Consider f(x)=2|x|
What is the rate of change over the interval 0≤x≤4?

How is the rate of change over this interval related to the form of the function?

Answers

Answer 1

Answer:

Please check the explanation.

Step-by-step explanation:

As we know that the average rate of change of f(x) in the closed

interval [a, b] is

[tex]\frac{f\left(b\right)-f\left(a\right)}{b-a}[/tex]

Given the interval [a, b] = [0, 4]

as

[tex]f(x)=2|x|[/tex]

[tex]f(b)=f(2)=2\cdot \:4[/tex]       ∵  [tex]\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0[/tex]

      [tex]= 8[/tex]

   

[tex]f(x)=2|x|[/tex]

[tex]f(a)=f(0)=2\cdot \:0[/tex]       ∵  [tex]\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0[/tex]

       [tex]= 0[/tex]

so the average rate of change  :

[tex]\frac{f\left(b\right)-f\left(a\right)}{b-a}=\frac{8-0}{4-0}[/tex]

              [tex]=\frac{8}{4}[/tex]

               [tex]= 2[/tex]

We know that a rate of change basically indicates how an output quantity changes relative to the change in the input quantity. Here, it is clear the value of y increase with the increase of input.


Related Questions

PLEASE help find measure of angle - TEst review today

Answers

Answer:

both measured would be 25 and 19

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

if x equals 4 then 21x+4 equals 88 and 23x-4 equals 88 too.

PLEASE HELP ME 16 POINTS PLEASE HELP

Answers

Is there any other more information for this

Answer:

the y-intercept is 0

Step-by-step explanation:

it goes straight through the origin

HURRRRY!!!! Thank you

Answers

Answer:

C

Step-by-step explanation:

Uhm I tried my best im so sorry if it's wrong

it is B yep he was right have a nice day

PLEASE HELP ME AND EXPLAIN.

Answers

Answer:

9*8=72 which would be more than enough to cover the wall

A car travels at a constant speed, as shown on the double number line. Double number line. Time, hours. Distance, kilometers. How far does the car travel in 14 hours? Explain or show your reasoning.

Answers

Answer:

980 km.

Step-by-step explanation:

The speed of the car is constant,

From the double number line:

When the time is 0 hour, the distance covered is 0 km.

When the time is 1 hour, the distance covered is 70 km.

When the time is 2 hours, the distance covered is 140 km,

which can be written as

when the time is 2 hours, the distance covered is 70 x 2 km.

Similarly,

When the time is 3 hours, the distance covered is 210= 70 x 3 km.

This can be generalized as,

When the time is n hours, the distance covered is  70 x n km, i.e

The distance traveled in n hours = 70 x n km.

So, for 14 hours, n= 14,

Hence, the distance traveled in 14 hours = 70 x 14= 980 km.

Alexa took a test and lost 3 points for each of the 7 questions she got wrong. She earned an additional 5 points for answering a bonus question correctly. How many points did Alexa receive or lose overall?

Answers

Answer:

Alexa lost 16 points overall

Step-by-step explanation:

To determine whether Alexa had a net receipt or loss of points, we will fine the total points received or lost, and find the difference:

points lost:

3 point for each of the 7 questions she answered wrong

lost point = 3 × 7 - 21 points

Points received:

5 points for answering a bonus question

point received = 5 point

The points lost (21) is greater than the points received (5), hence, there was a net loss. The net loss is calculated as follows:

points lost - points received

= 21 - 5 = 16

∴ Alexa lost 16 points overall

use the line tool and select two points to graph the line
graph f (x) = - 1.5x +6
PLEASE HELP !!!​

Answers

Answer:

Step-by-step explanation:

Make & the subject of the
Formula
6x ta=5(x+t)

What is the answer please

Answers

Answer is x = 5t-a

6x+a = 5(x+t) Expand the bracket
6x+a = 5x+5t Subtract the least x’s (so 5x)
x+a = 5t Subtract a to make x the subject
x = 5t-a

Answer:

x  = 5t - a

Step-by-step explanation:

The problem deals with making a variable the subject of the formula in the expression.

 Given expression:

            6x + a = 5(x + t)

  We are to make x the subject of the formula in the expression

   

Solution:

           6x + a  = 5(x+t)

On the right hand side, expand the parentheses and distribute the term outside;

          6x + a  = 5x + 5t

   Bring the term desired to be the subject to one side by adding (-5x) to both sides;

     6x + (-5x) + a = 5x + (-5x) + 5t

           x + a  = 5t

  Now add (-a) to both sides

         x + a + (-a) = 5t + (-a)

          x  = 5t - a

Select all that apply.
40 is what percent of 25. Hint: There are 2 correct answers.
А160%
B 62.5%
C 1600%
D625/1000
E 160/100
F1600/100

Answers

Answer:

B and D

Step-by-step explanation:

Hope this helps :3

if it did pls mark brainliest

Answer:

A & E

Step-by-step explanation:

First, multiply 40 by 100, giving you 4000. You then divide 4000 by 25, where you will get a quotient of 160. Now, this can be represented as 160% or 160/100 because a percentage is always out of 100.

A serving of bagel chips contains 20 grams of carbohydrates, 3 grams of fat, and 3 grams of protein. How many calories would be in the serving of chips?
1 gram of protein= 4 calories, 1 gram of carbs= 4 calories, 1 gram of fat= 9 calories.

Answers

Answer:

119 calories in a serving

Step-by-step explanation:

>>1 gram of carbs=4 cal

20 g of carbs times 4 calories per gram of carbs= 80 calories

>>1 gram of fat=9 calories

3 g of fat times 9 calories per gram of fat= 27 calories

>>1 gram of protein=4 calories

3 g of protein times 4 calories per gram of protein= 12 calories

<80+27+12=119 calories total in a serving of chips>

Jiro and Joey share a 30-ounce box of cereal. By the end of the week, Jiro has eaten 3/10 of the box, and Joey has eaten 3/5 of the box of cereal. How many ounces are left in the box?

Answers

Answer:

6 ounce of cereal

Step-by-step explanation:

Step one:

given that the box is 30 ounce of cereal.

for Jiro----who ate 3/10 of the 30 ounce

=3/10*30

=9 ounce

Jiro ate 9 ounce

step two:

for Joey----who ate 5/10 of the 30 ounce

=5/10*30

=15 ounce

Joey ate 15ounce

the total ounces that both of them ate is

=9+15

=24

therefore the ounce left

=30-24

=6 ounce of cereal

The left over is 6 ounce of cereal

can someone please answer the 2 questions in the photo, please let me know if you can or cannot see them.

Answers

Answer:

I have the same one! this isnt an answer but like i need help too-

Step-by-step explanation:

Find x (Type the number answer)

Answers

He’s with his other girl TvT

Answer:

18.41

Step-by-step explanation:

[tex]x^{2} = 12^{2} + 8^{2} - 2(12)(8)(cos 133)\\\\x= \sqrt{338.94} = 18.41[/tex]

The angles of a triangle are x,2x,3x. Find the value of x in degrees​

Answers

Answer: x = 30°
Sum of interior angles is 180°, and there are 6x’s. 180 divided by 6 is 30

Answer:

x=30°

Step-by-step explanation:

x +2x+3x=6x

since triangles are 180° in total. 6/180=30

so 30° is your answer.

Find the zero of the function.
f(x) = 4x2 – 12x + 9

The zero of the function is x=

Answers

Answer:

x= 3/2

Step-by-step explanation:

I apologize if it is wrong!

HELP:( I know I’m slow and all asking all these question today but...

Answers

Second answer

Step-by-step explanation:

What is the 10th term in the sequence -3, -8, -13, ..

Answers

Answer:

-48

Step-by-step explanation:

The full sequence until the tenth term is...

-3, -8, -13, -18, -23, -28, -33, -38, -43, -48,

Answer:

-48

Step-by-step explanation: You don't really care about the explanation. You already got the answer. What are you still doing here, reading this?

How many modes, if any, does the group of data have?
Kate, Tim, John, John, Angela, Tim, Sue 1 mode 2 modes no mode 3 modes

Answers

The number of modes in the dataset is 1. The dataset is unimodal. The correct option is therefore;

1 mode

What is a unimodal data?

A unimodal data is a set of data that has only one mode. The mode is a measure of central tendency.

The data in the question can be presented as follows;

Kate, Tim, John, John, Angelam, Tim, Sue

The frequency of each of the data is therefore;

Kate; 1, Tim; 1, John; 2, Angela; 1, Tim; 1, Sue; 1

The mode of a dataset, is the value that has the highest frequency, or that appears the most in the dataset.

The data that has the highest frequency is John, the mode of the dataset is therefore, John, which has a frequency of 1

The dataset, therefore, has only 1 mode.

Learn more on the measures of central tendency, mode median, and mean, of a dataset here: https://brainly.com/question/24994390

#SPJ1

Which of the following is the graph of y==(x-2) 0 - 5?
12
1
2
3
4
15
X
-
3
4
5
-6
-7
-8
-9
-10
-5 -4 -3 -2 -1
1
2.
3
4
5

Answers

answer: is -5
Explanation:

HELP PLEASE GET BRAINLIST!!

solve for x,
90 - 3/2x ≤ 30

Answers

Answer: x>- -40

Step-by-step explanation:

Challenger Elementary School has 800 students. Every Wednesday, 12% of the students stay after school for Chess Club. How many students attend on Wednesday’s?

Answers

Answer:

96 students attend chess club after school on Wednesday's.

Step-by-step explanation:

To solve this problem, simply multiply 800 x 0.12.

    800 x 0.12 = 96

I hope this was helpful to you! If it was, please consider rating, pressing thanks, and marking my answer Brainliest. It would help a lot. Have a great day!

Answer:

[tex]\huge\boxed{\text{96 students}}[/tex]

Step-by-step explanation:

In order to find how many students stay back for Chess Club, we want to find 12% of 800.

To do this, we can set up a percentage proportion.

[tex]\frac{12}{100} = \frac{x}{800}[/tex]

We can now solve for x by cross multiplying.

[tex]800 \cdot 12 = 9600\\9600 \div 100 = 96[/tex]

So, 96 students attend Chess Club on Wednesdays.

Hope this helped!

Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.

Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.

Let x = the number of packages of pasta and y = the number of jars of pasta sauce.

One package of pasta is the right amount to go with one jar of pasta sauce. What is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry?

How many packages of pasta?

How many jars of pasta sauce?

Explain your reasoning.

Answers

Answer:

8 packages of pasta and 8 jar of sauce which is $32 dollars and 20lbs in total

Step-by-step explanation:

8 pack of pasta is 8$ and 8lbs

8 jars of sauce is 24$ and 12lbs

8 plus 12 is 20 which is the max of lbs Tyler can carry.

find the x and y intercept
y=5x-13

Answers

Answer:

X int = 13/5    Y int= -13

Step-by-step explanation:

Find the third side in simplest radical form:
1&3

Answers

Answer:

[tex]\sqrt{10}[/tex]

Step-by-step explanation:

[tex]1^{2} + 3^{2} =x^{2} \\1+9=x^{2} \\10=x^{2} \\\sqrt{10} =x\\[/tex]

A store sells ice cream with assorted toppings. They charge $3.00 for an ice cream, plus 50 cents per ounce of toppings. If Elena’s ice cream cost $1.50 more than Jada’s ice cream, how much more did Elena’s toppings weigh?

Answers

Answer:

3 ounces more

Step-by-step explanation:

50*3 =1.50

3.00+1.50= 4.50

can someone help answer this??

Answers

Answer:4

Step-by-step explanation:

it shows it on the table

help its mathnnnnnnnnnnnnnnnnnnnnnnn

Answers

Answer:

1

Step-by-step explanation:

6 ÷ 2(1 + 2) ; use "please excuse my dear aunt sally", please for parenthesis

6 ÷ 2(3); now do "my" for multiplication

6 ÷ 6 ; now do "dear" for division

1

Find 0.038 as a fraction in its lowest terms

Answers

Answer:

19 / 500

Pls mark as brainliest!!!

Answer:

19/5

Step-by-step explanation:

If you're using a scientific calculator you will be able to find this answer by just simply pressing 0.038 x 100 divided by 1

(-4/3)x -6 =26

solve for x

Answers

Answer:x =24

Step-by-step explanation: If we reverse that we will get x= 32x3/4 which is 24

Answer:

x = -24

Step-by-step explanation:

(-4/3)x -6 =26

Add 6 to both sides:

(-4/3)x = 32

(-4/3) = -1.33333333

divide both sides by -1.33333333

x = -24

Substitute:

(-4/3)(-24) -6 =26

32 - 6 = 26

26 = 26

x = -24

Stan, Greg, and Seth were cleaning the school gym in shifts. Stan
cleaned first, then Greg, then Seth. If they each cleaned the same
amount of time for a total of 11 hours, how many minutes did each one
clean?

Answers

an hour is 60 minutes so we would do 60x11 which equals 660 then divide by 3 which is 220 so 220 minutes is your answer
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