Write the function as a sum of partial fractions. Do not determine the numerical values of the coefficients.(a) x/x^2+xâ2(b) 6âx/x^2â3xâ54

Answers

Answer 1

The correct equations in the question are:

(a) [tex]\dfrac{x}{x^2+x-2}[/tex]   (b) [tex]\dfrac{6-x}{x^2-3x-54}[/tex]

Answer:

Step-by-step explanation:

From above:

a) [tex]\dfrac{x}{x^2+x-2}[/tex]  

We are to find the roots of the quadratic equation at the denominator.

i.e.

x²+x-2 =  x² + 2x - x - 2

= x(x+2) - 1(x+2)

= (x -1 ) (x + 2)

Thus;

[tex]\mathbf{\dfrac{x}{x^2+x-2} = \dfrac{A}{x-1} + \dfrac{B}{x+2}}[/tex]

b) [tex]\dfrac{6-x}{x^2-3x-54}[/tex]

The quadratic equation roots can be calculated by finding two numbers that if we multiply then, we will get -54 and if we add or subtract them, we will get -3

x²-3x -54 =  x² - 9x +6x - 54

=  x(x-9) + 6(x-9)

= (x + 6) (x - 9)

[tex]\mathbf{\dfrac{6-x}{x^2-3x-54} = \dfrac{A}{x+6} + \dfrac{B}{x-9}}[/tex]


Related Questions

Check all apply 2x+2-9=5

Answers

Answer:

x=6

Step-by-step explanation:

2x=12 simplify and subtract

x=6

1. If 27.4578 is increased by 9.3456, what is the answer?
A. 36.8124
B. 35.8024
C. 36.8034
D. 35.8124​

Answers

Answer:

36.8034

not sure.....

Find the area of each square. Each grid square represents 1 square unit.

Answers

is there a picture..?

Ise9urgyobrhrstbydfdsfwefwefsdfewfds

Answers

Yeah I think x=12y on this one correct me if I’m wrong

MArking people as BRAINLIST only answer if you know

Answers

Answer:

Quad 4!

Hope I helped!

~PumpkinSPice1

$75 jacket: 5% markup​

Answers

Answer:

75*1.05 = $78.75

Step-by-step explanation:

You can just multiply by 1.05 or go the long route and divide by 100 and multiply by 105.  

The answer to your question is $78.75 that is the answer

write the slope intercept ​

Answers

Answer:

b = 4,

m = 4/3,

y = 4x/3 + 4

Step-by-step explanation:

We can see the line intercepts the x-axis in (-3,0) and the y-axis in (0,4). So, using the fact that the line equation in the slope-intercept form is:

[tex]y = mx+b[/tex]

We can substitute the points we know:

→ (0,4):

[tex]y = mx+b\\\\4 = m\cdot0+b\\\\4 = 0+b\\\\\boxed{b=4}[/tex]

→ (-3,0):

[tex]y = mx+b\\\\0 = -3m + 4\\\\3m = 4\\\\\boxed{m = \dfrac{4}{3}}[/tex]

So, the line equation in form requested is:

[tex]\boxed{y=\dfrac{4}{3}x+4}[/tex]

A school district wants to find out why dropout rates were lower at some schools rather than others. What statistical approach would be most appropriate?A) A regression with dropout rates as the independent variableB) A regression with dropout rates as the dependent variableC) A hypothesis test with a null hypothesis that the dropout rate is more than the highest dropout rateD) A confidence interval with the expected dropout rate as the meanE) A hypothesis test with a null hypothesis that the dropout rate is less than or equal to the highest dropout rate

Answers

Answer:

E) A hypothesis test with a null hypothesis that the dropout rate is less than or equal to the highest dropout rate

Step-by-step explanation:

The hypothesis test is the type of test that helped a scientist to determine the relationship between two variables-one constant independent variable and an dependent variable. For the dropout rates in the different schools, it would be better to use the hypothesis test for the evaluation.

What is the remainder when 19x^2 + 15x + 12 is divided by x - 2?

Answers

Answer:

R = 118

Step-by-step explanation:

Given

Represent the polynomial with P and the divisor with D

[tex]P = 19x^2 + 15x + 12[/tex]

[tex]D = x -2[/tex]

Required

Determine the remainder

We start by equating the divisor to 0

i.e.

[tex]D = 0[/tex]

[tex]x - 2 = 0[/tex]

[tex]x = 2[/tex]

Substitute 2 for x in the polynomial.

This gives remainder (R)

[tex]R = 19*2^2 + 15*2 + 12[/tex]

[tex]R = 19*4 + 15*2 + 12[/tex]

[tex]R = 76 + 30 + 12[/tex]

[tex]R = 118[/tex]

Hence, the remainder is 118

A group of 10 friends are in line to see a movie. It cost $15 for 3 people to see a movie. How much will the group pay?​

Answers

Answer:

50

Step-by-step explanation:

15/3=5

5*10=50

Answer:

So if it costs 15$ for 3 just multiply that by 3 (which equals the amount it’d cost for 9 people, which is 45$). And then divide 15 by 3 which is 5$ or the amount it’d cost for one person to see a movie. 45+5=50$. So the group will pay 50$.

A teacher had 52 boxes of chocolates with 34 pieces of
chocolate in each box. She wanted to give them to 26 girls and
to 32 boys. Each girl got 36 pieces of chocolate. How many
pieces of chocolate did each boy get?
__ pieces of chocolate

Answers

Answer:

each boy will get 26 pieces of chocolate

Answer:

The boys got 26 pieces of chocolate (gender inequality, lol)

Step-by-step explanation:

52 x 34 = 1768

26 x 36 = 936

1768 - 936 = 832

832/32 =

26

There’s your answer crack

Answers

Answer:

cool

Step-by-step explanation:

Answer:

what?

Step-by-step explanation:

vfgchgcbgjvygfcb

Why can prime number be a multiple of any other number except itself

Answers

Answer:

the factors of prime numbers are only 1 and itself

Answer:

A factor number can only be divided by itself or 1 meaning it cant be a factor anything more than that.

Step-by-step explanation:

A university president proposed that all students must take a course in ethics as a requirement for graduation. Three hundred faculty members and students were asked about their opinion on this issue. Find the probability that if one person is selected at random, from these 300 persons, this person is a faculty member or is in favor of this proposal.

Answers

You did not add the attachment for this question to be answered. I have added it

Answer:

0.5333

Step-by-step explanation:

We have

P(faculty) to be the probability of faculty being selected

= 70/300

= 0.233333333

We also have

P(favor) to be the probability of being in favor of this proposal

= 135/300

= 0.45

In answer to this question,

The required probability

= P(faculty) + p(favor) - p(faculty n favor)

p(faculty n favor) = 45/300

= 0.15

Probability = 0.233333333 + 0.45- 0.15

= 0.5333 approximately

The data below shows the duration of eruption (in seconds) of a geyser in a national park and the height (in feet) of the eruptions for a typical day. Use Excel to find the best fit linear regression equation, where duration of eruption is the explanatory variable. Round the slope and intercept to one decimal place.Duration Height240 140237 154122 140267 140113 160258 140232 150105 150186 160248 155243 125241 136214 140114 155272 130227 125237 125238 139203 125270 140218 140226 135250 141245 140120 139267 110103 140270 135241 140239 135Provide your answer below:y = _x + _

Answers

Answer:

ŷ = -0.08522X + 157.7779

The slope = - 0.1

Intercept = 157.8

Step-by-step explanation:

Given the data :

Duration __ Height

240 140

237 154

122 140

267 140

113 160

258 140

232 150

105 150

186 160

248 155

243 125

241 136

214 140

114 155

272 130

227 125

237 125

238 139

203 125

270 140

218 140

226 135

250 141

245 140

120 139

267 110

103 140

270 135

241 140

239 135

General regression equation :

y = mx + c

Where

y = predicted variable

x = predictor / explanatory variable

m = slope or gradient

c = Intercept

The regression equation obtained ;

ŷ = -0.08522X + 157.7779

To one decimal place :

ŷ = -0.1X + 157.8

The slope = - 0.1

Intercept = 157.8

6
Given the table below, tell the domain and range.
ON
x
y
0
-1
2
0
4.
1
6

Answers

Ok, this one is really easy your domain is all the x values and the range is all of the y values.

Thus, here is your answer...

Domain → { -2, -1, 0, 1 }

Range → { 0, 2, 4, 6 }

The rate of 225 mi in 7 hr written as a unit rate

Answers

Answer:

32.14 an hour

Step-by-step explanation:

Answer:

32.142857 miles per hour

Step-by-step explanation:

This is the answer because:

This is a fraction equal to

225 miles ÷ 7 hours

We want a unit rate where  1 is in the denominator,  so we divide top and bottom by 7 .

225/7 = 225/7 and 7/7 =  32.142857/1

Therefore, the answer is  32.142857 miles per hour.

Hope this helps!

Write a word problem using "less than"
someone help​

Answers

Answer:

Sandra had 500 beads in a jar, her sister, Dandra has 300 beads less than Sandra. How many beads does Dandra have?

:)

there are 120 calories in 2/3 cup. how many calories are in 1 cup?

Answers

Answer: 180

Step-by-step explanation: If of a 2/3 of a cup is 120 then 1/3 of a cup is 60. if 1/3 is 60 the 1 cup is 180.

For the following quadratic equation, find the discriminant.
-x^2 + 20x -126 =5
i need help please

Answers

Answer:

d=-124

Step-by-step explanation:

To find the discriminant use the equation b^2-4ac

So, 20^2-4(-131)(-1)

400-524= -124

d=-124

Please answer it I will wait to see for brainliest​

Answers

Answer:

D

Step-by-step explanation:

Answer:

ok so the odd one out is A) the measure of <ahd is 30°

Step-by-step explanation:

external angle is equal to the sum of the two interior angles on the opposite side

3x= x +15 +x +15

3x=x+x+15+15

3x= 2x +30

3x-2x= 30

x = 30

Sharise Brody folds and glues corrugated cardboard boxes at the rate of $0.57 per box. If she averages 40 boxes per hourhow much is her average hourly pay?

Answers

Answer:

she makes $22.80 a day

Step-by-step explanation:

since she makes $0.57 per box and averages at 40 boxes a day, we multiply 40 and 0.57. 40 x 0.57 = 22.8, or $22.80.

hope this helped!

A $250 suede jacket is on sale for 20%off how much should you pay for the jacket

Answers

250 * 0.20 = $50 sale
250 - 50 = $200
You will pay $200 after sale

Answer: $ 200

Step-by-step explanation:250 * 0.20 = $50 sale

250 - 50 = $200

please help, i need the answer soon

Answers

Answer: c

Step-by-step explanation:

Answer:

the answe is a

Step-by-step explanation:

Evaluate 5x ( x - 3 ) when x = 10

Answers

Answer:  

470

Step-by-step explanation:

Replace x with 10:  470

5(10)(10 - 3( = 500 - 30 = 470

470

-3 = 5 - 4x in algebra tiles

Answers

the answers is 2 cause you subtract 5 to the other side getting -8= -4x dividing both sides by -4 getting 2

CAN YOU PLEASE HELP ME WITH THIS );

Answers

Answer:

Across

5 across: percent of change

6. Ratio

7. Decrease

Down.

1. Percent

2 interest

3 proportion

4 sales tax

Step-by-step explanation:

Set up an equation and solve for x

Answers

Answer:

x=22

Step-by-step explanation:

3x+3+27+x+3+2x+18=180

6x+48=180

6x=132

x=22

PLEASEEE HRLPPPPPHELPPP PLEASEE :(((

Answers

Answer:

it's either the 1st choice or 4th

Margaret prepared and cooked the food
for their Thanksgiving feast for 5 hours and
25 minutes. She started at the time shown
below. What time did she finish

Answers

What’s the time she started?
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