Given that (7x-8)/(2x-1)(x-2)

Use Partial Fraction Decomposition to Find A and B.

Answers

Answer 1

We look for constants a and b such that

[tex]\displaystyle \frac{7x-8}{(2x-1)(x-2)} = \frac a{2x-1} + \frac b{x-2}[/tex]

Rewrite all terms with a common denominator and set the numerators equal:

[tex]\displaystyle \frac{7x-8}{(2x-1)(x-2)} = \frac{a(x-2)}{(2x-1)(x-2)} + \frac{b(2x-1)}{(x-2)(2x-1)} \\\\ \frac{7x-8}{(2x-1)(x-2)} = \frac{a(x-2)+b(2x-1)}{(2x-1)(x-2)} \\\\ \implies 7x-8 = a(x-2) + b(2x-1) = (a+2b)x - 2a - b[/tex]

Then

a + 2b = 7

-2a - b = -8

Solve for a and b. Using elimination: multiply the first equation by 2 and add it to the second equation:

2 (a + 2b) + (-2a - b) = 2(7) + (-8)

2a + 4b - 2a - b = 14 - 8

3b = 6

b = 2

Then

a + 2(2) = 7   ==>   a = 3

and so

[tex]\displaystyle \frac{7x-8}{(2x-1)(x-2)} = \frac 3{2x-1} + \frac 2{x-2}[/tex]

Answer 2

Answer:

a=3

b=2

Do whatever you want with that information^^


Related Questions

Halo
please help me

Answers with Solution, ok?

Answers

MATHEMATICS // ANSWER

The correct answer is letter C. 75. 36m³ :)

Here's the Solution:

V = π r²hV = (3.14) (2m)² (6m)V = (3.14) (4m²) (6m)V = (3.14) (24m³)V = 75.36m³

HOPE THIS HELPS. GOODLUCK:)

The answer is C.75.36m^3

HELPPPPPP!!!!!!!!!!!!!!

Answers

Answer:

7

Step-by-step explanation:

no need to panic !

it is actually totally easy.

we have the complete, big angle at U (imagine you turn VU around U into UT) = 178 degrees.

VT is almost a straight line (then that angle would be 180 degrees). but only almost ...

anyway, the other 2 angles are just parts of the big angle, and we see that together they sum up to the big angle, as there is no other space for a part of the big angle left.

so

(14x - 11) + (12x + 7) = 178

14x - 11 + 12x + 7 = 178

26x - 4 = 178

26x = 182

x = 7

Someone please help me on this!
Which statements are true about the
transformation (x,y) → (x - 1 y +4)?
A The transformation is a non-rigid
motion.
B The transformation slides the figure
to the left 1 unit and up 4 units.
C The transformation is a rigid motion.
D The transformation slides the figure to
the right 1 unit and down 4 units.

Answers

Answer:

b and c

Step-by-step explanation:

b is obvious since you can just plug In a point to solve

but c is a bit trickier a rigid motion is a transformation that doesn't change size or shape and we are just moving points which have same size so c is true.

union and intersection of sets

Answers

Answer:

The union of two sets contains all the elements contained in either set (or both sets). The union is notated A ⋃ B. The intersection of two sets contains only the elements that are in both sets. The intersection is notated A ⋂ B.

Answer:

Union

The union of a set A with a B is the set of elements that are in either set A or B. The union is denoted as A∪B. For example, if A is the set {♢,♡,♣,♠} and B is the set {△,♡,♠}, then A∪B={♢,♡,♣,♠,△}.

Intersection

Intersection of two given sets is the largest set which contains all the elements that are common to both the sets. To find the intersection of two given sets A and B is a set which consists of all the elements which are common to both A and B. The symbol for denoting intersection of sets is '∩'.

The vertical side of a right triangle measures 6 inches, and the horizontal side measures 8 inches
1.Write the ratio of the distance of the vertical side to the distance of the horizontal side as a reduced fraction
2.If the original triangle were enlarged by 3 times, what would the new dimensions be?
3.Does the ratio of vertical side to horizontal side change when scaling up? Explain.

Answers

9514 1404 393

Answer:

3/4vertical: 18 in; horizontal: 24 inno change

Step-by-step explanation:

1. The ratio is ...

  (6 in)/(8 in) = 6/8 = 3/4

__

2. The scaled dimensions are ...

  6 in × 3 = 18 in (vertical side)

  8 in × 3 = 24 in (horizontal side)

__

3. You know from your process of reducing the fraction in part 1 that multiplying numerator and denominator by the same value does not change the reduced ratio.

help me do this please!

Answers

Answer:

m<ABD = 37°

m<DBC = 58°

Step-by-step explanation:

m<ABD + m<DBC = m<ABC

2x + 23 + 9x — 5 = 95

11x + 18 = 95

     -18     -18

--------------------

11x = 77

/11      /11

---------------------

x = 7

Now, plug this into the equation for m<ABD and m<DBC to find their values.

m<ABD = 2x + 23

= 2(7) + 23

= 14 + 23

= 37

m<DBC = 9x — 5

= 9(7) — 5

= 63 – 5

= 58

Now, check to see if our values are right or not.

2x + 23 + 9x — 5 = 95

2(7) + 23 + 9(7) — 5 = 95

14 + 23 + 63 – 5 = 95

100 – 5 = 95

95 = 95 CORRECT

FIRST -CORRECT- ANSWER WILL GET BRAINLIEST!!

Find u.


A. 2√2

B. 2

C. 4

D. √2

Answers

Answer:

u=2 root 2

Step-by-step explanation:

All 45 45 90 degree triangles follow the same pattern

Find the surface area of a cylinder with a base radius of 2 in and a height of 5 in

Answers

Answer:

[tex]r = 2 \\ h = 5 \\ a = 2\pi \: rh + 2\pi {r}^{2} \\ = 2\pi \times 2 \times 5 + 2\pi {2}^{2} \\ = 20\pi + 8\pi \\ = 28\pi \\ = 28 \times 3.14 \\ = 87.92 {unit}^{2} \\ thank \: you[/tex]

can anyone help me out with this one?

Answers

a(n)=a1 + (n-1)d
a1=12
d=5-12=-7
a(n) = 12+(n-1)(-7)

9 * (-3/5) ^5


evaluate

pls help :)

Answers

Answer:

[tex] - \frac{2187}{3125} [/tex]

Step-by-step explanation:

[tex]9 \times ( \frac{ - 3}{5} )^{5} [/tex]

[tex]( \frac{ - 3}{5} {)}^{5} = \frac{( - 3 {)}^{5} }{ {5}^{5} } [/tex]

[tex] \frac{ - 243}{ {5}^{5} } = - \frac{ 243}{3125} [/tex]

[tex] - 9 \times ( - \frac{243}{3125} )[/tex]

[tex] = - \frac{2187}{3125} [/tex]

Which compound inequality could this graph be the solution

Answers

Answer:

A. 3x+14≥ 2 or 1-x ≥-5

Step-by-step explanation:

the solutions should be x≥ -4 or x ≤6

and the right answer is :

3x + 14≥ 2

3x ≥ -12

x≥ -4

1-x ≥ -5

-x ≥ -6

x ≤ 6

A. 3x+14≥ 2 or 1-x ≥-5

Help please! Find the converse

Answers

Answer:

Step-by-step explanation:

The  converse of ~q  =>  ~p  is  ~p  =>  ~q.

A man drove 13 miles directly east from his home, made a left turn at an intersection, and then traveled 9 miles due north to his place of work. If the road was made as described above, how much shorter would the man’s one-way trip be every day?

Answers

Answer:

ANSWER 5.3 miles

See IMAGE FOR SOLUTION

I will mark as brainliest if you can answer. :)

Answers

not enough information

Help please hurry I don’t have much time!!!

Answers

Answer:

The correct answer is D

Take D

I am a prime number. I am two digits.
The sum of my digits is 8.
My tens digit is 6 less than my ones digit.

Answers

Answer:

17

Step-by-step explanation:

17 is a prime number17 has two digitsThe digits in 17, 1 and 7, add up to 8The tens digit is 6 less than the ones digit place.

Answer: 17

Step-by-step explanation:

1+7=8

The ten digit is (1) 6 less than the one digit (7)

find the area of point b??

Answers

Answer:

78.5 in^2

or

506.7 cm^2

Step-by-step explanation:

r = 5 in = 12.7 cm

Area of circle

[tex] = \pi \times {r}^{2} [/tex]

I need help with this homework
2x^2+ 7x+ 5= 0

Answers

Answer:

x = -1 or/and -5/2

Step-by-step explanation:

:)

Y varies directly with x and y=8 when x=-5

Answers

Answer:

Y=K×X...... equation

When,Y=8 and X=-5

To find the constant (K)

we substitute for K in the equation

8=K×-5

8=-5K divide both sides by -5

8÷-5=-5K÷-5

K=-1.6

A lawn in the shape of a trapezoid has an area of 1,800 square meters. The length of one base is 50 meters, and the length of the other base is 40 meters. What is the width of the lawn?​

Answers

A=1/2H(b1+b2)
1800= 1/2h(50+40)
1800=1/2h(90)
1800=90h
h= 20
So the width is 20 meters

Miguel reads that the average low temperature today is −4.2°F and that the average high temperature is 9.1º F.

Miguel plots the points on the number line to determine the temperature change between these two readings.

What is the temperature change?

° F

Answers

Answer:  13.3

Step-by-step explanation:

took on k12 :]

The change in today's temperature between the two readings as measured by Miguel is 13.3°F

Miguel's temperature readings :

Average low temperature = -4.2°F

Avetage high temperature = 9.1°F

The change in temperature is the difference between the two temperature readings :

Average high temperature - Average low temperature

(9.1 - (-4.2))°F

(9.1 + 4.2)°F = 13.3°F

Hence, the change in temperature reading = 13.3°F

Learn more : https://brainly.com/question/2610134

if x = 5, y = 6, and z= 2, is V x2 + y2 + z2 + 50
rational or irrational? Explain.

Answers

Answer:

irrational

Step-by-step explanation:

because

5² + 6² + 2² + 50 = 25+36+4+50 = 115

and 115 is not a squared integer or rational number, so that sqrt(115) is one of these numbers with infinite digits after the decimal point but without any repeating pattern.

and that is per definition irrational.

(2x + 5) + (x + 4) =

Answers

Answer:

3x + 9

Step-by-step explanation:

(2x + 5) + (x + 4)

Distribute the + to all numbers/variables

2x + 5 + x + 4

Combine like terms:

2x + 5 + x + 4

3x + 5 + 4

3x + 9

Hope this helped.

Help please asap first answer get brainliest
Beging you please

Answers

Answers:

12. 2 3/5+1 4/6 = (2+1)+(3/5+4/6) = 3+19/15 = 64/15

13. 2/4*4/6 = 8/24 = 1/3

14. 3/4*3/6 = 9/24 = 3/8

15. 2/6*4/6 = 8/36 = 2/9

16. 2/4*1/6 = 2/24 = 1/12

17. 3/4/1/6 = 18/4 = 9/2

18. 3/4/2/4 = 12/8 = 3/2

19. 3/6/4/6 = 18/24 = 3/4

20. 5/7+2/7 = 7/7 = 1

21. 4/5+5/7 = 53/35

22. 3/5+5/5 = 8/5

23. 1/6-1/6 = 0

24. 3/7-2/3 = -5/21

25. 3/5-2/7 = 11/35

(X + ____ ) ^2 = _____

Answers

Answer:  1/4 first box  33/16 second box

Step-by-step explanation:

look at pictures for AnSwEr

19. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is (a) 20 (b) 23 (c) 169 (d) None of these​

Answers

Answer:

B

Step-by-step explanation:

Let the two numbers be a and b.

The product of the two is 120 and their sum of their squares is 289. In other words:

[tex]\displaystyle ab = 120 \text{ and } a^2 + b^2 = 289[/tex]

And we want to find the sum of the two numbers.

We can use the perfect square trinomial. Recall that:

[tex]a^2 + 2ab + b^2 = (a+b)^2[/tex]

From the first equation, multiply by two:

[tex]2ab = 240[/tex]

Add the two equations together:

[tex](a^2+b^2)+(2ab) = (289)+(240)[/tex]

Simplify and rewrite:

[tex]a^2+2ab+b^2 = 529[/tex]

Factor using the perfect square trinomial pattern:

[tex](a+b)^2 = 529[/tex]

And take the square root of both sides:

[tex]\displaystyle a + b = \pm\sqrt{529} = \pm23[/tex]

Hence, the sum of the two numbers is 23 or -23.

In conclusion, our answer is B.

How to make 10000 by only using number 8, No matter what the operation is​
BRAINLIEST will be marked

Answers

Here is the answer

[tex]\\ \sf\longmapsto 8888+888+88+88+8+8+8+8+8+8[/tex]

Similar Question .

Write 1000 using 8

Answer:-

888+88+8+8+8

Answer:

One of the options comes from this:

10000/8 = 1250

It means 10000 contains 1250 of 8's:

1250 = 1111 + 139 = 1111 + 111 + 28 = 1111 + 111 + 11 + 11 + 6

The 8's to make 10000 are:

10000 = 8888 + 888 + 88 + 88 + 8 + 8 + 8 + 8 + 8 + 8

When solving secθ=−4.2 for 180°≤θ≤360°, how many possible answers are there?

0
1
2
unable to determine

Answers

I believe there is only one answer

Math is?

At least 5 sentences

Answers

Answer:

1.The subject which we learn calculation multiplies devide substation etc.

2.Math is a kind of subject which we can practice more from this subject.

3.Math is an example of life process because if we are talent in math then we can solve the many kaild of problem related in our life..

4.Math also help as to increase our bran pour of we try to solve hard to hard problem..

Think you at last math is importent to as

Hi, can you help me with these?
It's really hard :(​

Answers

Rachel will earn $85 in 10 hours :)

Here's the Solution:

Direct Variation

Y = kx

Given:

$34=k(4)

k = 34/4

k = 17/2

Y = kx

Y = (17/2) (10)

Y = 85

Hope this helps :)

Other Questions
please solve its due 10. Why is 1619 such an important year?a.b. write the equation of a line in slope intercept form y=mx+b m=6, (0,5) Write an equivalent expression in standard form for (5x + 4)(7x+ -12x + 27). ) Erin owes her mom $25. She borrows another $15 from her mom. What is her balance now, that she owes her mom? excerpt from Of Plymouth Plantation by William BradfordAn Understanding with the Indians (1621)All this while the Indians came skulking about them, and would sometimes show themselves aloof off, but when any approached near them, they would run away. And once they stole away their tools where they had been at work and were gone to dinner. But about the 16th of March, a certain Indian came boldly amongst them and spoke to them in broken English, which they could well understand but marveled at it. At length they understood by discourse with him, that he was not of these parts, but belonged to the eastern parts where some English ships came to fish, with whom he was acquainted and could name sundry of them by their names, amongst whom he had got his language. He became profitable to them in acquainting them with many things concerning the state of the country in the east parts where he lived, which was afterwards profitable unto them; as also of the people here, of their names, number and strength, of their situation and distance from this place, and who was chief amongst them. His name was Samoset. He told them also of another Indian whose name was Squanto, a native of this place, who had been in England and could speak better English than himself.Being after some time of entertainment and gifts dismissed, a while after he came again, and five more with him, and they brought again all the tools that were stolen away before, and made way for the coming of their great Sachem, called Massasoit. Who, about four or five days after, came with the chief of his friends and other attendance, with the aforesaid Squanto. With whom, after friendly entertainment and some gifts given him, they made a peace with him (which hath now continued this 24 years) in these terms:That neither he nor any of his should injure or do hurt to any of their people.That if any of his did hurt to any of theirs, he should send the offender, that they might punish him.That if anything were taken away from any of theirs, he should cause it to be restored; and they should do the like to his.If any did unjustly war against him, they would aid him; if any did war against them, he should aid them.He should send to his neighbors confederates to certify them of this, that they might not wrong them, but might be likewise comprised in the conditions of peace.That when their men came to them, they should leave their bows and arrows behind them. After these things he returned to his place called Sowams, some 40 miles from this place, but Squanto continued with them and was their interpreter and was a special instrument sent of God for their good beyond their expectation. He directed them how to set their corn, where to take fish, and to procure other commodities, and was also their pilot to bring them to unknown places for their profit, and never left them till he died. He was a native of this place, and scarce any left alive besides himself. He was carried away with divers others by one Hunt, a master of a ship, who thought to sell them for slaves in Spain; but he got away for England and was entertained by a merchant in London, and employed to Newfoundland and other parts, and lastly brought hither into these parts by one Mr. Dermer, a gentleman employed by Sir Ferdinando Gorges and others for discovery and other designs in these parts.Readers can infer that Samosets visit to the community improves the relationship between the colony members and the Native Americans.Which detail from the passage best supports this inference? 1. He was a native of this place, and scarce any left alive besides himself.2. After these things he returned to his place called Sowams, some 40 miles from this place, but Squanto continued with them and was their interpreter3. He told them also of another Indian whose name was Squanto, a native of this place, who had been in England and could speak better English than himself.4. 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