Mathematics High School

Complete the sentences to describe the function f (x) = StartFraction 2 x squared + 16 x Over 16 x cubed minus x EndFraction.

The function is discontinuous at x =
.

To create the extended function, add f(x)=
.

Complete The Sentences To Describe The Function F (x) = StartFraction 2 X Squared + 16 X Over 16 X Cubed

Answers

Answer 1

Answer:

0 & -16,x=0

Step-by-step explanation:

Answer 2

The function is discontinuous at x = 0, x = 1/4 and x = -1/4.

To create the extended function, add f(x) = 0.

What does it mean when a function is discontinuous?

A function is discontinuous when the f(x) cannot be defined.

What is an extended function?

An extended function aims to make the function continuous at some values of the variable.

It is given that:

[tex]f(x)=\frac{2x^{2}+16x}{16x^{3}-x}[/tex]

StepsStep 1 of 2:

The function becomes discontinuous when the denominator becomes zero.

∴ 16x³ - x = 0

⇒ x(16x² - 1) = 0

⇒ x = 0 and 16x² -1 = 0

This is further simplified:

16x² -1 = 0

x² = 1/16

x = ±1/4

This means that the function is discontinuous at x = 0, x = 1/4 and x = -1/4.

Step 2 of 2:

The function can be extended as follows:

[tex]f(x)=\frac{2x^{2}+16x}{16x^{3}-x}\\f(x)= \lim_{x \to 0} \frac{2x^{2}+16x}{16x^{3}-x}\\= \lim_{x \to 0} \frac{x(2x+16)}{x(16x^{2}-1)}\\= \lim_{x \to 0} \frac{2x+16}{16x^{2}-1}\\[/tex]

We do not have to add anything to f(x) to extend it. Hence zero can be added to it.

Therefore, we have found that the function is discontinuous at x = 0, x = 1/4 and x = -1/4, and that we can create the extended function by adding 0.

Learn more about discontinuity here: https://brainly.com/question/1417220

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Related Questions

You manage a warehouse and need to replace a forklift.
Alocal retailer sells the model you want for $1,299 plus a
6% sales tax. A store located just over the state line sells
the same model for $1,359 plus a 4% sales tax.

Answers

Answer:

If youre trying to see which is cheaper, the local forklift would cost $1376.94 after tax. The other forklift would cost $1413.36.

Step-by-step explanation: Hope that helped

The cost after the sale will be $1376.94 and $1413.36.

What is the percentage?

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

You manage a warehouse and need to replace a forklift.

A local retailer sells the model you want for $1,299 plus a 6% sales tax. Then the cost after the sale will be

⇒ (1 + 0.06) x 1299

⇒ $1376.94

A store located just over the state line sells the same model for $1,359 plus a 4% sales tax. Then the cost after the sale will be

⇒ (1 + 0.04) x 1359

⇒ $1413.36

Your question was incomplete, probably the question was ...

What is the cost after the sale?

More about the percentage link is given below.

https://brainly.com/question/8011401

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A circle has two tangents AB and AC that intersect in the exterior of the circle. If the measure of the arc closest to the intersection is 118°, determine the measure of ∠A

Answers

Answer:

62

Step-by-step explanation:

[tex]360 - 118 = 242[/tex]

[tex] \frac{242 - 118}{2} = 62[/tex]

Angle a=62

For which value of x is the row in the table of values the incorrect? The function is quadric function y=5x^2

A. x=5
B. x=0
C. x=3
D. x=2

Answers

Answer:

x = 2

Step-by-step explanation:

Substitute x = 2 into y = 5x² , that is

y = 5(2)² = 5(4) = 20 ≠ 10

Thus (x, y ) = (2, 20 ) and not (2, 10 )

What is a tree diagram?

a
A drawing with branches of all possible outcomes
b
A written list of all possible outcomes
c
A description of all possible outcomes

Answers

The answer will be C and the reason why is because

Answer:

Ok so a tree diaphragm is used in math. The answer is b a written list because it’s a little small diaphragm used for math also I’m in sixth grade

Step-by-step explanation:

Sebastian grew 21-3 inches each year for the past 3 years. How many inches total has Sebastian grown in the past 3 years?

Answers

Answer:

the Answer is 21.3 x 3

Step-by-step explanation:

inches that grew each year for the past 3 years - 21.3

SO here 1 year = 21.3 inches

and it is asked about 3 years so we have to multiply 21.3 inches x 3 times ( 3 years).

Answer:

//

Step-by-step explanation:

HELP PLEASEEE I NEED IT

Answers

Answer:

See explanation

Step-by-step explanation:

1st photo:

(a) MKL ~ MLJ ~ LKJ

basically, you have to match the corners to each other (i dont have a better way of explaining this sorry)

(b) KL/KJ = KM/LK   AND    LJ/MJ = KJ/JL

match sides to each other

2nd photo:

(a) d = 7[tex]\sqrt{2}[/tex]

you have to use special right triangle rules for a 45-45-90 triangle

(b) a = [tex]\frac{4\sqrt{3} }{3}[/tex]

you have to use special right triangle rules for a 30-60-90 triangle

3rd photo:

x = 38.9°

[tex]cos^{-1}[/tex](7/9) = 38.9°

Can someone please help me?

Answers

Answer:

F. The mode of the data for Store 2 is greater than the mode of the data for Store 1

Step-by-step explanation:

The mode for Store 2 = 2 (2 appears most)

The mode for Store 1 = 1 (1 appears most)

Therefore, mode of the data for Store 2 is greater than mode of the data for Store 1

Statement F is supported by the information in the dot plots.

Can anyone help me please?
I’ll mark you as a brainliest

Answers

Answer:

A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

It is C because if you multiply each number on the left by 250 and then add 500, you will get the number on the right.

4 x 250 = 1000 + 500 = 1500

8 x 250 = 2000 + 500 = 2500

10 x 250 = 2500 + 500 = 3000

13 x 250 = 3250 + 500 = 3750

Which of the following numbers could not be used to describe a distance walked?
O 12 feet
O - 140 feet
130 feet
O |-125 feet
Home | Lesson AS...
acer

Answers

Answer:

You cant use acre to describe distance walked

Step-by-step explanation: Because 1 acre is 43560ft

Brother’s Burgers claim to make the best ½ pound burgers in all of Florida.
The hamburger patties are ½ pound before they put them on the grill. When they come off the grill, they are 1/3 pound. What is the change of percent in weight?
I like a lot of toppings on my Brother’s Burger, and after I get done, the total weight of my hamburger, bun, and toppings is 5/8 pound. What is the percent change from cooked weight to final weight?
What is the percent change from pre-cooked weight to final weight?

Answers

Answer:

new = 1/3  old = 1/2

new - old = 1/3 - 1/2 = 2/6 - 3/6 = -1/6

dividing by the old:  -1/6 divided by 1/2 = -1/6 * 2/1 = -1/3

multiplying by 100% :  -100/3 = -33 and 1/3 %

 It is a 33 and 1/3 % DECREASE

Step-by-step explanation:

Retail price: $745; discount rate: 12.5% what is the discount?

Answers

Answer:

mmmmmmmm

Step-by-step explanation:

the answer ................

Find BC.
Round to the nearest tenth.
А
84°
16
B
51°

Answers

If you want to round to the nearest tenth the answer would be 80• and 51•

Calculate the measures of spread for Mrs. Hampton’s class data. Justify your response by describing the process used to find each measure. (10 points)
Can you please help.
I'm kinda dum.b and I don't really understand whats going on. Please don't answer just for points.

Answers

Answer:

Step-by-step explanation: Dot plot for movies seen by a students in a month

To Find : measures of spread

Solution:

Movies frequency cumulative frequency

0 1 1

1 0 1

2 0 1

3 0 1

4 3 4

5 8 12

6 3 15

7 1 16

8 5 21

9 2 23

10 3 26

Range = 10 - 0 = 10

Q2 = (6 + 6)/2 = 6 (13th + 14t)/2

Q1 = 5 7th

Q3 = 8 20th

IQR = Q3 - Q1

= 8 - 5

= 3

WORTH 50 POINTS!!!!!!!!!!!!!!!

1. What is the degree of the monomial 3x^2y^3?

A. 2
B. 3
C. 5
D. 6

2. What is the simplified form of 8b^3c^2 + 4b^3c^2 ?

A. 12bc

B. 12b^3c^2

C. 12b^6c^4

D. 12b^9c^4

3. What is the simplified form of (4j^2 + 6) + (2j^2 + 3) ?

A. 6J^2 --- 3
B. 6J^2 + 3
C. 6J^2 + 9
D. 4J^4 + 3

4. what is the difference of the following polynomials?

(6x^3 - 2x^2 + 4)

- (2x^3 + 4x^2 - 5)
------------------------------------

A. 4x^3 - 2x^2 - 1

B. 8x^3 + 6x^2 - 1

C. 4x^3 - 2x^2 + 1

D. 4x^3 - 6x^2 + 9

( OKAY THIS ONE EVEN HARDER ;-; )

5. f (x) = 3x^3 - 4x^2 + 6x and g (x) = 5x^3 + 2x^2 - 3x. What is f (x) - g (x) ?

A. -2x^3 - 6x^2 + 9x

B. -2x^3 - 6x^2 - 3x

C. 2x^3 + 6x^2 + 3x

D. 8x^3 - 6x^2 - 9x
------------------------------------------------------------------------------------------------------------------
i need my grades to improve a bit so please help ;(

(if you wanna do some work while listening to sugarcrash for an hour then i will send you da link!)

Answers

Answer:

2. 6j^2 + 3

Step-by-step explanation:

Answer:

A=5283

Step-by-step explanation:

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! HELP !!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

I’m pretty sure it’s cube?

Help ASAP 15 Points
No spam answers please

Answers

No it is not a right triangle
Not really sure what the second part is asking but maybe 5=7=9

I am at 4 inches represents 240 miles what is the scale of the map

Answers

Answer: 1 inch = 60 miles

Step-by-step explanation:

This is simple

We need to take what we are given

240 miles with 4 inches

Let's divide 240 by 4 to get miles per inch

240/4

60 miles per inch

Answer:

60 miles per inch

Step-by-step explanation:

Hope this will help

A right triangle has a leg of 15 feet and a second leg of 24 feet. Find the length of the hypotenuse
to the nearest hundredth of a foot.

Answers

Answer:

9

Step-by-step explanation:

-

Please help, find the surface area and lateral area.

Answers

Answer:

1,764

Step-by-step explanation:

first you 6x7 then 3x4x3.5 then add the products together

p.s. your welcome

10 points...............

Answers

Answer:

It should be the second one 4,18,6

Step-by-step explanation:

Let me know if that is right . . .

Hope this helps!

help pls i will give brainliest

Answers

Answer: Option 'D' is correct.

Explanation:

We are required to find that length of sides which cannot be sides of triangle,

As we know that " Sum of two sides is always greater than the third side "

If any option does not follow the above postulate that will be our required answer :

D) 21 m, 6 m, 10 m

So, 21 m, 6 m, 10 m cannot be the length of any triangle as it does not satisfy the above mentioned postulate .

Please help me, I will give the best answer brainliest. I have a deadline finish of today, and I really want to get my work done... The following figures show the first two steps of a proof of the pythagorean theorem, which of the following statements about this proof is false? Thank you if you can help :)

Answers

Answer:

so since there isn't any pics to work with, here we go.

the pytha theorem states that a^2 + b^2 = c^2, you've probably seen/heard this all the time but really know what it means.

It means the the shorter side of the triangle (the ones that aren't the hypotenuse) multiplied by themselves, and then added together equals the hypotenuse also multiplied by itself.

So if i have a triangle with sides lengths of 3 and 4, and I want to calculate the hypotenuse length, the equation would be 3^2 + 4^2 = x^2

we then get 9 + 16 = x^2 –––––> 25 = x^2 ––––> √25 = x

so the hypotenuse equals 5.

hope this helps.

4. Three gallons of paint are used to paint 16 wooden signs. How
much paint did each sign use? Between what two whole numbers
does the answer lie?

Answers

Answer:

16/3 of a gallon; 5 and 6

Step-by-step explanation:

three gallons of paint are divided among 16 wooden signs. therefore, each sign used 16/3 of a gallon. this fraction is between the whole numbers of 5 and 6.

What’s the value of x?

Answers

Answer:

uhh

Step-by-step explanation:

i no get this

Whats -20x 50???????f

Answers

Answer:

-1000

Step-by-step explanation:

Since there's a negative in the equation, the answer is also a negative. This is also like 20 x 50, but you have to put a negative at the back.

Answer:

-1,000

Step-by-step explanation:

"Although Jhon was alive once more that doesn't mean that he was happy. he had fun with his dead mom and a gas truck. " which book is this from
harry poter
emile and the pengins
bob the builder
my wii is broke I need help
all and the panda of fireeeeeeee
cred we pop
can I see ur pe pe
thanks bro
also jk plz don't
Ngithanda iglu kuyinto enhle enamathelayo ngiyabonga bantu

Answers

Answer:

um i think all the panda of fireeeeeeee

Step-by-step explanation:

:D

Consider the triangles shown.

Which variable represents the length of an adjacent leg for a 40° angle?

A.c

B.x

C.y

D.z

Answers

The answer would be C

Which equations have 8 as a solution?
11−t=3
t+6=15
5t=40
64÷t=8

Answers

Answer:

64/t = 8

Step-by-step explanation:

If the answer is eight, then t + 8. Because 64/8 = 8.

PLZZ HURRYYYY ENEQUALITIES HELLLLLLPPPPPPP MEEEEE PLZZZZZZZZZ

Answers

Answer: x>5

Step-by-step explanation:

14-3x<-1

-3x<-15

3x>15

x>5

please i need this asap since it is due soon

Answers

Answer:

1. 6.56    2. 12.17

Step-by-step explanation:

I hope this helps!!

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