The work shows the first steps of writing a partial fraction decomposition. StartFraction negative 5 x cubed + 2 x squared + 9 x + 2 Over (x squared + 2) squared EndFraction = StartFraction A x + B Over x squared + 2 EndFraction + StartFraction C x + D Over (x squared + 2) squared EndFraction Negative 5 x cubed + 2 x squared + 9 x + 2 = (A x + B) (x squared + 2) + C x + D Negative 5 x cubed + 2 x squared + 9 x + 2 = A x cubed + 2 A x + B x squared + 2 B + C x + D For this partial fraction decomposition, find the unknowns. A = , B = , C = , and D =
Answers
Answer:
I'm certainly late, but it took me a while to figure this one out so I want to leave an answer.
A=-5 B=2 C=19 D=-2
Step-by-step explanation:
I looked back at the video and actually tried to pay attention and the way to figure these problems out is set up all of the degrees of x in an equation. So, take all of the coefficients that are attached to an x^3, and set them up equal to each other. This makes -5=A, which is the first answer. Repeat for x^2 and you have B=2. For x, it becomes 9=2A+C. A is equal to -5 (from the x^3), so you can substitute and get c=19. Repeat for the x^0 term (the constants), and you get 2=2B+D. Plug in the value for B, 2, and get 2=4+D, which then becomes D=-2. That's how you get the answer and I hope this helps somebody.
The values are A=-5, B=2, C=19 and D=-2
What is partial fraction?Partial fractions are the fractions used for the decomposition of a rational expression. When an algebraic expression is split into a sum of two or more rational expressions, then each part is called a partial fraction. Hence, basically, it is the reverse of the addition of rational expressions.
Given:(-5x³+2x²+9x+2) / x²+2 =(Ax + B)/x²+2 + (Cx + d)/x²+2 .......(1)
First, we have to perform the long division as follows
The long division gives
(-5x³+2x²+9x+2 )/ x²+2= ( -5x+2)+ (19x-2)/ x²+2
Now, we have to find the partial fraction for (19x-2)/ x²+2
But, as denominator cannot be factored, So no partial fraction can be calculated.
Thus, (-5x³+2x²+9x+2 )/ x²+2= ( -5x+2)+ (19x-2)/ x²+2
Comparing it with equation (1), we get
Hence, A=-5, B=2, C=19 and D= -2
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Related Questions
i need help to solve 4x^2-400=0
Answers
Answer:
x = 10
Step-by-step explanation:
Isolate the variable and get x by itself
4x^2 -400 = 0 add 400 to both sides
4x^2 = 400 divide both sides by 4
x^2 = 100. take the square root of both sides
x = 10
Please help!!
-5x+6y=12
y=5/6x+2
Answers
Answer:
this is the first answer
Step-by-step explanation:
hope this helps
Given two sides of a triangle, find a range of possible lengths for the third side.
4 cm, 17 cm
Answers
Determine whether the given value is a solution of the equation.
Answers
Answer:
84 is a solution.
Step-by-step explanation:
To find out if 84 is a solution or not, we plug in the value and simplify.
(84)/14 = 66 = 6Therefore, 84 is a solution.
PLEASE HELP WILL GIVE BRAINLIEST
Answers
So now solve for it to be sure if it is in fact a right triangle.
8^2+15^2=17^2
64+225= 289
289=289
Which means B is the error made.
Hope this helps!
PLZ HELP ILL MARK AS BRAINLIEST
Answers
Answer:
[tex]2,712 \: {yd}^{2} [/tex]
Step-by-step explanation:
Height of cylinder (h) = 24 yd
radius of cylinder (r) = 6 yd
Lateral surface area of the cylinder
[tex] = \pi {r}^{2} h \\ \\ = 3.14 {(6)}^{2}(24) \\ \\ = 2,712.96 \: {yd}^{2} \\ \\ \approx \: 2,712 \: {yd}^{2} [/tex]
It takes Skyler 10 hours to rake the front lawn while his brother, Sergio, can rake the lawn in 6 hours. How long will it take them to rake the lawn working together?
Answers
John has some apples, and two brothers, Jack
and Jim.
John eats 3 of his apples and splits the
remainder equally between himself and each
one of his brothers. Jack and Jim both eat half
the apples they have been given. Together the
three brothers have 4 apples left.
How many apples did John start with?
Answers
John now has X - 3
and splits the remainder equally between himself and his brothers
Each of the brothers now has (X-3)/3 apples (we have to assume here that Jack and Jim didn't have any apples to begin with).
Jack and John both eat half of the apples they have been given
They now have (X-3)/3/2, or just (X-3)/6
Together the three brothers have 4 apples left
Now we say 4 = (X-3)/3 (Jim) + (X-3)/6 (Jack) + (X-3)/6 (John)
From here it's algebra. A nice trick we can do here is to add (X-3)/6 + (X-3)/6 together first, since they have the same denominator:
4 = (X-3)/3 + (X-3)/3
From there we can do the same trick, since now we have two terms that are both something/3:
4 = 2(X-3)/3
Multiply both sides by 3, divide both sides by 2:
6 = X - 3
Add 3 to both sides
9 = X
Answer:
8 or 9
Step-by-step explanation:
John eats 3 gives brothers and himself the remainder they both eat half and both halves are left making it 1 so add up to how much was eaten 3+1=4 and they have 4 left making it 8. Or just say x-3-1=4 and x=8. It can also be 9 so hopefully, someone else answers because if we add the halves remaining to the altogether it becomes 9 instead. Hope it's right and makes sense.
what is the square root of 64?
Help ill give brainliest to the one that works
Answers
Answer:
8
Step-by-step explanation:
The square root of 64 is 8
Answer:
8
Step-by-step explanation:
The square root of 64 is 8
8 * 8 = 64
Hope this helps!
Anthony is going to invest in an account paying an interest rate of 4.6% compounded monthly. How much would Anthony need to invest, to the nearest ten dollars, for the value of the account to reach $240,000 in 20 years?
Answers
The principal investment required to get a total amount of $240,000.00 from compound interest at a rate of 4.6% per year compounded 12 times per year over 20 years is $95,812.95.
Computation of Compound InterestGiven Data
Interest Rate r= 4.6%
Final Amount A = $240,000
Time T = 20 years
Answer:
P = $95,812.95
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 4.6/100
r = 0.046 per year,
Then, solve the equation for P
P = A / (1 + r/n)^nt
P = 240,000.00 / (1 + 0.046/12)^(12)(20)
P = 240,000.00 / (1 + 0.003833333)^(240)
P = $95,812.95
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What is the bar model for 20-x=6
Answers
Answer:
14
Step-by-step explanation:
20-x=6
20-14=6
hope this will help you
Find the inverse of the matrix (3, -2)(-10, 9) if it exists.
Answers
Answer:
The answer is ' A '
Step-by-step explanation:
:D
The inverse of the matrix will be [tex]\left[\begin{array}{cc}\dfrac{9}{7}&\dfrac{2}{7}\\\dfrac{10}{7}&\dfrac{3}{7}\\\end{array}\right][/tex]. The correct option is A.
What is a matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a property of such an object in mathematics. For instance, consider a matrix with two rows and three columns.
Given that the matrix is [tex]\left[\begin{array}{cc}3&-2\\-10&9\\\end{array}\right][/tex]. The inverse of the matrix can be solved as below,
[tex]A^{-1} = \dfrac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right][/tex]
[tex]A^{-1} = \dfrac{1}{3\times9-20}\left[\begin{array}{cc}9&2\\10&3\\\end{array}\right][/tex]
[tex]A^{-1} = \dfrac{1}{7}\left[\begin{array}{cc}9&2\\10&3\\\end{array}\right][/tex]
[tex]A^{-1}=\left[\begin{array}{cc}\dfrac{9}{7}&\dfrac{2}{7}\\\dfrac{10}{7}&\dfrac{3}{7}\\\end{array}\right][/tex].
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Male mosquitos have pretty short lifespans. Males of a certain species have lifespans that are strongly skewed to the right with a mean of 888 days and a standard deviation of 666 days. A biologist collects a random sample of 505050 of these male mosquitos and observes them to calculate the sample mean lifespan. We can assume that the mosquitos in each sample are independent.
What will be the shape of the sampling distribution of the sample mean lifespan?
Answers
Answer:
Approximately Normal
Step-by-step explanation:
The sample size is large (n50≥30n), so the sampling distribution of the sample mean will be approximately normal even though the population is skewed.
make h the subject of formula
[tex]a = \frac{1}{2} bh[/tex]
Answers
Answer:
[tex]a = \frac{1}{2} bh \\ \\ h = a \div ( \frac{1}{2}b ) \\ \\ h = a \times \frac{2}{b} \\ \\ h = \frac{2a}{b} [/tex]
4. The Lopez family is buying a new home. The price of their home is
$345,800. They also pay for new furniture. In the amount they pay for
new furniture, the digit 5 is exactly 10 times less than it is in the
amount they paid for the house. What is one possible amount that
they could have paid for furniture?
Answers
One possible amount the could have paid for furniture is $340,500.
Since the Lopez family pay a price of $345,800 for their new home, and also pay an amount for the furniture in which the digit 5 is exactly 10 times less than it is in the amount they paid for the house.
Amount paid for furnitureSince they paid $345,800 for their home and the digit 5 in this amount is in the thousands place, that is 5000.
In the amount paid for the furniture, the digit 5 is exactly 10 times less than in the amount paid for their home.
So, the place of the digit 5 in the amount paid for the furniture is thus 5000 ÷ 10 = 500.
So, the digit 5 is in the hundreds place.
With that in mind, replacing the 8 in the hunderds place in $345,800, one possible amount the could have paid for furniture is $340,500.
So, one possible amount the could have paid for furniture is $340,500.
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Brainliest if correct
Answers
Answer:
w = 3
Step-by-step explanation:
-2 = w -5
Add 5 to both sides of the equation
-2+5=2-5+5
Simplify
w = 3
[RevyBreeze]
2(x - 10) = 59
What are the steps to come to the correct answer?
Answers
Answer:
39.5
Step-by-step explanation:
Open the bracket by multiplying the numbers in the bracket by 2
2x-20=59
collect like terms(-20 crossing over the equal sign will become +20
2x=59+20
2x=79
Divide both sides by 2
[tex]\frac{2x}{2} =\frac{79}{2}[/tex]
x=39.5
[tex] \sf \large↪2(x - 10) = 59[/tex]
[tex] \: \: [/tex]
[tex] \sf \large \: ↪2x - 20 = 59[/tex][tex] \: \: [/tex]
[tex]\sf \large \: ↪2x = 59 + 20[/tex][tex] \: \: [/tex]
[tex]\sf \large \: ↪2x = 79[/tex]
[tex] \: \: \: [/tex]
[tex] \sf \large \: ↪x = \cancel \frac{79}{2} [/tex][tex] \: \: [/tex]
[tex]\sf \large \color{purple} ↪39.5[/tex][tex] \: \: \: [/tex]
How do you Solve for x
Answers
Answer:
C. x=12
Step-by-step explanation:
Angles in a triangles add up to 180 degrees. We are given that one angle is a right angle which means it's 90 degrees so...
2x+1+5x+5+90=180
Add like terms
96+7x=180
Subtract 96 from both sides
7x=84
Divide both sides by 7
x=12
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
x+2
x+4
Answers
Answer:
A=x²+6x+8
Step-by-step explanation:
Answer: A=x²+6x+8
Step-by-step explanation: Since we are looking to find the area of the entire rectangle, we would use the formula. is the length and is width. You would approach this problem like any other area of the rectangle problem, except you are dealing with polynomials instead.
A study analyzed the average yearly salt intake in the United States from 2012 thru 2017. The data is summarized in the table:
Year Annual Salt Intake
(grams)
2012 3,554
2013 3,598
2014 3,603
2015 3,655
2016 3,718
2017 3,794
The study found that the data after the year 2012 can be modeled by the function f(x) = 52.3x + 3,548, where x is the number of years since 2012 and f(x) is the total amount of salt ingested in grams. Describe the significance of 3,548.
An estimate of the average grams of salt used in 2012
An estimate of the average grams of salt used in 2013
The average amount of salt in grams used in 2012
The average amount of salt in grams used in 2013
Answers
Answer:
The answer is A. AN ESTIMATE OOF THE AVERAGE GRAMS OF SALT USED IN 2012.
Step-by-step explanation:
This picture explains everything:
An estimate of the average grams of salt used in 2012.
How the value of x in f(x) is calculated?
Given the values are:
Year Annual Salt Intake
(grams)
2012 3,554
2013 3,598
2014 3,603
2015 3,655
2016 3,718
2017 3,794
Here, we have to find the significance value of 3,548.
f(x) = 52.3x + 3,548
x - number of years
If x = 0,
f(0) = 52.3 (0) + 3,548
= 3,548.
Thus, it is found that it was an estimate of the average grams of salt used in 2012.
So, Option A is the correct answer.
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(-4x-9)+(-2x-7) in simplest term
Answers
Answer:
-6x-16
Step-by-step explanation:
Combine like terms, (-4x-2x) + (-9-7) = -6x - 16
Step-by-step explanation:
We'll be combining like-terms.
Remove the addition sign, as it has no effect to the expression:
[tex] - 4x - 9 - 2x - 7[/tex]
Combine Like-Terms:
[tex] - 6x - 16[/tex]
-6x - 16 is your simplified expression.
2. Which of the following expressions is equal to (2g)^3
Answers
Answer:
8g³
Step-by-step explanation:
(2g)³ = 2³·g³
Danny and Delilah were playing a game where they drew digits and placed them on a game board. Danny built the number 247. Delilah built the number 724. How much greater is the value of the digit 2 in Danny's number than the value of the digit 2 in Delilah's number?
Answers
Answer:
• This student received Met because the student stated that the 2 in Danny’s number is ten times greater than the 2 in Delilah’s number. The student stated that the 4 in Delilah’s number is one tenth the value of the 4 in Danny’s number. The student stated that the 7 in Delilah’s number is 100 times the 7 in Danny’s number.
This student received Progressing because the student correctly stated that Danny’s number was ten times bigger. The student also stated that the 4 in Delilah’s number is ten times smaller. The student stated the value of the digit 7 without referring to how the values compared.
Step-by-step explanation:
hope this helps :) (:
Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and Golden Delicious apples are $1.25 each. Mary spent $21.00 on 22 apples.
How many Golden Delicious apples did Mary buy?
Answers
Answer:
Mary bought 9 Golden Delicious apples
Step-by-step explanation:
This can be solved by setting up a system of equations. Based on the information given, the equations would be set up as follows.
[tex].75d+1.25g=21.00\\d+g=22[/tex]
I prefer to solve using substitution, but elimination can be used as well
[tex].75d+1.25g=21.00\\g=22-d[/tex]
We can now plug in this g value to the first equation
[tex].75d + 1.25 (22-d)=21.00\\.75d + 27.5-1.25d=21\\27.5-0.5d=21\\-.5d=-6.5\\d=13[/tex]
This means mary bought 13 delicious apples. She bought 22 apples in total, so the total number minus the amount of delicious apples will give us the amount of golden delicious apples.
22 - 13 = g
9 = g
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`
Let me know if you have any questions! Spread the love.
To rent a certain meeting room, a collage charges a reservation fee of 49 dollars and an additional fee of 5 dollars and 40 cents per hour. The film club wants to spend at most 81 dollars and 40 cents on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room.
Answers
42 + 8.8t < 112.40
8.8t < 70.40
t < 8
They can rent the room for up to yet not including 8 hours.
Please a genius help me please
Answers
Answer:
B, D, and F
They match the graph
find the side of a cube whose surface area is 216 sq. m
Answers
Answer:
6 m
Step-by-step explanation:
Side = x
Surface area = [tex]6x^2[/tex]
[tex]6x^2 = 216[/tex]
[tex]x^2 =36[/tex]
x = 6
The answer is 6m
Hope this helps :)
Have a nice day!
The side length of the cube is calculated as 6m
Data;
Surface Area = 216 sq. medge length = xSurface Area of a CubeThe surface area of a cube is given as
[tex]A = 6x^2[/tex]
This indicates all the six sides in the cube.
Let's substitute the values and solve for x
[tex]A = 6x^2\\216 = 6x^2\\\frac{216}{6} =\frac{6x^2}{6} \\x^2 = 36\\x= \sqrt{36} \\x = 6[/tex]
The side length of the cube is calculated as 6m
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Simplify the expression 6h +(-7.7d) – 16 + 5d - 2.6h.
Answers
Answer:
3.4h-2.7d-16
Step-by-step explanation:
Before we even start, we can already simplify some things
For example, in this equation it says +(-7.7d)
We can simplify this to 6h-7.7d-16+5d-2.6h
Now we have to get all of the common variables together
So the d’s and h’s have to be combined together in this equation
This makes a new equation of 3.4h-2.7d-16
That is our answer!
Jonathan has 2 solids. One is a right cylinder, and
the other is a sphere. The radius of the base of the
cylinder is the radius of the sphere. The height of
the cylinder is 10 cm. The diameter of the sphere is
12 cm. What is the lateral surface area, in square
centimeters of the cylinder?
O 1847
O 60
O 787
0 120
Answers
If you multiply all of them you would get 787 so your answer would be C.
It would be 787
David has 400 yards of fencing and wishes to enclose a rectangular area against a pre-existing fence. What equation should David use to help him maximize the area?
A. f(x)=x(400-2x)
B. f(x)=x(400+2x)
C. f(x)=2x(400-x)
D. f(x)=2x(400+x)
Answer: f(x)=x(400-2x)
Answers
The equation for the area in terms of x gives the function David should
use to maximize the area.
Response:
The equation that David should use to help him maximize the area is option A.
A. f(x) = x·(400 - 2·x)How can the function for the area be obtained?The given parameter are;
Length of fencing David has = 400 yards
Area to be enclosed = Rectangular area with pre-existing fence (on one side)
Required:
The equation David should use to maximize the area.
Solution:
Let x represent the width of the area (the sides perpendicular to the pre-
existing fence), and let y represent the length of pre-existing fence
We have;
Length of fencing available = Opposite side to pre-existing fence + 2 × Width of the area
Opposite side to pre-existing fence = Length of pre-existing fence
Which gives;
Length of fencing available = Length of pre-existing fence + 2 × Width of the area
400 = y + 2·x
y = 400 - 2·x
Area = Length × Width
Which gives;
Area = y × x
Area as a function of x is therefore;
Area, f(x)= (400 - 2·x) × x
Which gives;
f(x) = x·(400 - 2·x)The correct option is therefore;
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