Answer:
A. [tex]\mathbf{\dfrac{x^4-2x^3+x^2+2x-1}{x^2-2x+1 }= x^2 + \dfrac{A}{x-1}+ \dfrac{B}{(x-1)^2}}[/tex]
B. [tex]\mathbf{\dfrac{x^2-1}{x(x^2+x+1)} = \dfrac{A}{x}+ \dfrac{Bx+C}{x^2 +x+1}}[/tex]
Step-by-step explanation:
A.
Given that:
[tex]\dfrac{x^4 -2x^3 +x^2+2x -1}{x^3 -2x +1}[/tex]
[tex]\dfrac{x^4 -2x^3 +x^2+2x -1}{x^3 -2x +1} =\dfrac{(x^4 -2x^3+x^2) +(2x-1)}{x^3 -2x +1}[/tex]
[tex]=\dfrac{(x^4 -2x^3+x^2)}{x^3 -2x +1} + \dfrac{(2x-1)}{x^3 -2x +1}[/tex]
[tex]= \dfrac{x^2(x^2-2x+1)}{x^2-2x+1}+ \dfrac{2x-1}{(x-1)^2}[/tex]
[tex]\dfrac{x^4-2x^3+x^2+2x-1}{x^2-2x+1 }= x^2 + \dfrac{2x-1}{(x-1)^2}---(1)[/tex]
Further, the partial fraction decomposition of [tex]\dfrac{2x-1}{(x-1)^2}[/tex] can be written as:
[tex]\dfrac{2x-1}{(x-1)^2} = \dfrac{A}{x-1}+ \dfrac{B}{(x-1)^2}[/tex]
From equation one, replacing the values; we have the partial fraction decomposition of the function to be:
[tex]\mathbf{\dfrac{x^4-2x^3+x^2+2x-1}{x^2-2x+1 }= x^2 + \dfrac{A}{x-1}+ \dfrac{B}{(x-1)^2}}[/tex]
B.
Given that:
[tex]\dfrac{x^2-1}{x^3+x^2+x}[/tex]
[tex]\dfrac{x^2-1}{x^3+x^2+x} = \dfrac{x^2-1}{x(x^2+x+1)}[/tex]
Therefore, the partial fraction of decomposition is:
[tex]\mathbf{\dfrac{x^2-1}{x(x^2+x+1)} = \dfrac{A}{x}+ \dfrac{Bx+C}{x^2 +x+1}}[/tex]
what is 17639x43
PLEASE FAST
Each table below shows the time and distance Samantha and her friends traveled on four different road trips. In which Table is there a linear relationship between time and distance?
Include explanation
Answer:
C
Step-by-step explanation:
C 160/2 = 80
240/3 = 80
400 / 5 = 80
480 / 6 = 80
C is linear
In table C, there is a linear relationship between time and distance
The correct answer is Table C
A linear relation is a relationship between distance (d) and time (t) when a distance changes over time at a constant rate.
From table A
At t = 2 hour, d = 120 miles
[tex]\frac{Distance}{Time} =\frac{120}{2}=60 miles/hour[/tex]
At t = 4 hour, d = 220 mile
[tex]\frac{Distance}{Time} =\frac{220}{4}=55 miles/hour[/tex]
The relationship between distance and time is not linear.
From table B
At t = 1 hour, d = 70 miles
[tex]\frac{Distance}{Time} =\frac{70}{1}=70 miles/hour[/tex]
At t = 2 hour, d = 150 miles
[tex]\frac{Distance}{Time} =\frac{150}{2}=75 miles/hour[/tex]
The relationship between distance and time is not linear.
From table C
At t = 2 hour, d = 160 miles
[tex]\frac{Distance}{Time} =\frac{160}{2}=80 miles/hour[/tex]
At t = 3 hour, d = 240 miles
[tex]\frac{Distance}{Time} =\frac{240}{3}=80 miles/hour[/tex]
At t = 5 hour, d = 400 miles
[tex]\frac{Distance}{Time} =\frac{400}{5}=80 miles/hour[/tex]
The relationship between distance and time is linear.
From table D
At t = 1 hour, d = 75 miles
[tex]\frac{Distance}{Time} =\frac{75}{1}=75 miles/hour[/tex]
At t = 2 hour, d = 150 miles
[tex]\frac{Distance}{Time} =\frac{150}{2}=75 miles/hour[/tex]
The relationship between distance and time is not linear.
Therefore, In Table C, there is a linear relationship between time and distance
For more information:
https://brainly.com/question/22246569
Pls help! Which of the following best describes the ordered pairs listed below? (-3, 2), (3, -10), (5, -14), (10, -24) A. function only B. both a relation and a function C. neither a relation nor a function D. relation only
Answer:
A. Function Only
Step-by-step explanation: There is no repeated x terms in the pairs listed so its function only
9) The original price of a coffee table is d dollars. You use a coupon and buy the table for (d - 4)
dollars. You paint the table and sell it for (3d + 1) dollars. Write an expression that represents
your earnings from buying and selling the coffee table. Interpret the expression.
Answer:
I dopnt know
Step-by-step explanation:
Im asking the same question lol
Answer:
(3d+1)-(d-4)=Profit
Step-by-step explanation:
So what you do here is you take the price you sold the table for, and subtract it from the price you bought it for.
This will end up giving you this equation:
3d+1-d+4=Profit
2d+5=Profit
A recipe calls for 5 cups of water for every cup of black beans how many cups of water should be used for 4 cups of beans
Answer:
20
Step-by-step explanation:
4*5=20
Answer:
20
Step-by-step explanation:
4 times 5= 20
a store is having a 35 percent off sale, if the original price of the shirt is $18 what is the price of the shirt after the discount is applied (not including tax)
3x 4y please let me know
Answer:
i think its 12xy but im not for sure
Step-by-step explanation:
it Given that f (x) = xsquared 2+3x+2 find f(0) the values of x for which f (x) =0
Step-by-step explanation:
f(x) = x^2 + 3x + 2
f(0) = (0)^2 + 3(0) + 2
= 2.
f(x) = 0
x^2 + 3x + 2 = 0
(x + 1)(x + 2) = 0
x + 1 = 0 x + 2 = 0
x = -1 x = -2
hence x = -1 or -2.
Algebraic expression for three more than a number is twenty less than three times the same number write equation form
Answer:
x+3 = 3x-20
Step-by-step explanation:
3+x = 20 - 3x
More than = adding
is is equal to
What the awnser pls help
it looks like its
1,1
Answer:
(1,1)
Step-by-step explanation:
The two lines intersect at the point (1,1). To find a point of a graph look at what x-value it is at and what y-value, then put the value in parentheses in that order, (x,y). In this graph, the point is one right and up from the origin, which is the point, (1,1).
Please help thank you
Answer:
y = 2x - 5
Step-by-step explanation:
at a bakery, the ratio of the number of pies to the number of cakes was 8:3. What is the fraction of the number of cakes to the number of pies.
Answer:
Step-by-step explanation:
Answer:
3
---
8
Step-by-step explanation:
the ratio of cakes to pies will be 3:8 if pies to cakes is 8:3
the fraction is 3/8
Find the mean of the following set numbers 10,15,25,30,30,50,55,55,60,80
Answer:
the pattern is add 5 then addd 10
Step-by-step explanation:
look at what you typed
Answer:
The answer is 41.
Step-by-step explanation:
To find the mean you have to add up all the numbers and then divide it by how many numbers there are.
Artificial Christmas trees are regularly priced at $220. If you get a discount of 35%, how much will the tree cost you?
Answer:
$81
Step-by-step explanation:
Answer:
$143
Step-by-step explanation:
220/ 100 = 2.2
2.2 x 35 = 77
$220 - $77 = $143
Hope this Helps :)
PLEASE HELP WILL MARK BRAINLIEST
Answer:
√(8) 2 4/5 3.1 π (pie) 2√(3)
Step-by-step explanation:
Write a generic exponential growth function A(t) that has initial value P and an annual growth rate (expressed as a decimal) of r.
Answer:
A(t) = P(1+r)^t
Step-by-step explanation:
A(t): amount after
P: initial value
t: time
r: growth as a decimal
This example shows compounding the growth once per year
The radius of a circle is 25 what’s the diameter
Solve
x - 8 = -5
a.-3
b.13
c.-13
d.3
Answer:
3
Step-by-step explanation:
-5+8=3
Answer:
d. 3
Step-by-step explanation:
x - 8 = -5
x = -5 + 8
x = 3
If I go out to eat and my food is $20.98 and the tax is 8.6% how much would I have to pay all together?
Answer:
$22.78
Step-by-step explanation:
Cost Price: 20.98
Tax is 8.6% of this: 20.98 x 0.086 = 1.80
Total price = Cost Price + Tax:
Total = 20.98 + 1.80 = $22.78
Brainliest would be nice :)
It is estimated that 30% of households own a riding lawn mower. A sample of 12 households is studied. What is the standard deviation of the number of households who own a riding lawn mower?
Answer:
I dont knowiwdjdhkjwdhjkahdkjsa
Step-by-step explanation:
dhjddgcjkgjkjv
A square tablecloth covers an area of 256 sq in it is folded in half some times until the area it covers is 8 sq in how many times is it folded
Answer:
8
Step-by-step explanation:
I solved it meantally, sorry if it’s wrong, if it is, I’ll give you the correct answers, let me know in the chat if it’s right or wrong.
18 3/4 x 1 7/25 help would be awesome
Answer:
25.23
Step-by-step explanation:
As a Fraction 24
Answer:
25.23
Step-by-step explanation:
i did this question a few days ago
A history teacher asks six of her students the number of hours that they studied for a recent test. The diagram shown maps the grades that they received on the test to the number of hours that they studied. a. Is the relation a function? if the function if the relation is not a function, explain why not
Answer:
No
Step-by-step explanation:
No, because a function is a process in other words lets just say steps of doing stuff. It does tell that the students are doing stuff step by step.
System AAA \text{\quad}start text, end text System BBB \begin{cases}4x+16y=12\\\\x+2y=-9\end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 4x+16y=12 x+2y=−9 \begin{cases}4x+16y=12\\\\x+4y=3\end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 4x+16y=12 x+4y=3 1) How can we get System BBB from System AAA?
Answer:
i am aware that this is already answered but here is proof that the person above is correct!
Step-by-step explanation:
Answer: A), No
Step-by-step explanation:
I need helllpppp
ppllsssss
Answer:
C
Step-by-step explanation:
Tip a positive number multiplied to a negative number is negative
140,000 = 1.4 x 105
True
O False
Answer:
this is false. hope this helps
Answer:
False.
Step-by-step explanation:
1.4 x 105 = 147 which is not 140,000
A case of deodorant costs $57. You get a business discount of 15%, and you have a coupon for 20% off. How much will the case of deodorant cost after you receive both discounts?
Answer:
$37.05
Step-by-step explanation:
If you take 15% and 20% you get (15%+20%) which is 35%, then you take 100%-35% you get 65%, 65% of 57 is 37.05.
Thus Your Answer: $37.05
Each day, Yumiko exercises by first doing sit-ups and then running. Use her data and the trend line y = 9x + 5 to estimate Yumiko’s exercise time if she runs 5 mi.
Estimate: about ______ minutes
Answer:
50
Step-by-step explanation:
Given the trend line equation :
y = 9x + 5
Exercise time if she runs 5 miles :
From the trend line equation :
y = exercise time
x = miles ran
If she runs 5 miles ; then x = 5
y = 9(5) + 5
y = 45 + 5
y = 50
Michael's family wants to sign up for a movie rental service. They have information on DVD plans from four different companies. The family plans
to watch 15 DVDs per month. Which plan is the BEST?
A. All-You-Can Watch DVD, pay $5 for each DVD, d, ordered
B. DVD-R-US pay $25 to join and $2 for each DVD, d, ordered
C. Cheap DVD, pay $20 to join and $2.50 for each DVD, d. ordered
D. DVD Land: pay $60 per month for unlimited amount of DVD rentals
Answer:
B
Step-by-step explanation:
DVD-R-US pay $25 to join and $2 for each DVD ordered
Convert 3.09 kilograms to grams
Answer:
3090
Step-by-step explanation:
