What is the partial fraction decomposition in terms of X? Review the work showing the first few steps in writing a partial fraction decomposition. 6 O + 121-25 B 2.x - 3 А + 2-3 (21 - 3)² 412-12: +9 (2x - 3) 6 43 - 12x - 25 = A(2x - 3) + B 2.x - 3 (2:- 3) 12x - 25 = 2Ax - 3A + B 6 7 + 2x - 3 (2x - 3)2 7 2x - 3 (2,-3)
Answers
After partial fraction decomposition the correct expression we get,
[tex]\frac{12x - 25}{4x^2 - 12 x + 9} = \frac{6}{2x-3} - \frac{7}{(2x-3)^2}[/tex]
Hence option fourth is correct.
Partial fractions is a technique used in mathematics to decompose a rational function into simpler fractions.
It involves breaking down a rational function with a denominator of a higher degree into a sum of fractions with simpler denominators.
The given expression is,
[tex]\frac{12x - 25}{4x^2 - 12 x + 9} = \frac{A}{2x-3} + \frac{B}{(2x-3)^2}[/tex]
[tex]\frac{12x - 25}{4x^2 - 12 x + 9} = \frac{A(2x-3) + B}{4x^2 - 12 x + 9}[/tex] [since (a-b) = a² + b² -2ab]
Simplifying we get
⇒ 12x - 25 = A(2x - 3) + B
⇒ 12x - 25 = 2Ax + (B - 3A)
Comparing the coefficients we get
2A = 12
⇒ A = 6
And B - 3A = -25
Put the value of A we get
B = -7
Hence,
After substituting the values of A and B in the given expression we get
[tex]\frac{12x - 25}{4x^2 - 12 x + 9} = \frac{6}{2x-3} - \frac{7}{(2x-3)^2}[/tex].
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Related Questions
3. The trapezoid below contains a square and two right triangles. Find the perimeter of the trapezoid.
Answers
Answer:
Perimeter of trapezoid = 25.66 cm
Step-by-step explanation:
Trapezoid ABCD contains two triangles ΔABF, ΔCDE and a square with side length 4 cm.
By applying Pythagoras theorem in ΔABF,
AB² = BF² + AF²
AB² = 4² + 3²
AB = [tex]\sqrt{16+9}[/tex]
AB = 5 cm
Similarly, By applying Pythagoras theorem in ΔCDE,
CD² = DE² + CE²
CD² = 4² + 4²
CD = [tex]\sqrt{32}[/tex]
CD =5.66 cm
Perimeter of the given trapezoid = AB + BC + CD + AD
= 5 + 4 + 5.66 + (3 + 4 + 4)
= 25.66 cm
Answer correctly !!!!!!!!! Will be marking Brianliest !!!!!!! URGENT URGENT !!!!!!!!!!!!!!!
Answers
Answer:
(5/2,2)
Step-by-step explanation:
3+2/2,0+4/2
5/2,4/2
5/2,2
(4,-4) is the answer
a lighthouse L is 40 km due north of a harbor H, a speedboat leaves H and travels on a bearing of 053 from H until it reaches a point P.
Point P lies on a bearing of 075 degrees from L.
calculate the distance traveled by the speedboat
Answers
Answer:
D
Step-by-step explanation:
Edg
Answer:
I have a document with examples, do you wanna it?
Step-by-step explanation:
8x + 3 = ? What answer
Answers
Answer:
8x+3 is not factorable
Step-by-step explanation:
When is the power to power rule used?
Answers
Answer:
The "power rule" tells us that to raise a power to a power, just multiply the exponents.
Step-by-step explanation:
math
A population of rabbits doubles every 4 months. If the population starts out with 8 rabbits how many will there be in 1 year
Answers
Given:
The initial population of rabbit = 8
Population of rabbits doubles every 4 months.
To find:
The number of population in 1 year.
Solution:
The exponential growth model is
[tex]y=a(b)^x[/tex] ...(i)
Where, a is the initial population, b is growth factor, x is time period.
We know that,
12 month = 1 year
So, there are 3 time period of 4 months in an year.
Initial population of rabbit (a) = 8
Population of rabbits doubles every 4 months. So, growth factor is 2, i.e., b=2 and the time period is 3, i.e., x=3.
Putting a=8, b=2, x=3 in (i), we get
[tex]y=8(2)^3[/tex]
[tex]y=8(8)[/tex]
[tex]y=64[/tex]
Therefore, the population of rabbit in 1 year will be 64.
What is the x-intercept for the equation: 3x + by = 18? *
Answers
Use the Distributive Property to simplify the expression.I GIVE BRAINLEST AWNSER
6(6+y)
Answers
Answer:
36+6y
Step-by-step explanation:
you have to multiply 6 on 6+y because distributive property basically means to share out so you do 6(6)+(6)y
6(6) equals 36 (6x6) and 6(y) is just 6y
36+6y
GIVING BRAINLIEST!
What is the slope of this graph?
Answers
Answer:
m = -1/2
Step-by-step explanation:
m = y1 - y2/x1 - x2
2 - 0/0 - 4
-2/4
Simplify
-1/2
Plz A total of 41 and 1/3 tons of gravel was split between four dump trucks. How many tons of gravel did each truck hold?
Answers
EXPLANATION
41 1/3 tons divided by 4 trucks = 10 1/3 tons per truck.
HOPE THIS HELPED HAVE A GUD DAY!
If Bob has 5 apples and he hasn't done his laundry how much time does it take him to find his ex?
Answers
Don needed 89% on his test to increase his overall letter grade. About how many of the 150 questions on the test did he need to answer correctly?
Answers
Answer:
134 questions
Step-by-step explanation:
150 x 0.89 = 133.5
What is the slope of the line below?
Answers
Answer:
-1/2
Step-by-step explanation:
slope=rise/run
rise is up or down
run is right or left
5/-10= -0.5= -1/2 or -5/10= -0.5= -1/2
the answer is -1/2
The height of 16 members of a basketball team was measured and gathered in the table below. Find the value of a.
A. 4
B. 3
C. 1
D. 2
Answers
Answer:
question not clear. Where is the table?
Solve the inequality 18<-3(4x-2)
Answers
Answer:
Choice 1
Step-by-step explanation:
Answer:
x<-1 and Number 1
Step-by-step explanation:
:)
Let f(x)=x√x-4
What is the average rate of change of f(x) from 8 to 14?
Answers
Answer:
Avg rate of change =
[ f(14 ) - f(8) ] / [ 14 - 8 ] =
[ ( √ [14 - 4] ) - (√ [8 - 4]) ] / 6 =
[ √10 - √4 ] / 6 =
0.19
Nyasia had 16 M&M's on her desk. She had 2 groups of M&M's with x
amount in each, and another group with 4 M&M's. How many M&M's were
in the identical group?*
Answers
Answer:
12
Step-by-step explanation:
if one group has 4,and there are a total of 16,
16-4=12.
In each identical group, there are 6 each.
Alyson opened a savings account with
$100. She saves $50 per month. Which
equation shows how many months, m,
Alyson will have to save to have a total of
$250 in her account?
Answers
Answer:
3 more months to get $250.
Step-by-step explanation:
She had 100 in her account. Thats 2 months. 3 months would give her 150 more dollars. So 100 + 150 = 250
James and Sarah went out to lunch. The price of lunch for both of them was $40. They tipped their server
10% of that amount.
How much did each person pay If they shared the price of lunch and the tip equally?
Each person pald
Answers
Answer:
20%
Step-by-step explanation:
Sixteen is 64% of what number?
12
48
32
25
A basketball player makes 75% of her free throws. If she made 84 free throws this season, how many has she attempted?
112
105
63
168
Answers
Answer:
the top one is 25
Step-by-step explanation:
the second one is 112
Three sides of a kite measure 8 inches, 10 inches, and 8 inches. What is the perimeter of the kite?
A 26 inches
B. 28 inches
C. 34 inches
D. 36 inches
Answers
Answer:
26
Step-by-step explanation:
8+10+8=26
The Perimeter of the Kite whose dimensions 8 in., 10 in. and 8 in. is 26 inches.
What is the Perimeter of Kite?
A kite has two pairs of equal size. Total distance around the outside is called the perimeter of a kite. This distance can be found by calculating the sum of the lengths of each pair.
Here, the perimeter of kite = a + b + c
= 8 + 10 + 8
= 26 inches.
Thus, the Perimeter of the Kite whose dimensions 8 in., 10 in. and 8 in. is 26 inches.
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help
Which of the following pairs of base and height produces the greatest area? All measurements are in centimeters.
(Remember, the area of a parallelogram can be found by multiplying the base \cdot⋅ height, A = b\cdot hb⋅h)
b=4, h=3.5
b=0.8, h=20
b=6, h=2.25
b=10, h=1.4
Answers
Answer:
second option: b = 0.8, h = 20
Step-by-step explanation:
areas are as follows:
14
16
13.5
14
What angle has a degrees over 180?
Right
Rex
Straight
Acute
Answers
Choose the correct answer: 15 is 3% of
(A) 1.5
(B) 2.5
(C) 500
(D) 5000
Answers
Answer:
c) 500
Step-by-step explanation:
3% = 0.03
multiply the decimal from of 3% by 500:
500 x 0.03
solve:
500 x 0.03 = 15
The school bus arrives late 2/7 of the time.
The probability that it rains during a hurricane is 1.
Answers
please only answer if you know the correct answer and answer all question please please please please please
Answers
Answer:
Part A: B) 3
Part B: $40
4. -1
7. 5x + 6y
8. Part A: y = 20x
8. Part B: $300
9. e > 12000 pounds
Step-by-step explanation:
Part A: x = 5t + 5
20 = 5t +5
15 = 5t
t = 3
Part B: x = 5t + 5
x = 5(7) + 5
x = 35 +5
x = 40
4. 24 - 5^2
24 - (5*5)
24 - 25 = -1
7. 2x + 4y + 5 + 2y - 5 + 3x
2x + 3x = 5x
4y + 2y = 6y
5 + (-5) = 0
5x + 6y
8. Part A:
Total = y
Lawns = x
Amount = $20
so y = 20x
8. Part B:
y = 20x
y = 20(15)
y = 300
9. The elephant weighs more than 12000 pounds
Elephant = e
More than = >
Pounds = 12000
e > 12000 pounds
paul got 72 marks in a maths test. 72 marks is 60% of the total number of marks. work out the total number of marks in the test
Answers
Answer:
115.2 total marks.
Step-by-step explanation:
If 72 is only 60% of the total marks, then to find the total number of marks we will need to multiply 72 by 60% to find the remaining marks, then add that back to 72.
72 × 0.6 = 43.2 remaining marks.
72 + 43.2 = 115.2 total marks.
The total number of marks in the test is 115.2 total marks.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have been given that paul got 72 marks in a maths test. 72 marks is 60% of the total number of marks.
When 72 is only 60% of the total marks, then to find the total number of marks.
We will need to multiply 72 by 60% to find the remaining marks, then add that back to 72.
Then, 72 × 0.6 = 43.2 remaining marks.
72 + 43.2 = 115.2 total marks.
Hence, The total number of marks in the test is 115.2 total marks.
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Sadie has been baking all weekend for her school's bake sale. She used 12 ounces of sugar to bake brownies. Then, she used 12 more ounces of sugar to bake cupcakes. Finally, she used 8 ounces of sugar to make frosting for the cupcakes. How many pounds of sugar did she use in all?
Answers
0.75+0.75+0.5
Explanation:
12+12+8= 32ounces
32 ounces divide by 16 ( this is the formula for ounces to pounds) = 2 pounds
HELP!! 37 points ! and brainliest !!
What is the volume of the right rectangular prism?
A. 75m3
B. 125m3
C.200m3
D. 250m3
Answers
Answer:
250
Step-by-step explanation:
B times height = volume add the Base and the width at the bottom (10 times 5 =50) 50 is the B and then multiply by the height (5) so 50 times 5 is 250. Ez
i need help btw i am in middle school
Answers
Answer:
A). 459 B). x ≤ 6 C). $2.20 for one bowl
Step-by-step explanation: