
Ivan and three acrobats are matched up against a team of grandmas. The result is a tie-- the two sides are evenly matched. How many grandmas were on the team? Explain your reasoning.
Bonus Round 5:
Create two teams of your choice in Round 5 that are not equally matched. Use Ivan and at least one acrobat and one grandma on either team. Explain which side will win and how you know.
Answers
Answer:
i
Step-by-step explanation:
HELP PLZ
Solve each proportion for the variable
Answers
Answer:
x = -1
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4/12-((x+2)/(2*x+5))=0
x + 2
Simplify ——————
2x + 5
1
Simplify again —
3
1 (x + 2)
— - ————— = 0
3 2x + 5
Find the Least Common Multiple
The left denominator is : 3
The right denominator is : 2x+5
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left , Right}
3 1 0 1
Product of all
Prime Factors 3 1 3
Number of times each Algebraic Factor
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left , Right}
2x+5 0 1 1
Least Common Multiple:
3 • (2x+5)
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 2x+5
Right_M = L.C.M / R_Deno = 3
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 2x+5
—————————— = ——————————
L.C.M 3 • (2x+5)
R. Mult. • R. Num. (x+2) • 3
—————————— = ——————————
L.C.M 3 • (2x+5)
Add the two equivalent fractions which now have a common denominator . Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2x + 5 - ((x + 2) • 3) -x - 1
——————————— = —————————
3 • (2x + 5) 3 • (2x + 5)
Pull out like factors :
-x - 1 = -1 • (x + 1)
-x - 1
—————————— = 0
3 • (2x + 5)
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now, to get rid of the denominator, multiply both sides of the equation by the denominator.
-x - 1
——————— • 3 • (2x + 5) = 0 • 3 • (2x + 5)
3 • (2x + 5)
Now, on the left hand side, the 3 • 2x + 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-x - 1 = 0
Solving a Single Variable Equation:
Solve : -x - 1 = 0
Add 1 to both sides of the equation :
-x = 1
Multiply both sides of the equation by (-1) : x = -1
Which illustration shows the particles of a solid.
Answers
Answer:
C
Step-by-step explanation:
The particles of a solid are tightly packed together. The one that is the most tightly packed is C. Also, B is the particles of a liquid, and A is the particles of a gas.
10 + 3x= 5 – 2x
What are the steps to finding the answer
Answers
Answer:
x=-1
Step-by-step explanation:
10+3x=5-2x (Add 2x to both sides)
10+5x=5 (Subtract 10 from both sides)
5x=-5 (Divide both side by 5)
x=-1
Answer:
x=-1
Step-by-step explanation:
10 + 3x= 5 – 2x
You first +2x on both sides
10 + 3x+2x= 5 – 2x+2x
subtract 10 on both sides
10-10+5x=5-10
Then divide 5 to isolate x
5 divide 5x=-5 divide 5
x=-1
Hope that helps :)
The volume of a box 4 in.wide,2 in.high and 5 in long is
Answers
Answer:
im gonna say 40 in
Step-by-step explanation:
Jaylen earns the same amount of money each month. His telephone bill is 1 20 of his monthly earnings, and he pays a total of $840 each year for his telephone service. How much does Jaylen earn each month, in dollars? Do not include commas or dollar signs.
Answers
Given :
Jaylen earns the same amount of money each month.
His telephone bill is 1/20 of his monthly earnings, and he pays a total of $840 each year for his telephone service.
To Find :
How much does Jaylen earn each month, in dollars.
Solution :
Monthly payment of telephone bill is :
[tex]M = \$ \dfrac{840}{12}\\\\M = \$70[/tex]
Let, his monthly salary is A.
So,
[tex]M = \dfrac{A}{20}\\\\A = 20\times M\\\\A = 20 \times 70\\\\A = \$1400[/tex]
Therefore, Jaylen monthly income is $1400.
Simplify the following functions:
8 2/3
Answers
Answer:
20/3
Step-by-step explanation:
8 times 3 plus 2 is 20. So 20/3
The table shows the relationship between the amount of candy bought (in pounds) and the total cost of the candy (in dollars) (5 points) Amount of Candy (pounds) 1 2 3 4 5 Cost (dollars) 65 120 195 220 300 Part A – Answer the question - Is cost proportional to pounds of candy bought? Why or why not? (You MUST show work to receive full credit!) Part B - – Write an equation to represent the relationship. The formula for the equation is y = kx
Answers
Answer:
65
Step-by-step explanation:
Answer:
(cost) is proportional to (amount of candy) because all of the values of the
ratios comparing cost to pounds are equivalent. All of the values of the ratios
are equal to . Therefore, every measure of (amount of candy) can be
multiplied by the number to get each corresponding measure of (cost).
10/5=2
8/4=2
12/6=2
16/8=2
20/10=2
Step-by-step explanation:
hope this helps also explanation is on the anwser part
Find the value of 3a + 2b -3 when a=-5 and b=-6
Answers
Answer:
-30
Step-by-step explanation:
Substituting values of a and b in equation
3(-5)+2(-6)-3
-15-12-3
-15-15
-30
Answer: -30.
Step-by-step explanation:
We start by multiplying 3 by -5 and 2 by -6.
So the new equation will be [tex]-15-12-3[/tex].
Then, we can either minus -12 by -3 or we can minus -15 by -12. Either way, we get the right answer.
[tex]-15-12=-27[/tex]
Then, the new equation will be [tex]-27-3[/tex].
[tex]-27-3 = -30[/tex].
Answer: [tex]-30[/tex].
Write the value of 6 in 34.65 in 2 ways
Answers
Answer:
After the decimal
Step-by-step explanation:
6 tenths and 00.6
y = 7-x when x = -1
Thank you so much !!
Answers
Answer:
Y = 8
Step-by-step explanation:
7- -1 is 8. If you're subtracting a negative, you're basically adding.
So 7+1 is 8.
DESPERATE (please answer with picture of the graph)
WILL MARK BRAINLIST AND THANKS
Answers
Answer:
4.8
Step-by-step explanation:
It would go closer to the five on the number line. Hope this helps!
If f(x) = 2x+1 and g(x) = 3x-2 Find f[g(1)] =
Answers
Answer:
3
Step-by-step explanation:
3(1)-2= 1
2(1)+1 = 3
Hello I am weak at maths! today was my math exam and I didn't do it well.Please help me daily when I ask questions in an easy manner so that I can understand well.Accept my humble request
Answers
Answer:
Nepali .!
from where? :::::::)))
3a + 7 + 2(3 + a)
what is this
Answers
Answer:5a+13
Step-by-step explanation:3a +7 +6+2a
= 3a +2a +7 +6
=5a+13
Combine the like terms.
brainliest please?
HELP PLEASE WILL MARK BRAINLIST
Answers
Because you do 8 across from the top times 5 blocks going down which is 40. Then you add the four half pieces which equals 2 so 40+2= 42
An organization has a goal to raised $50,000 for a scholarship fundraising project. They have raised 60% of their goal. How much money has the organization raised
Answers
Answer: 30,000
Step-by-step explanation: 50,000 x .60= 30,000
Graph the following inequality and upload the picture? Make sure it's legible
2x – 3y < -12
Answers
Answer:ok....
Step-by-step explanation:
put them in the order from least to greatest. You can use the number line to help.
Answers
Answer:
-1.85 -7/8 1 3/4
Step-by-step explanation:
It is about which one is to the farest right ▶️ from 0
1/5 ÷ 2
Explain how you could use multiplication to help check your answer to Number 1
Answers
Answer:
1/10
Step-by-step explanation:
you can find the reciprocal of 2 (which is 1/2) and multiply it to 1/5 and get 1/10, that is your answer
I hope this answer helped, and if it was correct, please mark this as brainliest! Thank you!
Answer:
1/10
Step-by-step explanation:
You first divide and then divide just becomes multiplication(I know its weird)
K(Keep) C(Change) F(Flip)
(1/5 ) (division becomes) x (The whole number 2 becomes the recipicol 1/2)
Then you multiply 1/5 times 1/2 =1/10