If f(x) = x2 + 2x + 3, what is the average rate of change of Rx) over the interval (-4, 6]?

Answers

Answer 1

Answer:

Step-by-step explanation:

The average rate of change of a function over an interval is simply the slope over the interval because:

[tex]let \: g(x)=f'(x)\\\frac{\int\limits^b_a {g(x)} \, dx }{b-a}(the\:average\:value\:of\:g)=\frac{f(b)-f(a)}{b-a}[/tex]

We have to know f(6) and f(-4)

[tex]f(x) = x^2 + 2x + 3\\f(6) = 6^2 + 2(6) + 3\\f(6) = 36 + 12 + 3\\f(6) = 51\\\\f(-4) = (-4)^2 + 2(-4) + 3\\f(-4) = 16 - 8 + 3\\f(-4) = 11\\\\\frac{f(6)-f(-4)}{6-(-4)} = \frac{51-11}{10} = \frac{40}{10} = 4[/tex]


Related Questions

Which of the following values are solutions to the inequality

Answers

i used socratic for that one

The first floor of a house consists of a kitchen, playroom, and dining room. The areas of the kitchen, playroom, and dining room are in the ratio 4 : 3 : 2 . The combined area of these three rooms is 189 square feet. What is the value of one box on the tape diagram ?

Answers

Answer:

The value of one box in the tape diagram will be 21 square feet

Step-by-step explanation:

Here, we have the total ratio added as 4 + 3 + 2 = 9

So the area of one box on the tape diagram will be the combined area divided by the total square feet

Mathematically, that will be;

189 square feet/9 = 21

Answer:

21

Step-by-step explanation:

^^^^^^

(first question btw)

please help i will mark brainliest if correct!

Answers

Answer:

(3,9)

Step-by-step explanation:

Because the translation moves 1 in the x direction and 4 in the y direction, you just add those to the starting x and y coordinates.

(2+1, 5+4)

(3, 9)

please help!!!!!!!!! ​

Answers

Answer:

1) 1:100

2)200 ml

3) 1:50:100

Step-by-step explanation:

Egg to milk = 3:100 or 1:100

3:100=2:x x=200

Eggs to flour to milk=

3:150:300.

Or 1:50:100

Hope this helps plz mark brainliest :D

what is the difference between 3/8 and 61/64 redosed

Answers

Answer:

Distance between points =  [tex]37/64\\[/tex]

Step-by-step explanation:

This is a relatively simple problem. Here we have to find the distance between two points on the number line.

The given two numbers are fractions and to find the difference between these two numbers, we have to make their denominators common.

One has denominator as 8 and the other as 64.

We make the common denominator as 64.

Then the fractions 24/64 are 61/64  and .

The distance between the two points = 61/64  - 24/64  

                                = 37/64

Step-by-step explanation:

A frosting recipe calls for adding 5 tsp of red food coloring for every 3 tsp of blue food coloring. If you used 15 tsp of blue food coloring, how many tsp of red food coloring would you use to get the same recipe of frosting ?

Answers

Answer:

tsp of red food coloring = 25

Step-by-step explanation:

Red food coloring = 5 tsp

Blue food coloring = 3 tsp

Red food coloring : Blue food coloring = 5 tsp : 3 tsp

Blue food coloring = 15 tsp

how many tsp of red food coloring would you use to get the same recipe of frosting ?

Let

x = tsp of red food coloring

Red food coloring : Blue food coloring = x tsp : 15 tsp

Equate the ratios to find x

Red food coloring : Blue food coloring

5 tsp : 3 tsp = x tsp : 15 tsp

5 / 3 = x / 15

Cross product

5 * 15 = 3 * x

75 = 3x

Divide both sides by 3

x = 75 / 3

= 25

x = 25 tsp

tsp of red food coloring = 25

In a board game, Judy scored 5 points more than twice the number of points Ann scored. There was a total of 65 points scored. If Judy scores x points and Ann scores y points . How many points did Judy score?

Answers

Just earned 35 points and Ann earned 30 points

Judy scored 45 points in the board game.

What is the system of equations?

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

In a board game,

Judy scored 5 points, more than twice the number of points Ann scored.

If Judy scores x points and Ann scores y points,

that means,

x = 2y + 5

x - 2y = 5.   {equation 1}

There was a total of 65 points scored.

x + y = 65  {equation 2}

Subtract the equation 2 to equation 1,

we get,

-3y = -60

y = 20

Then, x = 45.

Therefore, 45 points Judy scored.

To learn more about the system of equation;

brainly.com/question/13729904

#SPJ2

The brown family has 5 liters of lemonade. Each liters of lemonade weighs 1 kilogram. At the end of the day they have 290 grams of lemonade left. How many grams of lemonade did they drink.

Answers

Answer:

4710grams of lemonade.

Step-by-step explanation:

Step one:

given data

the brown family has 5 liters of lemonade that weighs 1 kg per liter

this implies that they have 5kg of lemonade.

convert 5kg to grams we have 5*1000= 5000grams

(because 1000g is equal to 1kg)

Step two:

if at the end of the day there was 290grams left, then they drank

=5000-290

=4710

They drank 4710grams of lemonade.

Find the distance between (0,5) and (8,9). Round your answer to the nearest tenth.
The distance is about
units.

Answers

Answer:

8.9 units

Step-by-step explanation:

sqrt[(x2-x1)^2+(y2-y1)^2]

sqrt[8^2+4^2]

sqrt(80)

8.9 units

please help i will mark brainliest

Answers

Answer:

180, i already commented it but like i even looked it up a straight line is 180

Step-by-step explanation:

how long is 74% of 60 min
A. 50
B. 35
C.45

Answers

Answer:

Its c

Step-by-step explanation:

Answer:

yes it is C

Step-by-step explanation:

Need help ASAP!! Tysm will mark brainliest

Answers

Answer:

about 30 then you will still fall short of that mark

HOPE IT HELP I AM NOT WANTING TO BE INCORRECT

Step-by-step explanation:

this is idiotic sense all the 3's will fall short

HELP PLEASE ASAP!! WILL GIVE BRAINLIEST ❤️

Find the slope of the line. Enter your answer in simplest form.

Answers

Answer:

slope=4

Step-by-step explanation:

m=y2-y1/x2-x1

4-(-4)=8

5-3=2

8/2=4

hope this helps :3

if it did pls mark brainliest

Fred opened a bank account with $310. He then deposits $55 per week. Stan started his bank account with $650 and withdraws $30 per week. Set up an equation to represent this situation. After how many weeks, w, will their bank accounts have the same amount in them

Answers

Answer: 4 weeks

Step-by-step explanation:

What is the correct answer for all? ​

Answers

Answer: 13.B

  14.B

15.C

16.A

17.D

18.A

Step-by-step explanation:

find the sum of the first 20 terms 1.5, 1.45, 1.40, 1.35

Answers

Answer: 20.5

Step-by-step explanation:

subtract 0.05 from each answer until you get 20 terms then add those terms up

PLEASE HELP
find the first 5 terms in the sequence
A) 6, 12, 24, 48, 96
B)1, 2, 3, 4, 5
C)6, 7, 8, 9, 10
D) 6, 11, 21, 41, 81

Answers

Answer:

The first five terms are 6, 11, 21, 41, 81 ⇒ D

Step-by-step explanation:

∵ The rule of the sequence is a(1) = 6; a(n) = 2 a(n - 1) - 1 for n ≥ 2

∴ The first term of the sequence is 6

∴ The value of n represents the position of the term

∵ n = 2

∴ a (n - 1) = a(2 - 1) = a1

∵ a1 = 6

→ Substitute a1 by 6

∴ a(2) = 2(6) - 1 = 12 - 1

a(2) = 11

∵ n = 3

∴ a (n - 1) = a(3 - 1) = a2

∵ a2 = 11

→ Substitute a2 by 11

∴ a(3) = 2(11) - 1 = 22 - 1

a(3) = 21

∵ n = 4

∴ a (n - 1) = a(4 - 1) = a3

∵ a3 = 21

→ Substitute a3 by 21

∴ a(4) = 2(21) - 1 = 42 - 1

a(4) = 41

∵ n = 5

∴ a (n - 1) = a(5 - 1) = a4

∵ a4 = 41

→ Substitute a4 by 41

∴ a(5) = 2(41) - 1 = 82 - 1

a(5) = 81

∴ The first five terms are 6, 11, 21, 41, 81

Given: O ∈ AB , ON is ∠ bisector of ∠AOC, OF is ∠ bisector of ∠COB, m∠FOB=70°. Find: m∠AON

Answers

Answer:

AOC = 20 degrees

Step-by-step explanation:

We know that FOB is 70 degrees, and COF is 90 degrees. So just add 70+90 and get 160 degrees. Then you subtract that from AOB which is 20 degrees.

Translate each expression then write the expression in factored form.
Ten times a number subtract from eighteen.

Answers

Answer:

I think the is 18-10s

Step-by-step explanation:

hope that helps

Which expression is equivalent to -6(-2/3+2x)
-4-12x
-4+2x
4-12x
4+12x

Answers

C. Is your answer to the question
Answer:4-12xStep-by-step explanation:brainliest plzs

HELP! GIVING OUT BRAINIEST AND 10 POINTS!!!

Answers

Answer:

i think it's 18

Step-by-step explanation:

no need to

Answer:

x=12

Step-by-step explanation:

If you add HG and GE together, you would get the value for HE. You also get HE if you add HF and FE. Setting HG+GE equal to HF+FE gives us a true equation we can use to solve for x. The math is attached.

two trapezoids-shaped tabletops are congruent to each other trapezoid FGHI =trapezoid WXYZ must be congruent to GH

A. XY

B. WX

C. YZ

D. WZ

Answers

Answer: B: WX

Step-by-step explanation:

7 less than the difference of 12 and 5

Answers

Answer:

the difference of 12 and 5 is 7 so it would be 0

Please someone please help, will mark you Brainliest


Read the problem carefully and write the required information:


Community Gym charges a $50 membership fee and a $55 monthly fee. Workout Gym charges a $200 membership fee and a $45 monthly fee. After how many months will the total amount of money paid to both gyms be the same? What will that amount be?


What are you looking for?


Define a variable:


Write the equation:



Solve the equation:


What will the amount of money be when the total amount of money paid to both gyms is the same?

Answers

Answer:

Step-by-step explanation:

Community gym

=> membership fee = $50

=> monthly fee = $55

=> First month = 105$

=> 50 + 55(x)

=> 50 + 55 (15)

=> 50 + 825

=> 875

Workout gym

=> membership fee = $200

=> monthly fee = $45

=> First month = 245$

=> 200 + 45(x)

=> 200 + 45(15)

=> 200 + 675

=> 875

On the 15th month, community gym and workout gym will both get the same amount of $875.

Answer: what are you looking for? after how many months will the total amoung of money paid to both gyms be the same? Define a variable: I'm not sure. Write the equation, community Gym 50 + 55(x), workout gym 200 + 45(x), solve the equation. on the 15th month, community gym and workout gym will both get the same amount of $875.

Step-by-step explanation:

Find the slope plz help help plz

Answers

Answer:

-2

Step-by-step explanation:

Please help me with this

Answers

X>-1 is the base function

To make different equations you just have to alter both sides of the equation in the same way
Ex.
X+2>-1+2. Add 2
X+2>1. Simplify

Xx4>-1x4. Multiply by 4
4x>-4. Simplify
4x+3>-4+3. Add 3
4x+3>-1. Simplify

Ex answers
X+2>1
4x+3>-1

Hope this helps!! If so please give it brainliest!!

what is the solution to this equation? 14 - 3x = 6 - 5x

Answers

Answer:

x=-4

Step-by-step explanation:

14-3x = 6-5x

-3x         -3x

14      =   6-2x

-6            -6

-2x     =   8

x         =  -4

Hope this helped! :)

14 -3x = 6 -5x Add 5x to both sides
14 +2x = 6 Subtract 14 from both sides
2x = -8 Divide both sides by 2
x = -4

What is the domain and range of these graphs ?

Answers

1=a 2=c 3=b ..................

2x+3y=122, x, plus, 3, y, equals, 12
Complete the missing value in the solution to the equation.
((left parenthesis
,8),8)

Answers

she me he sid sud iebe Howie

PLEASE HELP WILL GIVE 20 POINTS

Use I = PRT to solve.
(time is in years)
P = $450
R = 5%
T = 7 years
Find I.

Answers

Answer:

$150.50

Step-by-step explanation:

I = 450 × 0.05 × 7 = 157.5

I = $ 157.50

The simple interest accumulated

on a principal of $ 450.00

at a rate of 5% per year

for 7 years is $ 157.50.

Hellooo :)

The answer is I = $ 157.50

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