Given f(x) = ax + b/x,
f(1) = 1, and f(2)= 5, find constants a and b

Answers

Answer 1

Answer:

a = 3, b = - 2

Step-by-step explanation:

Given f(1) = 1 and f(2) = 5, that is

substitute x = 1 and equate to 1, substitute x = 2 and equate to 5

a + b = 1 → (1)

2a + [tex]\frac{b}{2}[/tex] = 5 → (2)

Multiplying (1) by - 2 and adding to (2) will eliminate a

- 2a - 2b = - 2 → (3)

Add (2) and (3) term by term to eliminate a

0 - [tex]\frac{3}{2}[/tex] b = 3

- [tex]\frac{3}{2}[/tex] b = 3 ( multiply both sides by - [tex]\frac{2}{3}[/tex] )

b = - 2

Substitute b = - 2 into (1)

a - 2 = 1 ( add 2 to both sides )

a = 3

Then a = 3 and b = - 2


Related Questions

can you please help me!

Answers

Answer:

113.04

Step-by-step explanation:

All you have to do is substitute the r in the equation.

And of course pi is equal to 3.14

V = 4/3(3.14)3^3

That gives you a volume of around 113.04

What is the rectangle area triangle area

Answers

Answer:

1,200 area of rectangle

20 x 40 divided by 2 = 400

both added will be: 1,600

Alexa surveyed 7 students and found 2 like scary movies.based on this information how many students would like scary movies out of 35 students

Answers

The answer is 10 10 students liked scary movies out of 35

What is the perimeter of the composite figure?

A. 119.5 cm

B. 85 cm

C. 107.5 cm

D. 97 cm

Answers

Perimeter of Rectangle: 17 + 17 + 22 + 22
To find missing side of triangle: 19^2 + (22 - 10)^2 = c^2
361 + 144 = c^2
505 = c^2
sqrt of 505 = 22.5

Add everything together and you get A! Hope this helped!

Write and Solve 2 Step Equations. Show all your work
15.) In a week, Tara earns $15 less than three
times what Carrie earns. Tara earns $105.
How much does Carrie earn?

Answers

Answer:

Carries earns [tex]40[/tex] dollars

Step-by-step explanation:

Given -

Tara earns $15 less than three  times what Carrie earns.

Total earning of Tara [tex]= 105[/tex] dollars

Let  "X" be the earning of Carrie

[tex]3X - 15 = 105\\3X = 120\\X = 40[/tex]

Carries earns [tex]40[/tex] dollars

show your work please and thank you best anwser gets brainly ​

Answers

Answer:

a9

Step-by-step explanation:

5+4= 9 and its the same variable.

Convert 1 4/16 into a percent.

Answers

Answer:

it is 25 percent

Step-by-step explanation:

Answer:

the answer is 1.25 un decimal

which of the x values are solutions both of the following inequality 30> x and x > 15

Answers

Answer:

B and C

Step-by-step explanation:

its the answer trust me

Answer:

22 and 29

Step-by-step explanation:

22 is less than 30 but greater then 15

29 is less than 30 but greater than 15

WILL GIVE BRILLIANTIEST Select the better deal in the pair. Then give the unit rate for the better deal.
$90 $222
or
3g 69
The (select) y deal is better. The unit rate of the better deal is $
Vg.

Answers

The $90/3g is better because the unit rate is $30/1g. If you use the same unit rate and try to see how much times it fits into the $222/6g, you can see that the $90/3g is the better option.

Answer:

The first deal is better, unit rate is 30

Step-by-step explanation:

90/3 is 30, 222/6 is 37. 90 is the better deal

1. James has 43 game coins. James has 7 more than 4 times as many game
coins as Steven. If x represents the number of game coins Steven has,
which equation can be used to determine the possible number of game
coins Steven has?
A 7x + 4 = 43
1
B 4x - 7 = 43
a 7 + 4 = 43x
D 4x + 7 = 43
2:15 PM
3/1/2021

Plz help me it due in like ten minutes

Answers

D hope it helps you

Charlie is watching hot air balloons Balloon A has risen at a 60° angle Balloon B has risen at an 82 angle. If the distance from balloon A to the ground is 1,400 feet, how far

is balloon B from balloon A? Round your answer to the nearest whole number

Balloon A

Balloon B

Ground

Charlie

999 feet

1,005 feet

1,052 feet

1,102 feet

Answers

Answer:

Step-by-step explanation:

Assume that B is directly above A.

x = horizontal distance between Charlie and balloons

 = 1400/tan(60°)

altitude of B = x·tan(82°) ≅ 5751 ft

distance between A and B = 5751-1400 = 4351 ft, which doesn't fit any of the choices. So my initial assumption was incorrect.

Is there any other information? A picture?

The distance between balloon A and balloon B is 1005 feet if Charlie is watching hot air balloons Balloon A has risen at a 60° angle Balloon B has risen at an 82 angle option second 1005 feet is correct.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

Charlie is watching hot air balloons Balloon A has risen at a 60° angle Balloon B has risen at an 82 angle

In right angle triangle ACD,

tanx = AC/CD

tan60 = 1400/CD

CD = 808.3

In triangle BDE,

tany = BE/DE

tan82 = 1400/DE

DE = 196.8

The distance between balloon A and balloon B:

= CD + DE

= 808.3 + 196.8

=   1005 Feet

Thus, the distance between balloon A and balloon B is 1005 feet if Charlie is watching hot air balloons Balloon A has risen at a 60° angle Balloon B has risen at an 82 angle option second 1005 feet is correct.

Learn more about trigonometry here:

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A new bank customers with 3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.1% a. How much interest will the customer earn in 20 years? b. What will be the account balance after 20 years?

Answers

Answer:

$660

Step-by-step explanation:

one of the factor of 36 is​

Answers

1 2,3,4,6
Hope this helps

HELPPP I WILL MARK BRAINLIEST

Answers

Answer:

D

Step-by-step explanation:

Answer:

D m-2

Step-by-step explanation:

Because you can see that input is m and the answer is the output

35-2=33

36-2=34

hope this helps!

pls brainliest

केविन अपनी छुट्टी के लिए स्नोबोर्डिंग जाना चाहता था। बताएं कि वह बॉक्स प्लॉट्स से बर्फबारी के आंकड़ों के आधार पर रिज़ॉर्ट ए या रिज़ॉर्ट बी में जाने के बारे में अपना निर्णय कैसे ले सकता है।

Answers

Answer: I ate my dogs bone

Step-by-step explanation:

The blue dot is at what value on the number line?
The blue dot is at what value on the number line? PLEASE HELP!

Answers

Answer:

-3

Step-by-step explanation:

Answer:

I think it is 0

Step-by-step explanation:

the 9 goes down by 3 so maybe each point goes down 3


3x – 9y = -39
-3x – 7y = -25 systems of elimination

Answers

Answer:

y= 4 , x= -1

Step-by-step explanation:

3x-9y= -39

-3x-7y= -25

-16y= -64

y= -64/-16

y= 4

substitute y into any equation

3x -9(4) = -39

3x-36= -39

3x= -39+36

3x= -3

x= -3/3

x= -1

What is the polar form of 7 StartRoot 3 EndRoot minus 7 i?

Answers

In polar form the expression is ( 14 , 30 )

How the rectangular form is converted to Polar form ?

To convert the expression x +iy  to polar form ( r , [tex]\rm \theta[/tex] ) , the standard equations used are

r = [tex]\rm \sqrt {x^2 + y^2}[/tex]

tan [tex]\rm \theta[/tex] = y/x

The given expression is

7 √3 - 7i

x = 7 √3

y = -7

r = [tex]\rm \sqrt {(7\sqrt{3})^2 +(-7)^2}[/tex]

r = √196

r = 14

tan [tex]\rm \theta[/tex] = (-7)/(7√3)

[tex]\rm \theta[/tex] = 30 degree

Therefore in polar form the expression is ( 14 , 30 ).

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Answer:The polar form of 7 StartRoot 3 EndRoot minus 7 i is 14(cos(330o) + i sin(330o))

Step-by-step explanation:

Andy is buying a car.
He negotiated a 7% decrease on a £6 500 car.
He will pay the full balance in 12 equal monthly payments.
Calculate the amount paid each month.

Answers

Answer:

£503.75

Step-by-step explanation:

Andy is buying a car.

Step 1

We calculate the decrease

He negotiated a 7% decrease on a £6 500 car.

Decrease = 7% × £6500

= $455

Step 2

We calculate the new price of the car.

= Old price - Decrease

= £6500 - £455

= £6045

Step 3

We calculate the amount he pays every month.

We are told that:

He will pay the full balance in 12 equal monthly payments.

Andy's monthly payments =

New price/12 months

= £6045/12

= £503.75

Therefore, the amount he would be paying each new month = £503.75

responda a expressão 5x+6y+x+2:​

Answers

[tex]\tt{}5x + 6y + x + 2[/tex]

[tex]\tt{}6x + 6y + 2[/tex]

[tex]\tt{}2(3x + 3y + 1)[/tex]

143=n-27. PLZ HELP DUE TOMORROW

Answers

Answer:

n=170

Step-by-step explanation:

add 27 to 143

then the equation is n=170

-n= -27 -143
-n= -170


Answer
n=170

10/2
20/2
50/2
100/2

Answers

Answer:

10/2 =5

20/2=10

50/2=25

100/2=50

Please help! Really easy math, need it asap!!! It's in the picture

Answers

Answer:

answers are: (-1,-2), (1,2), (-1,5), (1,-5). in other words, option 2, 6, 7, and 8.

Step-by-step explanation:

hope it helps

Choose the model that represents the same function as the graph of f(x)

Answers

Answer:

x × 1/2 - 3

Step-by-step explanation:

in slope intercept form an equation is written in y=mx+b where m is the slope and b is the y intercept

from the graph you can see the line goes up 1 and right 2, up 1 right 2, etc. that means the slope is positive 1/2

the line cross the y access at -3, therefore the y intercept is -3

so

[tex]y = \frac{1}{2} x - 3[/tex]

solve the following equation
-3x = 27​

Answers

Answer:

x= - 9

Step-by-step explanation:

x = 27 / - 3

x = -9

Hope this helps

Answer:

x=9

Step-by-step explanation:

-3x=27

or, x=27/-3

or, x= -9

Ramon and his brother go to an amusement park. They each go on the Ferris wheel that costs $6 per ticket and a roller coaster that costs $9 per ticket. Ramon pays for all the tickets. How much does Ramon pay altogether?

Answers

Answer:

6+6=12

9+9=18

12+18=30

30 dollars

Answer:

$30

Step-by-step explanation:

6+6=12

9+9=18

18+12=30

I would assume this was the right answer if not i would need more information to go with the question

Please help! With explanation! EASY FOR MOST

Answers

9514 1404 393

Answer:

  (x, y, z) = (124, 112, 42)

Step-by-step explanation:

Opposite angles in an inscribed quadrilateral are supplementary, so ...

  y° = 180° -68° = 112°

The angle marked 71° subtends an arc twice that measure, so ...

  2(71°) = 100° +z°

  z° = 142° -100° = 42°

The angle marked y° subtends an arc twice that measure, so ...

  2y° = 100° +x°

  x° = 2(112°) -100° = 124°

True or false
hey is for horses

Answers

Answer:

false.

hay is for horses, not hey

Step-by-step explanation:

What is the approximate volume of a sphere with a diameter of 20 feet? Use 3.14 for it.

Answers

Answer:

4,188.79 and when its rounded its 4,188.8

Step-by-step explanation:

Volume of a sphere with a diameter of 20 feet is 4189.33 cubic feet.

What is Three dimensional shape?

Three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given,

sphere with a diameter of 20 feet

Diameter is two times of radius

Diameter=2Radius

Radius =Diameter/2

Radius = 20/2=10 feet.

Volume of sphere=4/3πr³

π=3.142

Volume of sphere=4/3(3.142)(10)³

=4/3×3.142×1000

=4189.33 cubic feet.

Hence, volume of a sphere with a diameter of 20 feet is 4189.33 cubic feet.

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Which set of ordered pairs does not represent a function? {(-3, -3),(-6, -7), (6,-3), (–9, 2)} {(8,–8), (-9,5), (9,-2), (-2,-8)} {(-7, -3), (-6, -1), (-6,8), (6, -6)} {(6,2), (-8,1), (-7,1),(5,-2)}​

Answers

Step-by-step explanation:

{(-3, -3),(-6, -7), (6,-3), (–9, 2)} {(8,–8), (-9,5), (9,-2), (-2,-8)}

{(-7, -3), (-6, -1), (-6,8), (6, -6)}

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