f(x) =
4/x²+1
Asymptotes

Answers

Answer 1

Answer:

vertical asymptotes at

x

=

±

1

horizontal asymptote at

y

=

0

Step-by-step explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non-zero for these values then they are vertical asymptotes.

solve:

x

2

1

=

0

x

2

=

1

x

=

±

1

x

=

1

and

x

=

1

are the asymptotes

Horizontal asymptotes occur as

lim

x

±

,

f

(

x

)

c

(a constant)

divide terms on numerator/denominator by the highest power of x, that is

x

2

f

(

x

)

=

4

x

x

2

x

2

x

2

1

x

2

=

4

x

1

1

x

2

as

x

±

,

f

(

x

)

0

1

0

y

=

0

is the asymptote

Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here (numerator-degree 1 , denominator-degree 2) Hence there are no oblique asymptotes.

graph{(4x)/(x^2-1) [-10, 10, -5, 5]}


Related Questions

what is the absoulute value
pls help
thanks so much ​

Answers

4. -5
5. -3
7. 17
8. 5
9. -101
10. 0
11. 16

Everything else you did is correct
Hope this helps ya

- Josh and Gerald are having a throwing contest. Josh's first throw landed 20 feet away from the throwing line. They also measured that the
highest point of the throw occurred when the ball was 10 feet away from Josh and 30 feet in the air. Which equation models the path of Josh's
throw?

Answers

Answer:

y = -3x^2/10 + 6x

Step-by-step explanation:

please explain i really don’t understand

Answers

Answer:

22.5°

Step-by-step explanation:

First we need to figure out the size of the interior angles on the inside.

The formula of figuring out the total degrees of all the interior angles of any shape is (n-2)×180°.

N is the number of sides.

If we substitute our number of sides (8) we get this:

(8-2)×180°

6×180° = 1080°

Then we divide 1080 by 8 since this is a regular octagon (all angles are equal in a regular shape).

1080° ÷ 8 = 135°

Focusing on the triangle now, we now know that the angle on the tip of the triangle is 135° as it has not been split by the line.

Using the rule of angles in a triangle add up to 180°. We do this sum:

180° - 135° = 45°

There are 2 angles left in the triangle so we do:

45° ÷ 2 = 22.5°

Therefore the angle of x is 22.5°.

3.
Use the Pythagorean Theorem or knowledge on special right triangles to
find the missing variable in the following triangles.
Part A:
Part B:
45°
9
30v2
45°
30V2
b

Answers

Answer:

Part A: [tex]l = 60[/tex], Part B: [tex]b = \frac{9\sqrt{2}}{2}[/tex]

Step-by-step explanation:

The Pythagorean Theorem determines the length of the hypotenuse of right triangle ([tex]r[/tex]) by means of following formula:

[tex]r^{2} = x^{2}+y^{2}[/tex] (1)

Where [tex]x[/tex], [tex]y[/tex] are respective lengths of each leg.

Now we proceed to solve on each triangle:

Part A: ([tex]r = l[/tex], [tex]x = y = 30\sqrt{2}[/tex])

[tex]l^{2} = (30\sqrt{2})^{2}+(30\sqrt{2})^{2}[/tex]

[tex]l^{2} = 3600[/tex]

[tex]l = 60[/tex]

Part B: ([tex]r = 9[/tex], [tex]x = b[/tex], [tex]y = \frac{9\sqrt{2}}{2}[/tex])

[tex]9^{2} = b^{2}+\left(\frac{9\sqrt{2}}{2} \right)^{2}[/tex]

[tex]81 = b^{2}+\frac{81}{2}[/tex]

[tex]b^{2} = \frac{81}{2}[/tex]

[tex]b = \frac{9\sqrt{2}}{2}[/tex]

100 points ASAP!
A scale drawing of Julie's living room is shown below:



A rectangle is shown. The length of the rectangle is labeled as length equal to 8 cm, and the width is labeled as width equal to 6 cm.


If each 2 cm on the scale drawing equals 4 feet, what are the actual dimensions of the room?

Length = 16 feet, width = 12 feet
Length = 10 feet, width = 8 feet
Length = 32 feet, width = 24 feet
Length = 14 feet, width = 12 feet

Answers

Answer:

Length = 16 feet, width = 12 feet

Step-by-step explanation:

The length is 8 cm. So divide this by 2 to find out how many 2 cm are in 8 cm. You get 4. Multiply 4 x 4 (ft) to find out the real length. This means the length is 16 feet.

Do the same steps with the width. The real length is 12 feet.

Hope it helps!

Answer

First off, nice 100 point scam, don't do it again, because you could get warned or even worse banned, second off Have a great day!

Length = 16 feet, width = 12 feet

Step-by-step explanation:

The length is 8 cm. So divide this by 2 to find out how many 2 cm are in 8 cm. You get 4. Multiply 4 x 4 (ft) to find out the real length. This means the length is 16 feet.

Do the same steps with the width. The real length is 12 feet.

Hope it helps!

Step-by-step explanation:

An expression is shown below. Which expression is equivalent to the expression shown?
- 2x(x + y - 3) + 3(-x + 4y) + y(3x + 5y - 3)
- 2x2(5y2 + xy + 3x + 9y
- 2x2 + 5y2 + xy - 6x +9y
- 5x2 + 5y2 + xy + 3x + 9y
- 5x2 + 5y2 + xy - 6x + 9y

Answers

Note: In option A, it should be "+" instead of "(".

Given:

The expression is

[tex]-2x(x+y-3)+3(-x+4y)+y(3x+5y-3)[/tex]

To find:

The equivalent expression.

Solution:

We have,

[tex]-2x(x+y-3)+3(-x+4y)+y(3x+5y-3)[/tex]

Using distributive property, we get

[tex]=-2x(x)-2x(y)-2x(-3)+3(-x)+3(4y)+y(3x)+y(5y)+y(-3)[/tex]

[tex]=-2x^2-2xy+6x-3x+12y+3xy+5y^2-3y[/tex]

On combining like terms, we get

[tex]=-2x^2+5y^2+(-2xy+3xy)+(6x-3x)+(12y-3y)[/tex]

[tex]=-2x^2+5y^2+xy+3x+9y[/tex]

The expression [tex]-2x^2+5y^2+xy+3x+9y[/tex] is equivalent to the given expression.

Therefore, the correct option is A.

the monthly revenue for printer ink for a large office supply store is r(x) =-x^2 +12x+13, where x is the price of an ink cartridge in dollars and r(x) is in hundreds of dollars. what is the maximum monthly ink revenue​

Answers

Answer:

6u77vhy46yvt g vgj v6. hy

Step-by-step explanation:

guv yg

giving out brainliest!!

Answers

Answer:

A.

Step-by-step explanation:

55% of students spent their trackouts on Netflix. What fraction of students
watched Netflix?

Answers

Answer:

11/20

Step-by-step explanation:

11/20

Answer:

55/100

Step-by-step explanation:

Beacsue % only equal %/100

The cost of a taxi journey is
£4 plus £3 per mile.
What is the cost of a journey of 7 miles?
A £7
B £21
C £25
D £31

Answers

Answer:

its C

Step-by-step explanation:

it's because 3x7 is 21 add 4 to that its 25 and that's your answer

A CD usually sells for $15.00. If the CD is 10% off, and sales tax is 6%, what is the total price of the CD, including tax?

Answers

Answer:

the total price of the CD, including tax is $14.31

Step-by-step explanation:

The computation of the total price of the CD including tax is shown below:

= Sale price - off percentage + sales tax

= $15 - ($15 × 10%) + 6% of the remaining value

= 15 - $1.5 + 6% of the remaining value

= $13.50 + 6% of $13.50

= $13.50 + $0.81

= $14.31

Hence, the total price of the CD, including tax is $14.31

A stick 1 meter long casts a shadow 0.5 meters long. A building casts a shadow 16 meters long. How tall is the building?

Answers

Answer:

I think 8

Step-by-step explanation:

i think 8 because if you have 1 meter with .5 a meter shadow then i would think 16 meters would cast half of itself which would be 8

sorry if im totally wrong

PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!
PLSSSS SHOWWW THE WORKKK!!!!

Answers

Answer:

no hablo inglés xd no te puedo ayudar

Answer:

y^4/x^2

Step-by-step explanation:

i wish i could show the work but tbh i just use the link i comment under

Its helpful

A weather station on top of a mountain reports that the temperature is currently 0 degrees Celsius and has been falling at a constant rate of 4 degrees Celsius per hour. What will the temperature be in 5 hours?

Answers

Answer:

-20 degrees celsius

Step-by-step explanation:

The temperature is falling so the rate is -4 degrees per hour.

It is five hours so: 5 x -4 = -20 degrees celsius.

what is x if :-1/3x-9=2

Answers

Answer:

x = -33

Step-by-step explanation:

-1/3 x - 9 = 2 add nine to both sides

-1/3 x = 11 multiply both sides by -3

x = -33

Hope that helps

x/5 + 2 = 19 x______​

Answers

Answer:

47x=5

or 5/47

Step-by-step explanation:

Answer:

x=85

Step-by-step explanation:

x/5 + 2 = 19

5(x/5 + 2) = 5(19) *multiply both sides of the equation by 5 to get rid of the fraction

x + 10 = 95

x = 85 *subtract 10 on both sides

Check:

x/5 + 2 = 19

85/5 + 2 = 19

17 + 2 = 19

19 = 19

An angle measures 172° more than the measure of its supplementary angle. What is the measure of each angle?

Answers

Step-by-step explanation:

x+ 172= 180-x

x+ 172= 180-x2x= 8

x+ 172= 180-x2x= 8x= 4°

180-4= 176

the angle is 4° and the measure of the other angle is 176°

Answer:

8

Step-by-step explanation:

EXPERTS PLEASE HELP!!!!!!!!!!!!!!

Answers

Answer:

1. D

2. x=65

Step-by-step explanation:

Hi!

Your answer is D because 78 is 120% of x

120% in decimal point is 1.2.

So it's 1.2x is the same as 120% of x

For question 8:

1.2x=78

Isolate x by divide 1.2 on both sides

78/1.2=65

Which of the following is a true statement?
A. All squares are rectangles.
B. All rectangles are squares.
C. All rhombuses are squares.

Answers

A should be correct

PLEASE HELP ME I WILL GIVE YOU BRAINLIEST IF YOU HELP ME PLEASE I REALLY NEED HELP

Answers

Answer:

60º

Step-by-step explanation:

they key word here is difference meaning we need to subtract

specifically, we need to subtract 75 from 135 to find the difference in degrees, hence the number of degrees between the two settings:

135º - 75º = 60º

Factor out the greatest common
factor: -16x? + 12x?

Answers

Answer:

4x is the greatest common factor of those two.

Step-by-step explanation:

(-16x + 12x)

4x (-4 + 3)

4x is the GCF

Why you may ask is 4x the GCF because when you divide 4x from both you're left with -4 + 3...... you can't take out the negative from the 16 because when you check your work negative 4x times 3 gives you negative 12x which isn't the equation you started with. So positive 4x times 3 give you 12x.

Hopes this helps!!!

For every pound a company spends on advertising, it spends £0.26 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.

Answers

Answer:

Can you convert pounds to dollars?

Step-by-step explanation:

PLZ HELP ME THIS IS 7TH GRADE MATH I NEED HELP ASAP

Answers

Step-by-step explanation:

To get the circumference of a circle: 2[tex]\pi[/tex]×radius

Your circle has a given diameter of 3 feet.

To get the radius: 3 ÷ 2 = 1.5

To get circumference of this circle: 2 × [tex]\pi[/tex] × 1.5 = 9.424777961......

Answer:

Approximately 9.424 feet

Answer:

i am in 7th grade as well the answer is 9.42 rounded to the nearset of a tenth would be 9.4

Step-by-step explanation:

first find the radius by doing diameter ÷2

3÷2=1.5

1.5xπ

Solve the system of equations by graphing. Check your solution. y=-3x+7 3x+y=4

Answers

Answer:

Step-by-step explanation:

Answer:

there are no solutions

Step-by-step explanation:

In y=-3x+7, -3 is the slope, and 7 is the y-intercept.  In 3x+y=4, this equation also equals -3x+4=y. So, -3 is the slope, and 4 is the y-intercept. Once you graph the equations(as seen in the picture below) you should find where the lines intersect. Although, the lines are parallel since the slopes are the same.

Which answer choice gives three lengths that WILL form a triangle when put
together?

5,7,13

12, 18, 35

107,8,9

4.5.10

Answers

Answer:

none of them

Step-by-step explanation:

in order for them to be triangle lengths the two shorter size added together have to be greater than the longest side and in each answer choice if you add the two shorter sides none of them are greater than the longer side if that makes sense

Answer: what you need to find is the one where the two lowest numbers add up to be bigger than the biggest number. For example, if it was 3,7,5 then those could be right because 5+3=8 and 8 is bigger than 7. It is supposed to be that any two added is bigger than the third, but it's mist important that the smaller numbers equal more than the third

Step-by-step explanation:

please answer will give brainliest

Answers

Answer:

2 Gallons

Step-by-step explanation:

20.5ft x 16.4ft = 336.2

336.2 divided by 200= 168 gallons

Since you can not buy 1.68 gallons you will have to buy 2 galllons instead.

What is 1 and 2/3 in decimal form

Answers

Answer:

1.66666667

Step-by-step explanation:

plz mark brainlest

Answer:

1.67

Step-by-step explanation:

Step 1: Multiply the whole number by the denominator:

1 × 3 = 3

Step 2: Add the product you got in Step 1 to the numerator:

3 + 2 = 5

Step 3: Divide the sum from Step 2 by the denominator:

5 ÷ 3 = 1.666667

What is the measure of angle QZP

Answers

Answer:

22 degrees

Step-by-step explanation:

so if we take this here we know for sure that DZP is equal to 90 degrees

so DZP is split by QZD and QZP

so we take the 90 degrees we know for sure and then we take the two angle measurements we know

and we make this equation

9x + 5 + 3x + 1 = 90

and then we simplify this and it leaves us with

12x + 6 = 90

12x = 84

x = 7

so now that we have what x equals we plug that into QZP in order to find the actual measurement of this angle

3x + 1

3 (7) + 1

21 + 1

leaving us with our answer 22 degrees

and if you want to double check this answer just do the same thing we just did with QZD and plug in x into the equation and then add our answer 22 and the other answer you get for QZD and if that adds up to 90 then that is correct!

hope this helps!

Easy Cooking is a cooking supply company. Last year, the company sold a total of 5,340 ovens. This year, they sold 7,743 ovens. What is the percent of increase in the annual sales of ovens?

Answers

Answer:

45%

Step-by-step explanation:

Given data

Last year, the company sold a total of 5,340 ovens

This year, they sold 7,743 ovens

Percent increase=   final-initial/initial*100

substitute

Percent increase=  7,743-5,340/5,340*100

Percent increase= 2403/5,340*100

Percent increase=0.45*100

Percent increase=45%

Hence the increase is 45%

An investment of £200 increases by 4% each year for 3 years

Calculate the value of the investment at the end of the period.


(Will give brainliest and 10 points)

Answers

Answer:

£224

Step-by-step explanation:

Given data

P= £200

R=4%

T=3 years

Simple interest

A= P(1+rt)

Substiute

A= 200(1+0.04*3)

A=200(1+0.12)

A=200*1.12

A=£224

Hence the investment at the end of the period is £224

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