Answer: 3 :3 :3
$8.88
Step-by-step explanation:
Use a system of equations to find the partial fraction decomposition of the rational expression. Solve the system using matrices.
[tex] \frac{3x ^{2} + 3x - 2 }{(x + 1)^{2} (x - 1)} = \frac{a}{x + 1} + \frac{b}{x - 1} + \frac{c}{(x + 1)^{2} } [/tex]
A=
B=
C=
Combine the fractions on the left with a common denominator:
[tex]\dfrac a{x+1} + \dfrac b{x-1} + \dfrac c{(x+1)^2} = \dfrac{a(x+1)(x-1) + b(x+1)^2 + c(x-1)}{(x-1)(x+1)^2}[/tex]
It follows that
[tex]3x^2+3x-2 = a(x+1)(x-1) + b(x+1)^2 + c(x-1)[/tex]
Expand the right side and collect like powers of x :
[tex]3x^2+3x-2 = a(x^2-1) + b(x^2+2x+1) + c(x-1)[/tex]
[tex]3x^2+3x-2 = (a+b)x^2 + (2b + c)x -a +b - c[/tex]
Then we have the system of equations
[tex]\begin{cases}a+b=3\\2b+c=3\\-a+b-c=-2\end{cases}[/tex]
or in matrix form,
[tex]\begin{bmatrix}1&1&0\\0&2&1\\-1&1&-1\end{bmatrix} \begin{bmatrix}a\\b\\c\end{bmatrix} = \begin{bmatrix}3\\3\\-2\end{bmatrix}[/tex]
Compute the determinant of the coefficient matrix:
[tex]\det\begin{bmatrix}1&1&0\\0&2&1\\-1&1&-1\end{bmatrix} = -4[/tex]
Then the inverse of the coefficient matrix is equal 1/det times the adjugate of the coefficient matrix (a.k.a the transpose of the cofactor matrix):
[tex]\begin{bmatrix}1&1&0\\0&2&1\\-1&1&-1\end{bmatrix}^{-1} = \dfrac1{-4} \begin{bmatrix}-3 & -1 & 2 \\ 1 & -1 & -2 \\ 1 & -1 & 2\end{bmatrix}^\top = -\dfrac14 \begin{bmatrix}3&-1&-1\\1&1&1\\-2&2&-2\end{bmatrix}[/tex]
Multiply both sides of the equation by the inverse :
[tex]\begin{bmatrix}a\\b\\c\end{bmatrix} = -\dfrac14 \begin{bmatrix}3&-1&-1\\1&1&1\\-2&2&-2\end{bmatrix} \begin{bmatrix}3\\3\\-2\end{bmatrix} = \begin{bmatrix}2\\1\\1\end{bmatrix}[/tex]
So, we have a = 2 and b = c = 1, and the partial fraction decomposition is
[tex]\dfrac{3x^2+3x-2}{(x+1)^2(x-1)} = \dfrac 2{x+1} + \dfrac 1{x-1} + \dfrac 1{(x+1)^2}[/tex]
Answer:
A = 2B = 1C = 1Step-by-step explanation:
One can solve for a, b, c a little more directly than using a system of 3 equations.
If we multiply the rational expression by (x+1)², we get ...
(3x² +3x -2)/(x -1) = (x+1)²(a/(x+1) +b/(x-1)) +c
Evaluating this for x = -1 gives ...
(3(-1)² +3(-1) -2)/(-1 -1) = c
-2/-2 = 1 = c
Similarly, multiplying by (x -1) gives ...
(3x² +3x -2)/(x +1)² = (x -1)(a/(x +1) +c/(x +1)²) + b
Evaluating this for x = 1 gives ...
(3·1² +3·1 -2)/(1 +1)² = b
4/4 = 1 = b
Now, we need to find the value of 'a'. The identity will hold true for any value of x, so we can see what happens when we substitute x=0. We can use the values of 'b' and 'c' that we found above.
(3·0² +3·0 -2)/((0 +1)²(0 -1)) = a/(0 +1) +1/(0 -1) +1/(0 +1)²
-2/-1 = a -1 +1 ⇒ a = 2
_____
System of equations solution
When the terms of the right-side expansion are combined, the numerator of the result is ...
a(x +1)(x -1) +b(x +1)^2 +c(x -1) = (a+b)x² +(2b+c)x +(-a+b-c) ≡ 3x² +3x -2
Equating the coefficients gives the system of equations whose augmented matrix is:
[tex]\left[\begin{array}{ccc|c}1&1&0&3\\0&2&1&3\\-1&1&-1&-2\end{array}\right][/tex]
Transforming this to reduced row-echelon form using any of a variety of available tools gives ...
[tex]\left[\begin{array}{ccc|c}1&0&0&2\\0&1&0&1\\0&0&1&1\end{array}\right][/tex]
which tells you the solution is (A, B, C) = (2, 1, 1).
pls help with number 12 i will give brainliest
Answer:
My man Zachary is right!
Step-by-step explanation:
The rule is so very simple!
Whenever a negative, anywhere in the equation multiples to another negative, it is always a positive!
Whenever a positive number multiples to a negative number anywhere in the equation, it is always a negative number!
So Negative*Negative is Positive (-10 x -10 = 100)
And Positive*Negative is always negative (-10 x 10 = -100)
And we both know that Positive times positive is positive. (10 x 10 = 100)
© Write
[tex] \sqrt{8} [/tex]
power of 2
Answer:
2³
Step-by-step explanation:
2×2×2=8
so √8 = 2³
Hope this helps you
if line 1 has a slope of -4 and line 2 has a slope of 1/4, they are parallel
True
O False
round to the nearest hundred 104,549 help 6th
grade
Translate the following word phrase into an algebraic expression: Nine times a number y.
Answer:
9×y
Step-by-step explanation:
the
answer
of
the
given
is 9y
Help quick 20points please please
Answer:
AB = 23.6
BC = 18.5
CD = 23.6
DA = 18.5
Step-by-step explanation:
4.
Both sets of opposite sides are parallel, so this is a parallelogram.
In parallelogram ABCD:
AB≅CD
AD≅BC
Knowing that, you can write 2 equations with the given information:
[tex]2a-20.4=a+1.6\\a-3.5=18.5[/tex]
You can solve whichever one you want, but I'll do both to be sure.
[tex]2a-20.4=a+1.6\\2a=a+1.6+20.4\\2a-a=1.6+20.4\\a=22[/tex]
Now for the second one:
[tex]a-3.5=18.5\\a=18.5+3.5\\a=22[/tex]
a = 22, so now you can solve for the side lengths.
[tex]2(22)-20.4=23.6\\22-3.5=18.5\\22+1.6=23.6\\18.5=18.5[/tex]
14 blue cars out of 70 cars
Answer:
66 cars
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Answer:
14-70=56
Step-by-step explanation:
its subtraction so you just need 70 and take away 14.
reasoning being that theyre all still cars no matter the color and you just need to take away 14 from 70, leaving you with 56.
I have less than 100 tennis balls. When i put them in tubesof 8, I have 5 left over.when i put them in tubes of 11 i have 3 leftover. How many tennis balls do i have in totals
Answer:
69
Step-by-step explanation:
8's 8's+5 11's 11's+3
8 13 11 14
16 21 22 25
24 29 33 36
32 37 44 47
40 45 55 58
48 53 66 69
56 61
64 69
What temperature is halfway between:
6 and -2
Answer:
The answer is 2
Step-by-step explanation:
-2, -1, 0, 1, 2, 3, 4, 5, 6
If you remove the first 4 and the last 4 numbers you are left with 2 which is also the median / middle value. Therefore, the temperature is 2.
1/2+y=5 1/4 complete the following addition equations
Answer:
So first you can find a common denominator to make this equation solvable
in this case 4 is the common denominator
2/4+y=5 1/4
Now subtract to isolate the variable (y)
4 3/4 =y
1) Trent made a scale drawing of the elementary school. The schoolyard, which is 85
meters wide in real life, is 102 millimeters wide in the drawing. What scale did Trent use?
6 millimeters:
The scale Trent used for his elementary school which has a school yard of 85
meters wide in real life and 102 millimetre wide in drawing is 51 : 42500
Firstly, let's do the conversion of the units
1 meters = 1000 millimetres
85 meters = ?
cross multiply
length in millimetres = 85 × 1000 = 85000 millimetres
Since the schoolyard width is 85000 millimetres in real life but it's 102 millimetres wide in drawing , the scale will be as follows:
= 102 / 85000
= 51 / 42500
Therefore, the scale is as follows:
51 : 42500
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A scale is chosen to plot the large graphs on smaller paper representing each unit by a supposed unit.
1.2 mm is used to represent 1 meter.
In the scale given the 102 mm is drawn to represent 85 meters.
So dividing the graph line with the original length the scale Trent has used can be found.
102/85= 1.2
This shows that 1.2 mm is used to represent 1 meter.
Multiplying 85 with 1.2 gives 102 .
https://brainly.com/question/25798457
Let represent the number of typographical errors made per page typed by a receptionist during a particular day at the office. The following table lists the probability distribution of .
= 0 1 *** 4 5 ( = ) * ** 0.40 0.13 0.02
Assuming that * = 2 (**) and E(X) = 12.77
(a) Find the values of ‘*’, ‘**’, and ‘***’.
(b) Determine P(1 ≤ < 4).
Using the principle of expected value and discrete probability distribution, the missing values are :
* = 0.30** = 0.15*** = 30P(1 ≤ Y ≤ 4) = 0.28The Expected value, E(X) is defined thus :
E(X) = Σ[(X) × (P(X)]The cummulative sum of the probability is 1 :
(* + ** + 0.40 + 0.13 + 0.02) = 1 - - - (1)* = 2(**)Hence, we have ;
2** + ** + 0.40 + 0.13 + 0.02 = 1
3** + 0.55 = 1
3** = 1 - 0.55
3** = 0.45
** = 0.45 / 3
** = 0.15
Hence,
* = 2(0.15)
* = 0.30
To find *** :
E(X) = (0 × 0.30) + (1 × 0.15) + (*** × 0.40) + (4 × 0.13) + (5 × 0.02)
12.77 = 0 + 0.15 + 0.40*** + 0.52 + 0.10
12.77 = 0.77 + 0.40***
12.77 - 0.77 = 0.40***
12.00 = 0.40***
*** = 12.00/0.40
*** = 30
B.)
P(1 ≤ Y ≤ 4) = P(y = 1) + P(y = 4)
P(1 ≤ Y ≤ 4) = 0.15 + 0.13 = 0.28
Learn more : https://brainly.com/question/25716562
5 numbers have a mean of 4, a range of 6, mode of 2 and a median of 3. What could the numbers be? Is this the only answer?
Step-by-step explanation:
x1, x2, x3, x4, x5
(x1 + x2 + x3 + x4 + x5)/5 = 4
x5 - x1 = 6
x3 = 3
2 appears more often than any other number (at least twice), otherwise there would have been multiple modes.
x1 + x2 + x3 + x4 + x5 = 4×5 = 20
x3 = 3
x1 + x2 + 3 + x4 + x5 = 20
x1 + x2 + x4 + x5 = 17
x5 = x1 + 6
x1 + x2 + x4 + x1 + 6 = 17
2×x1 + x2 + x4 = 11
since we did not have the number 2 yet (and we made x5 the harvest number, which has to be larger than 2), and it has to appear at least twice.
so, two numbers out of x1, x2, x3 must be 2. not all three of them can be 2, because 2×2 + 2 + 2 = 8 and not 11 as the last equation demands.
we have therefore 2 different solutions, as either
x1 and x2, or x2 and x4 can be 2.
x1 and x4 is the same solution per the last equation as x1 and x2 (as the variables are interchangeable for the number assignment, only x1 is different, because it has an additional factor in the last equation).
solution 1 (x1 and x2 are 2) :
2×2 + 2 + x4 = 11
4 + 2 + x4 = 11
6 + x4 = 11
x4 = 5
so,
x1 = 2,
x2 = 2,
x3 = 3
x4 = 5
x5 = x1 + 6 = 2 + 6 = 8
solution 2 (x2 and x4 are 2) :
2×x1 + 2 + 2 = 11
2×x1 + 4 = 11
2×x1 = 7
x1 = 7/2
so,
x1 = 7/2
x2 = 2
x3 = 3
x4 = 2
x5 = x1 + 6 = 7/2 + 12/2 = 19/2
A car was valued at 380,000 in the year 2014. By 2019, the value had depreciated to 110,000. If the cars value continues to drop by the same percentage,what will it be worth by 2017?
Please help thanks and Godbless
Answer:
160000
Step-by-step explanation:
How do I do this problem?
Answer:
hey you can use scan and search
Answer:
I got : 0.42264973
Step-by-step explanation:
1/ -√3 + 1
-√3 = -1.73 ( 2 decimal place )
1/ -1.73 + 1
and found the answer
Write the expression 4^4(4^-7)(4) using a single exponent
[tex]4^4(4^7)4\implies 4^4\cdot 4^7\cdot 4^1\implies 4^{4+7+1}\implies 4^{12}[/tex]
Answer:
real answer 4^-2
Step-by-step explanation:
just did on edge
please help me !
• don’t use this for points, or send any gross links.
• if you actually KNOW the answer, please do comment / help me!
this is: KS3 — YEAR 8 ! ❤️
TICKET MONEY for age 16 and over,
155-49 =106
1 person pays £18.60
106 = 106 × £18.60
=£1,971.6
TICKET MONEY for under 16
1 person pays £12.80
49 people =49 × £12.80
= £627.2
TOTAL NUMBER OF TICKETS
£ 1,971.6 + £6272.2
= £2,598.8
The price of an item has risen to $343 today. Yesterday it was $140. Find the percentage increase.
Answer:
145% increase
Step-by-step explanation:
343 - 140 = 203
203/140 = 1.45
1.45 x 100 = 145
lets simplify
please help step by step
Please find attached photograph for your answer.
Hope it helps.
Do comment if you have any query.
can anyone solve this step by step for me
Answer:
0.5 ㏑ | 1-2x | +c
Step-by-step explanation:
Formula: ∫ 1/ax+b dx = 1/a ln Iax+bI +c
through: (1, 3) and (-3,-5)
m = (Y2 - Y1)/(X2 - X1)
m = (-5 - 3)/(-3 - 1)
m = -8/-4
m = 2
Solve for q.
7q+17q–14q–8q=14
q=
[tex](7 + 17 - 14 - 8)q = 14[/tex]
[tex](24 - 22)q = 14[/tex]
[tex]2q = 14[/tex]
Divide both sides by 2
[tex] \frac{2q}{2} = \frac{14}{2} \\ [/tex]
[tex]q = 7[/tex]
There u go...
Have a great day ❤
What is the inequality shown?
o
I
1
1
-9
-8 -7 -6 -5
-4 -3 -2 -1
I
0
| 1
1 2
1 1
3 4
T 1
5 6 7
00
8
9
Answer:
-4 < n ≤5
Step-by-step explanation:
The lower limit is -4. It has an open circle, so there is no equal sign
-4 < n
The upper limit is 5. It is a closed circle so there is an equals sign
-4 < n ≤5
epic gamer question, i'll mark brainlist
Answer:
It has to be an isosceles because it has 2 congruent sides (and angles) in the same relative position. The two congruent angles both measure 30 degrees each; the total of degrees in any triangle is always 180. So, the other side has an angle measure of 120 degrees, which is more than 90. Therefore, it is
an obtuse isosceles
Lol pls hurry!!
I need this asap
Answer: 2, D
Step-by-step explanation: f=-2, so 4x-2 would give -8 add 10 would give 2 as it is for the negative
need some help with these!!
Answer:
RS = XY
Step-by-step explanation:
Corresponding sides will be equal. So
RS = XY
Assume the average amount of caffeine consumed daily by adults is normally distributed with a mean of 240 mg and a standard deviation of 47 mg. In a random sample of 600 adults, how many consume at least 320mg of caffeine daily?
The confidence interval is between (48.2%, 57.7%)
Using the proportion formula expressed as:
[tex]CI=p\pm z\cdot \sqrt{\frac{p(1-p)}{n} }[/tex]
Get the proportion:
p = 320/600 = 0.53
[tex]z=\frac{x- \mu}{\sigma}[/tex]
[tex]z = \frac{320-240}{47}\\z=\frac{80}{47}\\z= 1.70[/tex]
Substitute into the formula to get the confidence interval to have:
[tex]CI=0.53\pm 1.7\cdot \sqrt{\frac{0.47}{600}}\\CI = 0.53\pm 0.04757\\CI = (0.53-0.04757, 0.53+0.04757)\\CI = (0.482, 0.577)[/tex]
Hence the confidence interval is between (48.2%, 57.7%)
Learn more on confidence interval here: https://brainly.com/question/20066592
Simplify the following and write your answer in simplest radical form:
√-14*√-22
Steps are in the attachment.
Note :-
=》2 is taken as negative & also taken out of the square root as it's the common factor.
______
⚜ Hope it helps :))
what is the area of the rectangle below?
Answer:
B. 120sq. unitsStep-by-step explanation:
The area A of a rectangle is given by the formula, A=lw , where l is the length and w is the width.
so
8 * 15 = 120sq. units