First we have to factorise the denominator [tex]\rm{x^3+1.}[/tex]
It can be factorised as,
[tex]\rm{x^3+1=(x+1)(x^2-x+1)}[/tex]
Then the fraction can be written as,
[tex]\longrightarrow\rm{\dfrac{x^2+1}{x^3+1}=\dfrac{x^2+1}{(x+1)(x^2-x+1)}\quad\dots(1)}[/tex]
This fraction can be resolved into partial fractions by writing it as the sum of a fraction having denominator [tex]\rm{x+1}[/tex] and a fraction having denominator [tex]\rm{x^2-x+1.}[/tex]
Since [tex]\rm{x+1}[/tex] is a first degree polynomial, the numerator of the fraction having this term as denominator should be a zero degree polynomial, or a constant term, assumed as [tex]\rm{A.}[/tex]
Since [tex]\rm{x^2-x+1}[/tex] is a second degree polynomial, the numerator of the fraction having this term as denominator should be a first degree polynomial, assumed as [tex]\rm{Bx+C.}[/tex]
So let,
[tex]\longrightarrow\rm{\dfrac{x^2+1}{(x+1)(x^2-x+1)}=\dfrac{A}{x+1}+\dfrac{Bx+C}{x^2-x+1}}[/tex]
[tex]\small\text{$\longrightarrow\rm{\dfrac{x^2+1}{(x+1)(x^2-x+1)}=\dfrac{A(x^2-x+1)+(Bx+C)(x+1)}{(x+1)(x^2-x+1)}}$}[/tex]
Equating numerators,
[tex]\longrightarrow\rm{x^2+1=A(x^2-x+1)+(Bx+C)(x+1)}[/tex]
[tex]\small\text{$\longrightarrow\rm{x^2+1}=\cal{(A+B)}\rm{x^2}+\cal{(-A+B+C)}\rm{x}+\cal{(A+C)}$}[/tex]
Equating corresponding coefficients,
[tex]\rm{A+B=1}[/tex]
[tex]\rm{-A+B+C=0}[/tex]
[tex]\rm{A+C=1}[/tex]
Solving these three equations we get,
[tex]\rm{A=\dfrac{2}{3}}[/tex]
[tex]\rm{B=\dfrac{1}{3}}[/tex]
[tex]\rm{C=\dfrac{1}{3}}[/tex]
Thus,
[tex]\small\text{$\longrightarrow\rm{\dfrac{x^2+1}{(x+1)(x^2-x+1)}=\dfrac{2}{3(x+1)}+\dfrac{x+1}{3(x^2-x+1)}}$}[/tex]
[tex]\small\text{$\longrightarrow\rm{\dfrac{x^2+1}{(x+1)(x^2-x+1)}=\dfrac{1}{3}\left[\dfrac{2}{x+1}+\dfrac{x+1}{x^2-x+1}\right]}$}[/tex]
So (1) becomes,
[tex]\longrightarrow\underline{\underline{\bf{\dfrac{x^2+1}{x^3+1}=\dfrac{1}{3}\left[\dfrac{2}{x+1}+\dfrac{x+1}{x^2-x+1}\right]}}}[/tex]
Hence the given fraction is resolved into partial fractions.
find the circumference of the given circle pls pls
Step-by-step explanation:
circumstance of circle = 2πr= 2 × 22/7 × 2 = 88/7 cm. circumstance = 12.57 cm*WILL GIVE BRAINLIEST FOR THE BEST ANSWER NO VIRUS LINKS OR ILL REPORT YOU*
Which of these statements best describes a biased sample?
A. The sample is small
B. The sample has results that are incorrect predictions
C. The sample does not accurately represent the population
D. The sample was chosen randomly
Answer:
C) The sample does not accurately represent the population
Answer:
C
Step-by-step explanation:
If you go to go o g l e and search up "bias sample examples" it will give you examples! I hope I helped :)
Roxanne set a goal o drinking 2.5 liters of water each day.By 10:00 a.M., she drank 3/4 liter, and at lunch she had another 600 ml. In the afternoon. She purchased a ottle of water of water that contained 1.1 liters
Answer:
She has to drink 0.05 liters more
Step-by-step explanation:
She has to drink 2.5 liters of water each day.
The total amount of water she drank is
3/4 liters + 0.6 liters + 1.1 liters + x liters = 2.5 liters
0.75 liters + 0.6 liters + 1.1 liters + x liters = 2.5 liters
2.45 liters + x liters = 2.5 liters
x liters = 2.5 liters - 2.45 liters
x liters = 0.05 liters
She has to drink 0.05 liters more or has not drunk 0.05 liters.
If she drinks 0.05 liters more she will reach her set goal.
3/4 liters
1 liter= 1000ml
3/4 liters= 3* 1000/4 ml
3/4 liters= 3000/4 ml
3/4 liters= 750 ml
750 ml/ 1000ml = 0.75 liters
Sarah is going to invest $280 and leave it in an account for 9 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for Sarah to end up with $410?
Plzzz helppp
Answer:
4.2%
Step-by-step explanation:
Which of the following events below will have an equally likely chance of happening?
A. If an event has a 5% chance of happening
B. If an event has a 50% chance of happening
C. If an event has a 100% chance of happening
D. If an event has a 0% chance of happening
Answer:
well this is obviusly 50% chance because 100 divided by 2 is 50
Brainliest plezzzz ;)
Step-by-step explanation:
The events below will have an equally likely chance of happening. If an event has a 50% chance of happening.
What is theoretical probability?Probability which is derived theoretically, irrespective of what outcome comes, is called theoretical probability.
Probability which is based on the outcomes of experiments performed is called experimental probability.
Suppose we want to find the probability of an event E.
where favorable cases are those elementary events that belong to E, and total cases are the size of the sample space.
The events below will have an equally likely chance of happening.
If an event has a 50% chance of happening
Learn more about experimental and theoretical probabilities here:
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well this is obviusly 50% chance because 100 divided by 2 is 50
PLEASE ANSWER THIS QUESTION ASAP NO GUESSING!!!!!!!!!!!
Answer:
3.5 works because 18-1.666 (2/3) X 3.5 = 12.169 which is less than 15.
4.5 works because 18-1.666 (2/3) X 4.5 = 10.503 which is also less than 15.
8.0 works because 18- 1.666 (2/3) X 8.0 = 4.672 which is also less than 15.
By looking at the number line included 4.5 is the only choice that is included in the shaded line part. So I think that that is the correct answer here.
Step-by-step explanation:
Hope that this helps! :)
Have a great rest of your day/night!
PLZ HELP I CAN'T FIGURE IT OUT!!!!!!
Parker needs to buy bouquets for table centerpieces. Her client has a budget of $250. If the bouquets cost $14.95 each, which direct variation equation can you use to determine the number of flower bouquets Parker can purchase?
A. x=14.95y
B. y=250x
C.250=14.95x
D. y=250(14.95)
Answer:
C
Step-by-step explanation:
as stated by the questions, the client has a budget of $250, which means we can't exceed $250. This will be our y (dependent variable, as the cost for y depends on how many bouquets we will purchase).
the bouquets cost 14.95 each, so if we have x bouquets , that means that the cost will be 14.95x (independent variable, as this gives the value of y).
therefore, the equation is 250=14.95x, which is C
but let's do process of eliminiation to double check:
if we look at the options, B and D are out (the cost of the bouquets isn't $250 each and also we can't have 250 bouquets , that would be too expensive for the client).
that leaves A and C
A isn't the correct answer. At first glance, it looks like we just switched x and y around. However, it cannot work because x is always the independent variable while y is the dependent variable (the value of y depends on the value of x, while the value of x doesn't depend on y).
Also, there's no mention of the $250 budget in A
by process of elimination and by the explanation above C is the correct answer.
Hope this helps!
9 and 10 pls help :)
Answer:
Question 9
Option A
Question 10
Option A
Please mark as brainliest for further answers :)
Can someone Help me please
Step-by-step explanation:
Given,In triangle ABC. In triangle DBC
AB. = DB.
[Given]
<ABC. = <DBC
[Given]
BC. = BC
[Common side]
Hence,
As two sides and one angle of triangle ABC and triangle DBC are equal.
Therefore,Triangle ABC is congruent to Triangle DBC
really need help asap!!
Answer:
Step-by-step explanation:
the parallelogram will have equal distances from center to along each diagonal. It is hard to explain with words and not being able to draw it.
So 2a+ 14 = 5a - 4 and a = 2b
solve the frist equation for a then the second equation for b
2a+ 14 = 5a - 4
18 = 3a
6 = a a = 2b 6 = 2b
3 = b
please help im not good at this kind of math T-T 20 points :)
Answer:
Step-by-step explanation:
huh
Answer:
Step-by-step explanation:
y=13-3x
when x=0
y=13-3(0)
y=13
when x=1
y=13-3(1)
y=13-3
y=10
when x=2
y=13-3(2)
y=13-6
y=7
when x=3
y=13-3(3)
y=13-9
y=4
when x=4
y=13-3(4)
y=13-12
y=1
(3a²b-4ab²+a²b²)-(2ab²+a²b²+5a²b)
Answer:
8ab
Step-by-step explanation:
Answer:
-2a^2b-6ab^2
Step-by-step explanation:
(3a²b-4ab²+a²b²)-(2ab²+a²b²+5a²b)
3a²b-4ab²+a²b²-2ab²+a²b²+5a²b
(3a^2b-5a^2b)+(-4ab^2-2ab^2)+(a^2b^2-a^2b^2)
-2a^2b-6ab^2
(10x-1)+(17x-8)=180
What is X?
Thanks so much xx
Answer:
X= 7
Step-by-step explanation:
Well first combine like terms
27x-9=180
Isolate from the variable
27x=189
x=7
The final answer is 7
Answer:
x =7
Step-by-step explanation:
( 10x -1) +(17x -8 ) =180
step 1 : since you have a plus sign in between it make it easy
so take care of the parentheses first
10x -1 + 17x - 8 = 180
step 2 : put together thw variable x
10x + 17x -1 -8 = 180
27x -9 =180
step 3 : take out -9 to the right and the sign will change
27x = 180 +9
27x = 189
x = 189 ÷ 27
x = 7
The measure of central angle LOP is °. The length of LP is units. The length of MP is units.
Answer:
2.87units
Step-by-step explanation:
Find the diagram attached
The length of MP can be gotten using the pythagoras theorem
LP² = LM² + MP²
8.5² = 8² + MP²
72.25 = 64 + MP²
MP² = 72.25 - 64
MP² = 8.25
MP = √8.25
MP = 2.87units
Hence the length of MP is 2.87units
The measure of central angle LOP is 180°. The length of LP = 17 units. The length of MP = 15 units.
What is Pythagoras's theorem?Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
The given is given in the question, as shown.
As per the question, we can see that
The measure of central angle LOP is 180°.
LM = 8 units
LP = 2OP
LP = 2(8.5)
LP = 17 units
So the length of LP = 17 units.
As we know that the Pythagorean Theorem,
LP² = LM² + MP²
17² = 8² + MP²
289 = 64 + MP²
MP² = 289 - 64
MP² = 225
MP = 15 units
Thus, the length of MP = 15 units.
Learn more about Pythagoras' theorem here:
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The question seems incomplete, the missing part has been attached below
What is the answer? Answer with correct answer and no wrong ones
Answer:
C
1/2 of the circle which means half is blue!
please give brainliest!
c. 1/2
its that answer only because the grey side is half and half is also 1/2 and since its shaded its one half. get it?
If a figure can be rotated 6 times, it has how many lines of rotational symmetry?
Answer: The answer is 7
Step-by-step explanation:
Please help will mark brainliest
Need ASAP! Will give brainliest!
Which is equivalent to 64 1/4
2 4v4
4
16
16 4v5
What’s (10 x 0.4) + (10 x 0.8)?
Answer:
12
Step-by-step explanation:
There are 56 marbles in a bin and 25% of the marbles are red. How many red marbles are in the bin?
Answer:
14
Step-by-step explanation:
25 percent of 56 is 14
Step-by-step explanation:
100%=56
1%=56÷100=0.56
25%=0.56×25=14
0.14 cm = ______ m
Conversions
Answer:
0.14 cm = 0.0014m
Step-by-step explanation:
So the phrase is:
“King Henry Died Belly Up Drinking Chocolate Milk”
The c is centimeters and meters is in between "died" and "drinking".
So 0.14 cm = 0.0014m
Because you are moving 2 to the left on the phrase so you move the decimal point 2 to the left.
***Belly up is bolded because it stands for base unit (meters, liters, gram, etc.)
I hope this makes sense!
PLEASE HELP ILL GIVE BRAINLIEEST
SHOW WORK
You know that it's a bot when it says "explanation in file".
They forgot to put a question, there's nothing to answer...
5. Find the missing reference angle using arcsin, arccos, or arc tangent. (Round to
the nearest whole number)
14
48
50
Your answer
Answer:
16°
Step-by-step explanation:
Reference angle = [tex] \theta [/tex]
Side Opposite to reference angle = 14
Adjacent side = 48
Hypotenuse = 50
Let's apply arcsin:
Thus:
[tex] \theta = sin^{-1}(\frac{Opp}{Hyp}) [/tex] (recall: SOHCAHTOA)
Plug in the values
[tex] \theta = sin^{-1}(\frac{14}{50}) [/tex]
[tex] \theta [/tex] = 16.2602047° = 16°
PT=y,TR=x+3,QT=2y,TS=3x-1 I'm confused and u really need help. My teacher isn't the greatest and wasn't much help.
Answer:
y=10, x=7
Step-by-step explanation:
Since the diagonals of a parallelogram bisect each other, PT should be equal to TR and QT should be equal to TS. So, y=x+3 and 2y=3x-1. Multiplying the first equation by 3 gives you 3y=3x+9. Using elimination to subtract these two equations gives you y=10. And since y=x+3, substitute y=10 there. 10=x+3, x=7.
Help ASAP!!!!! Can someone help me??
(And no I’m not gonna click a link)
Answer:
Sorry i couldnt upload the file i uploaded it onto a file host link is below
brainly.com
also im joking ;)
Answer:
1: 3x^2+2x+2
2: x = 1/4 or 4x+1. (I don't know which way your teacher likes it)
Step-by-step explanation:
Message if want work
Please please ASAP ASAP please ASAP thank you so
No links or files
Answer:
c
Step-by-step explanation:
Molly's family traveled 5/8 of the distance to her uncle's house on Saturday. They traveled 1/3 of the remaining distance on Sunday. What fraction of the total distance to her uncle's house was traveled on Sunday?
Answer: [tex]\dfrac{1}{8}[/tex]
Step-by-step explanation:
Given
On Saturday, Molly's family traveled [tex]\frac{5}{8}[/tex] of the total distance
On Sunday, they traveled one-third of the remaining distance.
Suppose the total distance is x
Distance traveled on Saturday is [tex]\dfrac{5x}{8}[/tex]
Remaining distance is
[tex]x-\dfrac{5x}{8}=\dfrac{3x}{8}[/tex]
On Sunday, they travel
[tex]\dfrac{1}{3}\times \dfrac{3x}{8}=\dfrac{x}{8}[/tex]
fraction of total distance traveled on Sunday is [tex]\dfrac{1}{8}[/tex]
need help no ilnks please
Answer:
D
Step-by-step explanation:
By looking at this scatter plot we can see that the points generally go down when looking at the graph from left to right.
This somewhat straight line that is created is going in a negative direction.
That means that it is not only a linear finction, but is also negative.
Please help no links or files answer both question will give brainliest
Answer:
-8.4 and 2 2/9
Step-by-step explanation:
p/1.2=-7 /×1.2
p=-8.4
20/30=3/10y /×10/3
20/9=y=2 2/9