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
Kayla thinks that the slope of a vertical line is undefined, while Joshua argues that the slope of a vertical line is zero. Who is correct? *
Answers
Answer:
Kayla is correct
Step-by-step explanation:
For a vertical line, the x-value is the same
This means there is no change in the x value
A slope is calculated by dividing by the change in x value
since in this case , we will be dividing by zero, it means that the value of our slope is going to be undefined
This means that Kayla is correct
An apple juice factory produced 830.87 gallons of apple juice in 4 days. How much apple
juice, on average, did the factory produce each day?
Answers
Answer:
207.7175
Step-by-step explanation:
take the 830.87 and divide it by 4 to see how much is made in 1 day. thats the average.
A box contains 5 chocolate chip cookies, 4 sugar and 6 oatmeal raisin. What is the probability of picking a chocolate chip cookie?
1/9
1/3
2/21
2/3
Answers
The probability of picking a chocolate chip cookie is 1/3.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, A box contains 5 chocolate chip cookies, 4 sugar, and 6 oatmeal raisin.
N represents no. of.
So, N(S) = 5 + 4 + 6 = 15.
N(CC) = 5, N(SR) = 4 and N(OR) = 6.
∴ The probability of picking a chocolate chip cookie is = N(CC)/N(S).
= 5/15.
= 1/3.
learn more about probability here :
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Gabby has 20 coins in her pocket that are quarters, dimes, and nickels. The total value of the coins is $2.70. The number of nickels that she has is equal to the number of quarters plus the number of dimes. Choose the system of equations that can be solved to find the number of quarters, 9, dimes, d, and nickels, n, that Gabby has.
Answers
Answer:
There's 9 nickels and no dimes
Step-by-step explanation:
the quarters equal $2.25
so there is at least 9 nickel's witch equals .45 cents add them and get $2.70 so
The system of equations to find the number of quarters, 9, dim, d, and nickels, n, that Gabby has are;
n = q + dn = 10q +d = 10Since, the total value of quarters, dim, and nicke is; $2.70.
Since the number of nickels that she has is equal to the number of quarters plus the number of dimes; we have;
n = q + dSince, Gabby has 20 coins in her pocket.
n + q + d = 20Therefore 2n = 20 from n = q + d
n = 10Read more on system of equations:
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How to put 1/25 as fraction simplified
Answers
Answer:
1/25
Step-by-step explanation:
1/25 is simplified, as 1 and 25 have no common factors.
(Unless you're saying 1/5 * 1/5?)
Fraction 1/25 is Already in its simplest form. It may be expressed in decimal form as 0.04
To simplify the fraction, we have to divide the numerator and denominator by their greatest common divisor (GCD).
Do the factorization of numerator and denominator
1 can be written as [tex]1\times1[/tex]
And 25 can be written as [tex]1\times5\times 5[/tex].
After factorization, we see that 1 is the greatest factor, which is common in both.
Divide the numerator and denominator by their greatest common divisor (1).
[tex]\dfrac{1 \div 1}{25\div1}[/tex]
[tex]=\dfrac{1}{25}[/tex]
Hence, 1/25 can not be further simplified.
Learn more about fractions here:
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write a quadratic polynomial, sum of whose zeroes is 2 and product is -8
Answers
Answer:
x^2 +2x-8
Step-by-step explanation:
Here, we want to write the quadratic polynomial given the sum of the root and the product
mathematically, we can have the factors as -2 And +4
So we have the equation as;
(x-2)(x + 4)
= x^2+ 2x - 8
target sells sweaters and sneakers in the ratio 1:3.The store sold 9 sweaters yesterday.How many sneakers were sold?
Answers
Answer: 27
Step-by-step explanation: since the ratio is 1:3 u mutiply
1 by 9 which equals nine and then u multiply 3 by 9 and u get 27. This should be right I am sorry if it isn't.
help plz I really need to finish
Answers
Answer:
[tex]26x^6y^4[/tex]
Step-by-step explanation:
the volume is like
[tex]V = length\cdot width\cdot depth[/tex]
so we have
[tex]V= 4yx^5\cdot 3xy\cdot 2y^2\\\\V=(4\cdot 3\cdot 2)(y\cdot y \cdot y^2)(x^5 \cdot x)\\\\V = 24(y^4)(x^6)\\\\V=24x^6y^4[/tex]
There are 54 new houses being built in a neighborhood. Last month, 1/3 of them were sold. This month, 2/3 of the remaining houses were sold. How many houses are left to be sold?
Answers
Answer:
Step-by-step explanation:
I need help with my math!
The diagram compares the ratio of girls in the chorus to boys in the chorus. What is the ratio of girls to boys? If there are 50 students in the chorus, how many are girls, and how many are boys? ??50 The ratio of girls to boys is too. The number of girls in the chorus is. The number of boys in the chorus is.
Answers
Answer:
there are a total of 20 boys and 30 girls in the choir of 50 students
Step-by-step explanation:
Scale the ratio 2:3. so that the numbers on either side sum to 50 . 2+3=5 , and 50÷5=10 , so we scale our ratio by a factor of 10 . So there are a total of 20 boys and 30 girls in the choir of 50 students
98 = 3y - 4 whats tha answer
Answers
Answer:
y = 34
Step-by-step explanation:
Answer:
34
Step-by-step explanation:
you would add 4 to both sides and get
102=3y
then you would divide by three and get
34=y
Select the correct answer.
ОА
Which equation represents the line that is perpendicular to y = $5 + 23 and passes through (-40,2012
- 15
y = - = - 30
= 5 + 52
= - 56
ОВ.
Ос. y =
OD.
Answers
Answer:
The question is written kinda bad, so i take the next two assumptions:
The original line is:
y = 5*x + 23
And we want to find a perpendicular line that passes through the point (-40, 2012)
Suppose that we have a linear equation:
y = a*x + b
A perpendicular line to this one, will have a slope equal to -(1/a)
Then a random perpendicular line to the one above, is:
y = -(1/a)*x + c
In this case, we start with the line:
y = 5*x + 23
Then the family of perpendicular lines to this one, will be like:
y = (-1/5)*x + c
Where c can be any real number.
Now, we also want this line to pass through (-40, 2012)
This means that when x = -40, the value of y must be 2012
We could replace these values in our equation above and solve it for c.
2012 = -(1/5)*(-40) + c
2012 = 40/5 + c
2012 = 8 + c
2012 - 8 = c = 2004
Then the equation is:
y = -(1/5)*x + 2004.
What is the solution to this equation?
-0.20% – 20) = 44-x
A x= -90
B. X=-50
C. x = 50
D. X=90
Answers
Answer:
C. x = 50
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
QUESTION 8
Some seventh-, and eighth-grade students.spend time at
the elementary school tutoring students. Of the students
who tutor, 21 are seventh-graders and 18 are
eighth-graders. What percent of the tutors are
seventh-graders?
A) 54%
B) 46%
C) 52%
D) 21%
Answers
You add the two together to get 39, then divide 21 by 39. This gives you 0.538, which turns into 54%
How do i get the answer x= 3, -1 for equation (3/x^2)+ 2/x =1
Answers
Answer:
Steps below
Step-by-step explanation:
(3/x²)+ 2/x =1 (x ≠ 0)
(3/x²) + 2x/x² = 1
(3 + 2x) / x² = 1
3 + 2x = x²
x² - 2x - 3 = 0
(x + 1) (x - 3) =0
x = -1 or x = 3
find the values of y for which the distance between the point p2,-3 and q 10, y is 10 units
Answers
Answer:
y = - 9, y = 3
Step-by-step explanation:
Calculate distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, - 3) and (x₂, y₂ ) = (10, y)
d = [tex]\sqrt{(10-2)^2+(y+3)^2}[/tex]
= [tex]\sqrt{8^2+(y+3)^2}[/tex]
Given distance between points is 10, then
[tex]\sqrt{64 +(y+3)^2}[/tex] = 10 ( square both sides )
64 + (y + 3)² = 100 ( subtract 64 from both sides )
(y + 3)² = 36 ( take the square root of both sides )
y + 3 = ± [tex]\sqrt{36}[/tex] = ± 6 ( subtract 3 from both sides )
y = - 3 ± 6 , thus
y = - 3 - 6 = - 9
y = - 3 + 6 = 3
kristen is building a pattern using triangles, the table shows the number of triangles in the first 4 terms of that pattern. which formula describes the number of triangles in the nth term of the pattern.
A. n=t+2
B.n=t+3
C. n=2t-1
D. n=2t + 3
Answers
Answer:
its C. im doing test to i saw different page
Step-by-step explanation:
diff pge
A bottle contains 15 marbles: 9 are white and 6 are green. What is the
probability of picking a white?
Answers
Answer: 3/5
Step-by-step explanation:
Fist find out how many whites are there and divide it by the total to find the probability.
9/15 simplify it to 3/5
SIMPLE INTEREST
Interest = ?
Principal = $1450
Interest rate = 9%
Time = 5 years
Answers
652.50
Step-by-step explanation:
1450 x .09 x 5 = 652.50
If you can explain and show me the answers that would be great!
Answers
Answer:
1) B=-12
2) 189.69
Step-by-step explanation:
Explanation 1: To find B, we have to replace the given points in the equation, that is , x=2 and y=1
[tex]3x+By+6=0\\3.2+B.1+6=0[/tex]
Then we solve for B.
[tex]6+B+6=0\\B+12=0\\B=-12\\[/tex]
Hence , B=-12
explanation 2: you have the following equation for the number of liters 3% milk:
[tex]0.03+0.1(200)-x=0.05(200)[/tex]
Solve the previous equation for x:
[tex]0.03x+20-x=10[/tex]
[tex]0.03-x=10-20\\-0.97x=-10\\x=10.31[/tex]
Hence , there are 10.31 liters of 3% milk
Add the numbers of liters 10% butterfat is :
[tex]200-10.31=189.69 liters[/tex]
PLEASE MARK ME AS BRAINLIEST
Han earns $33.00 for babysitting 4 hours. At this rate, how much will he earn if he
babysits for 7 hours. You may solve with any method but you must show your work.
Answers
Step-by-step explanation:
First, you want to find the unit rate, or how much Han earns per hour
You can do this by setting up an equation
x= amount earned per hour
4x= 33 Initial equation
4x/4 = 33/4 Isolating the variable
x = 33/4 = 8 1/4 = 8.25 The unit rate
Now you want to set up a new equation to find out how much he makes for 7 hours
x= amount earned per hour
y = total amount earned
y = 7x Initial equation
y = 7 ( 8.25) Substitution
y = 57.75 The answer
Han earns $57.75 for every 7 hours
Checking the answer....
y = 7x
57.75 = 7x Substitute y instead
57.75/7 = 7x/7
8.25 = x
Your answer should be correct
Hope this helps!!!
John works for a company that cuts down dead trees for the city. He needs to determine the height of the tree to ensure safety. He chooses a point 10 m from the base of the tree. From this point, the angle of elevation to the top of the tree is 46°. Determine the height of the tree to the nearest tenth of a meter.
Answers
Answer:
10.4m
Step-by-step explanation:
We solve the above question using the Trigonometric function of Tangent.
The formula is given as:
tan θ = Opposite/Adjacent
θ = Angle of Elevation = 46°
Opposite = Height of the tree = x
Adjacent = Distance from the base of the tree = 10m
Hence:
tan 46 = x/10
Cross Multiply
x = tan 46 × 10
x = 10.355303138m
Approximately to the nearest tenth = 10.4m
if 12% = £54
what does 100% =
Brainliest to first correct answer :)
Answers
Answer:
£450
Step-by-step explanation:
12%=£54
100%=?
we will criss cross it then 12%×?=100%×£54÷12
=£450
Pls help me It would help alot
Answers
Answer: A=4πr2
I really hope this helped!!
The double number line shows that 5 kilograms of avocados cost $9 dollar .
Based on the ratio shown in the double number line, what is the cost for 1 kilogram of avocados?
Answers
Answer:
hii hope it helps
Step-by-step explanation:
sorry for these pics
On Tuesday at lunch time, it was 29°C. By sunset , the temperature had dropped to 16°C
Answers
Answer:
whats the question?
Step-by-step explanation:
QUESTION 23
Tamara has $50 to spend on craft supplies. She spends $30
plus a 5% tax at the store. How much change should she
receive?
Answers
Answer:
the answer is $18.5
Step-by-step explanation:
30 + tax is $31.50
Answer:
$18.50
Step-by-step explanation:
Before Tax Price: $30
Sales Tax Rate: 5%
After Tax Price: $18.50
How can you find how much the sales tax is? Let's say you're buying a $100 item with a sales tax of 5%. Your math would be simply:
[cost of the item] x [percentage as a decimal] = [sales tax]
Step 1 : $30 x .05 (5%) = $1.50 Step 2 : $30 + $1.50 = $31.50Step 3 : $50 - $31.50 = $18.50The number of pages in an Algebra 1 book is 99 less than the number of pages in a gemomerty book. Write and solve an equation to find the number n of pages in the geomerty book
Answers
Answer:
n = a + 99
Step-by-step explanation:
Given that :
a = number of pages in algebra book 1
n = number of pages in geometry book
a = n - 99
The number, n of pages in a geometry book is ;
Pages in algebra book = (pages in geometry book - 99)
a = n - 99
a + 99 = n - 99 + 99
a + 99 = n
An ice cream shop offers a choice of three types of cones and 31 flavors of ice cream a customer gets to choose a cone and a type of ice cream how many events are described
Answers
Answer:
2 events are described.
Step-by-step explanation:
Because only three types of cones and 31 flavours of ice cream.
Slope of a line that passes through 19,3 and 4,3
Answers
Answer:
0
Step-by-step explanation:
y2-y1/x2-x1
3-3/4-19
0/-15
So its 0