What is the correct form of the partial fraction decomposition for the expression StartFraction 13 x minus 7 Over (x + 2) (4 x minus 3) EndFraction?
StartFraction A Over x + 2 EndFraction + StartFraction B Over 4 x minus 3 EndFraction
StartFraction A Over x + 2 EndFraction + StartFraction B x + C Over 4 x minus 3 EndFraction
StartFraction A Over (x + 2) (4 x minus 3) EndFraction + StartFraction B Over (x + 2) (4 x minus 3) EndFraction
StartFraction A Over (x + 2) (4 x minus 3) EndFraction + StartFraction B x + C Over (x + 2) (4 x minus 3) EndFraction
Answers
The correct form of the partial fraction decomposition for the expression (13x - 7)/((x + 2)(4x - 3)) is;
Option B; [A/(x + 2)] + [(Bx + C)/(4x - 3)]
The given complex fraction is;
(13x - 7)/((x + 2)(4x - 3))
Now partial fractions are simply decomposition of complex fractions into simpler fractions. For example we want to decompose the complex fraction;
4/[(x - 1)(x + 5)]
The right format will be;
[A/(x - 1)] + [B/(x + 5)]
Applying this same pattern above to our question, we can decompose the fraction (13x - 7)/((x + 2)(4x - 3)) into;
[A/(x + 2)] + [(Bx + C)/(4x - 3)]
In conclusion, the correct answer is Option B.
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The correct form of the partial fraction decomposition for the expression (13x - 7)/((x + 2)(4x - 3)) is; Option B; [tex]\dfrac{A}{(x + 2)} +\dfrac{Bx + C)}{(4x - 3)}[/tex]
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
The given complex fraction is;
(13x - 7)/((x + 2)(4x - 3))
Now partial fractions are simply the decomposition of complex fractions into simpler fractions. For example, we want to decompose the complex fraction;
4/[(x - 1)(x + 5)]
The right format will be;
[A/(x - 1)] + [B/(x + 5)]
Applying this same pattern above to our question, we can decompose the fraction (13x - 7)/((x + 2)(4x - 3)) into;
[A/(x + 2)] + [(Bx + C)/(4x - 3)]
In conclusion, the correct answer is Option B.
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Related Questions
i got 4.9 and 40 i dont know if im right
Answers
Answer:
I got 40 aswell
Step-by-step explanation:
Given a 30-60-90 triangle with a hypotenuse of 11 mm solve for the other sides. (Explain)
Answers
Answer:
Need a calculator
Step-by-step explanation:
This will be hard to explain without the ability to draw an example.
The one thing you can memorize is SOH - CAH - TOA
This stands for SIN(Opposite/Hypotenuse), COS(Adjacent/Hypotenuse) and TAN(Opposite/Adjacent).
When you know the angles of a right triangle and at least one side length, you can get the length of all the sides.
So a right triangle has two legs (sides) and the hypotenuse. If you use the first angle ( 30 degrees) you can use the formulas above to calculate the side length.
Pick either the SOH or the CAH. Let's use SOH and write out the equation:
SIN(30 degrees) = Opposite Side divided by the Hypotenuse (11mm)
You can solve for the Opposite Side by multiplying both sides of the equal sign with 11mm. You end up with SIN(30 degrees) X 11m = Opposite Side.
So the side directly across from the 30 degree angle should be 5.5mm
You can do the exact same thing with the 60 degree angle.
SIN(60 degrees) = Opposite Side divided by Hypotenuse (11mm) OR
SIN(60 degrees) X 11mm = Opposite Side
This comes out to about 9.5mm
You can check the math by using the other equation CAH
Start with the 30 degree angle and solve for the adjacent side. This is the side that is touching the 30 degree angle. Equation will be
COS(30 degrees) X 11mm = Adjacent Side or about 9.5mm
The other equation will give you the side that is touching the 60 degree angle.
COS(60 degrees) X 11mm = Adjacent Side or 5.5mm
You can also use one last thing to check your math. The Pathagorean Theorem says in a right triangle [tex]A^{2}[/tex] + [tex]B^{2}[/tex] = [tex]C^{2}[/tex] where C is the hypotenuse and A and B are the two sides.
[tex]5.5^{2}[/tex] + [tex]9.5^{2}[/tex] should equal [tex]11^{2}[/tex]. Give or take a few decimal places, it's almost exactly 11 (10.977 to be exact).
how much of earths surface is covered by earth ? write answer in scientific notation
Answers
Answer:
100% of earth is covered in earth, I'm starting to think you mistyped the question, cause it makes no sense
Can sum1 please help me on this ty!! ❤️✌
Answers
Answer:
I need more information for the first graph but I can answer the second one:
So for the X column on the SECOND graph, it should be: 5,6,9,14,15,18,20,24,25
And for the Y column it should be: 25,30,45,70,75,90,100,120,125
Step-by-step explanation:
It is a Pattern the pattern is Multiplying 5
It takes 14 ppl to play a 42 minutes football game. How many ppl would it take to play a 60 minute football game
Answers
Answer:
20 people
Step-by-step explanation:
Step 1:
14/42 = x/60 Equation
Step 2:
42x = 840 Multiply
Step 3:
x = 840 ÷ 42 Divide
Answer:
x = 20
Hope This Helps :)
Answer:
20 people
42/14=3
Then, you divide 60/3=20 people
is it true or false?
Answers
Answer:
TRUE
Step-by-step explanation:
helpppppppppp please
Answers
Answer:
-2, 4, 6, 8
6, 4, 2 ,0
NEED HELP FINDING X ASAP
Answers
-16 I think I used an online algebra calculator want the link?
how many seconds in 4 minutes? its for PE class-
Answers
the answer is 240 seconds :)
give the other person brainliest
Select which angle is supplementary to angle 1
Answers
Answer:
Angle 2
Step-by-step explanation:
Suplementary - 2 angles which equal 180 degrees
when j= -8 and k= 7, the value of the expression is
Answers
Answer: 539
Step-by-step explanation: PLATO and Edmentum
Expression will have a value of 116 for the specified values of j and k.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given an expression -4j + 12k
where given, j = -8
and k = 7
Substituting the values in the given expression
=> -4 * -8 + 12 *7
=> 32 + 84
=> 116
Therefore, the value of expression for the given values of j and k will be 116.
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Complete question:
when j= -8 and k= 7, the value of the expression -4j + 12k is_____.
solve the fraction below 2 4/5 - 5/8
Answers
Answer:
I believe its 2.175 (as a decimal)
or 2 7/40 ( as a fraction)
I need help with this one question ASAP
Answers
A store orders 22 boxes of light bulbs. Each box has 148 bulbs.
Which is the best estimate of the total number of bulbs the store orders?
A.
20
×
100
B.
20
×
150
C.
25
×
150
D.
25
×
200
Answers
Answer:
b
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
A hotel manager found that his gross receipts for the day, including a 5% sales tax, were $1645.35. Find the amount of sales tax collected.
Answers
Answer:
The amount of sales tax collected is $78.35
Step-by-step explanation:
Percentages
The gross receipts for the day were $1645.35, including a 5% sales tax.
If a percentage is already included (added) to a certain quantity, then it's not the original quantity or 100%.
The problem states that the gross receipts already include a 5% sales tax, thus the receipts are 100+5=105% of the net sales.
This means the net sales were $1645.35 / 105 * 100 = $1567
Subtracting $$1645.35 - $1567 = $78.35 we get the amount of sales tax.
The amount of sales tax collected is $78.35
Steven and Gina each wrote an expression, but only Steven’s expression is equivalent to 4x - 8. What could be Gina’s expression?
Question options:
2(2x - 8)
2(2x - 4)
-(-4x + 8)
4(x - 2)
Answers
2(2x - 8) should be Gina's expression as it is not equivalent to 4x - 8.
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Given, Steven and Gina each wrote an expression, but only Steven’s expression is equivalent to 4x - 8.
∴ Gina's expressions should be the one that is not equivalent to 4x - 8.
After observing the given options and applying distributive properties we conclude that 2(2x - 8) is Gina's expression as it is 4x - 16.
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6x - 2 - 3x = 16 steps ?
Answers
Answer:
i am very sure but i think this the answer
Step-by-step explanation:
3x • (2x - 1)
[tex]\bold{Explanation:}[/tex]6x-2-3x=16
3x-2=16
3x=18
x=6
what are the solutions of the equation below
(x-2)(x+9)=0
Answers
Answer: {2, -9}
Step-by-step explanation: Think of these two binomials, x -2 and x + 9,
as two numbers that are multiplying together to equal zero.
In order for two numbers to multiply together to equal zero,
either one number or the other number must equal zero.
So for two binomials to multiply together to equal zero,
either one binomial or the other binomial must equal zero.
So we can split this problem up into two parts.
If (x - 2)(x + 9) = 0, then either x - 2 = 0 or x + 9 = 0.
On the left, add 2 to both sides and we have x = 2.
On the right, subtract 9 from both sides and we have x = -9.
For our final answer we use set notation.
So our answer is {2, -9}.
Answer:
2 and -9
Step-by-step explanation:
x-2=0
x=2
x+9=0
x=-9
Plz help me I’ll give brainliest
Answers
Answer:
5/1
Step-by-step explanation:
If, on average, a person with a bachelor's degree earns $57,181 per year, how
much, on average, can a person with a master's degree expect to earn per
year?
O A. Less than $28,590
B. More than $28,590 but less than $57,181
C. $57,181
D. More than $57,181
Answers
Answer: D. More than $57,181
Step-by-step explanation:
Because a masters degree is higher than a bachelors degree, they should make more money
Answer: D
Step-by-step explanation: Because a master’s is higher than a bachelor’s so master’s would get more money.
f(x)=3x-1 Find f(-8)
Answers
Answer: y=-25
Step-by-step explanation:
Plug in -8 for x
3(-8)-1
-24-1
-25
Answer:
x= -25
Step-by-step explanation:
-8(3)-1=
-24-1=
-25
Garrett has one dollar less than three times as much money as Liz has. Together they have $179. What equation would you set up to find out how much Money Garrett has?
Answers
Answer:
1-x=179
Step-by-step explanation:
Renee says that y = mx can be rewritten in the form y = mx + b. Is she right? Explain why or why not.
Answers
Answer: I did the test i used this and i got it right trust me the answer is below good luck
Step-by-step explanation:
Renee has it right because one of the line passes through the origin the questions remain the same a more extensive version of Y=mx is y=mx +b.
4. A toy rocket is fired into the air from the top of a barn. It's height (h) above the ground in
yards after t seconds is given by the function: h(t) =- 5t^2+ 10t+ 20.
a) What was the maximum height of the rocket?
b) How long was the rocket in the air before it reached its highest height?
Answers
Answer:
A) 25
Step-by-step explanation:
You use x= -b/2a in order to get your maximum so x= -10/ 2(-5) and you get x=1. You plug 1 into the function as h(1)=-5(1)^2 + 10(1)+ 20 which gets you 25
A function assigns the values. The time it will take for the rocket in the air before it reached its highest height is 1 second.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A.) The maximum height of the rocket can be found by differentiating the function to get the maximum value of the height funciton.
dh/dt = -5(2t) + 10
Substitute the differentiated value with 0,
0 = -10t + 10
-10t = -10
t = 1
Therefore, the maximum height will be attained when the time is 1 second.
Now, substitute the value of t as 1 second to get the maximum height,
h(t) =- 5t²+ 10t+ 20
h(1) =- 5(1)² + 10(1)+ 20
h(1) = -5 + 10 +20
h = 25 yards
Hence, the maximum height of the rocket is 25 yards.
B.) The time it will take for the rocket in the air before it reached its highest height is 1 second.
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what is the equation of ( 1, 6) and (2, 3) and (4, 15).
Answers
Answer:
y = − 3 x + 9
Step-by-step explanation:
Andre ran 2 kilometers in 15 minutes, and Jada ran 3 kilometers in 20 minutes. Both ran at
a constant speed.
In kilometers, How far did Andre run in 60 minutes?
Answers
60/15 =4
4x2=8
How do I solve permutations and combinations?
Answers
Answer:
by formulas . you can solve permutations and combinations by formulas .
Ms.smith has 132 stickers to give to her students. she has 25 students. if she gives the same number of stickers to each of her students how many stickers will she have left over?
Answers
Answer:
Step-by-step explanation:
If Ms. Smith hands out 130 of her stickers between all 5 of her students each will have 26. Which means she will have 2 remaining
__/5=9 the / is a divide sign
Answers
Answer:
45
Step-by-step explanation:
45/5=9
16
Chompy has $25 to purchase a fishing pole and some fishing balt. The fishing pole costs $12.50 and the fishing bait costs $0.78 each.
Create an inequality that Chompy could use to find out how much fishing bait he can buy.
Answers
The number of fishing bait he can buy will be 16.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Chompy has $25 to purchase a fishing pole and some fishing bait. The fishing pole costs $12.50 and the fishing bait costs $0.78 each.
The expression will be formed as below:-Let the number of fishing bait is x.
12.50 + 0.78x = 25
0.78x = 25 - 12.5
0.78x = 12.5
x = 12.5 / 0.78
x = 16
Therefore, the number of fishing bait he can buy will be 16.
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