Consider the function given by f(x)= x² +3. Find its average rate of change from x = -2 to x = 4.
Carefully show the work that leads to your final answer.

Answers

Answer 1

Answer:

[tex]Rate = 2[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x^2 + 3[/tex]

Required

Determine the average rate of change from -2 to 4

This is calculated using:

[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]

In this case:

[tex]a = -2[/tex]

[tex]b = 4[/tex]

So, we have:

[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]

[tex]Rate = \frac{f(4) - f(-2)}{4 - (-2)}[/tex]

[tex]Rate = \frac{f(4) - f(-2)}{4 +2}[/tex]

[tex]Rate = \frac{f(4) - f(-2)}{6}[/tex]

Calculate f(4):

[tex]f(x) = x^2 + 3[/tex]

[tex]f(4) = 4^2 + 3[/tex]

[tex]f(4) = 19[/tex]

Calculate f(-2)

[tex]f(x) = x^2 + 3[/tex]

[tex]f(-2) = (-2)^2 + 3[/tex]

[tex]f(-2) = 7[/tex]

So:

[tex]Rate = \frac{f(4) - f(-2)}{6}[/tex]

[tex]Rate = \frac{19-7}{6}[/tex]

[tex]Rate = \frac{12}{6}[/tex]

[tex]Rate = 2[/tex]

The average rate of change is 2.


Related Questions

Using eight eights and addition only, can you make 1000?

Answers

Answer:

888 + 88 + 8 + 8 + 8 = 1000

simple

Help with geometry please

Answers

9514 1404 393

Answer:

  27/36

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the tangent relation is ...

  Tan = Opposite/Adjacent

  tan C = AB/CB

  tan C = 27/36

Out of these, which is not an inequality?

a. 435 ≥ 5p + 4

b. g - 7 < 100

c. 18x + 9y

d. a > 6b​

Answers

Answer:

C. 18x+9y

Step-by-step explanation:

Answer:

I think its the third one, C. Hope this helps!

need help like every time :{

Answers

Answer:

I need free points but all ik is the -4 needs to be divided by 4 then u have 5g+14=5g/-1

Step-by-step explanation:

step 1: multiply both sides:
20g + 56 = 5g - 4
step 2: move the terms
20g - 5g = -4 -56
step 3: collect like terms and calculate
15g = -60
step 4: divide both sides
g = -4
a good app for help with solving equations is photomath! it shows you the solving steps, hope this helps!

What is the leading coefficient of the polynomial f(x) defined below

Answers

Answer:

1

Step-by-step explanation:

The answer is simply 1 as the leading term, x^4 has a coefficient of 1.

Write the following rate in simplest forms.

1. 333 calories burned in 55 minutes.

2. 4 million hits on a website in 16 months.

3. 279 points in 27 games.

4. $49 for 448 photos.

5. 6 pounds of zucchini for 24 servings.

Answers

Answer(s): 333/55, 1/4, 31/3, 7/64.


Explanation: 333/55 is already in simplest form
(4/16)/(4/4)=1/4

(279/27)/(9/9)=31/3

(49/448)/(7/7)=7/64


What is the area of a rectangle whose width is 6 feet and length is 19 feet?

Answers

Answer:

114

Step-by-step explanation:

A= length x width

A= 6x9

A=114

ङ-आपको कौन-सी ऋतु पसंद है और क्यों ?​

Answers

Answer:

हेलो मेरा पसंदीदा मौसम गर्मियों का है, मैं इसे प्यार करता हूं क्योंकि मैं अपने दोस्तों के साथ तैराकी करता हूं और मुझे तैराकी पसंद है क्योंकि मैं ट्रैक रन करता हूं, मुझे सिर्फ गर्मी से प्यार है

Step-by-step explanation:

The midpoint of AB is M (4,-2) . If the coordinates of A are (3,-6) , what are the coordinates of B

Answers

Answer:

The coordinates of B are (5,2).

Step-by-step explanation:

Given that,

The midpoint of AB is M (4,-2).

The coordinates of A are (3,-6)

We need to find the coordinates of B. Let the coordinates of B are (x,y).

The mid point is given by :

[tex]M=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})\\\\(4,-2)=(\dfrac{3+x}{2},\dfrac{y-6}{2})\\\\\dfrac{3+x}{2}=4\ \text{and}\ \dfrac{y-6}{2}=-2\\\\3+x=8\ \text{and}\ y-6=-4\\\\x=5,y=2[/tex]

So, the coordinates of B are (5,2).

14 ÷ 3/8
I need help plis :(​

Answers

Answer:

[tex]\frac{112}{3}[/tex]

Step-by-step explanation:

14 ÷ 3/8 = 14 • 8/3

= 112/3

Answer:

37 1/3

Step-by-step explanation:

use Keep Change Flip when dividing with fractions! :) It's helpful

for example: 14 ÷ 3/8

14 (keep as 14)

* (change to multiplication)

8/3 (flip the fraction)

14 times 8/3= 37 1/3

A. Identify which of the following points: (2,-5),(4,1),(3, 3),(6,3) are solutions of the linear equation: 2x - y = Graph each point that is a solution of the linear equation from Part A. ​

Answers

Answer: It will be (2,-5) and (6,3) because they are one the slope line

Step-by-step explanation:

Hope is Helped

f(x) = x2 - 4x – 8,
Graph

Answers

Answer:

-2x-8

2x= -8

x = -4

or

( x - 2 )(x + 2 )

x=2

x= -2

Sameer woke up one morning and saw frost on the windows. It was -7°C outside. Later in the day, the frost melted. At 3 p.m. it was 2°C outside. Which expression represents the difference between the two temperatures?

Answers

Answer:

[tex]d = 9[/tex]

Step-by-step explanation:

Given

[tex]Morning = -7^{\circ}C[/tex]

[tex]Afternoon = 2^{\circ}C[/tex]

Required

What represent the difference

The expression that represents the difference (d) are:

[tex]d = |Morning - Afternoon|[/tex]

Substitute values for Morning and Afternoon

[tex]d = |-7 - 2|[/tex]

[tex]d = |-9|[/tex]

[tex]d = 9[/tex]

Becky made 63 carnival masks which is 30 % less than the number her brother made How many carnival masks did beck and her brother make in total?

Answers

Answer:

sorry im not smart

Step-by-step explanation:

sorry

THis is akward lol

Type the correct answer in the box. If necessary, use / for the fraction bar and simplify the fraction. cos(75°)cos(15°) =

will mark brainliest

Answers

Answer:

1/4

Step-by-step explanation:

using the product-to sum formulas, this is

1/2 (cos(75+15) + cos(75-15))

Answer:

1/4

Step-by-step explanation:

PLATO USER

Describe how you would evaluate this algebraic
expression: 7-2m when m=2

Answers

Answer:

Step-by-step explanation:

Just plug in

7 - 2(2) = 3

Answer:

3

Step-by-step explanation:

By substituting m for 2, you would get:

7 - 2(2) =

7 - 4 = 3

ASK YOUR TEACHER PRACTICE ANOTHER Suppose that 178 cars were sorted by model and color. Assume that 10 were Fords but not blue, 72 were blue but not Fords, and 84 were neither blue nor Fords. Make a Venn diagram using Fords and blue cars, and include the numbers in each region of the diagram.

Answers

Answer:

Fords Neither Blue

10 84 72

Please help this is due today!

Calculate the unknown missing angle measures.

Do not answer this with one answer ,blank, or a ridiculous answer.... this is serious please.

Answers

123-a and b is 55...
123-a and b is 55.Hope this helpsss

Heyy can someone help me ¿? ;-; is for today ;-;


Zuleima puts her pebbles on the table. Make groups of 3 and have 1 left. Then make groups of 5 and have 2 left. How many stones does Zuleima have?

Answers

Step-by-step explanation:

she has 3 because she make group of five n have one and then make a group of five and had two, so add two plus one it will give u three

Bill drove his car at a constant speed while on a trip. Kevin drove his car at a different constant speed while on the same trip. The graph and the table show information about the trips Bill and Kevin took.



​Which sentence correctly compares the rates Bill and Kevin drove on their trips​

Answers

I thought to say the second sentence because it says that he’s going at a different constant speed but he doesn’t say compared to who... I’m leaning more to the last sentence.
What do you think?

solve and receive brain list ​

Answers

Answer:

x = 19/22

Step-by-step explanation:

8x-12+36x = 26

44x - 12 = 26

44x = 38 (add 12 on both sides)

x = 19/22 (divide bot sides by 44 and simplify)

238% of what number is 47,600?

Answers

Answer:

I think 200

Step-by-step explanation:

47600/238=200

200*238=47600

Answer:

the answer is actually 20000

Step-by-step explanation:

238%             x  =47,600

2.38x=47,600

47,600/2.38= 20000

Let f(x) = - 2x + 5 and g(x)=x2 + 5.
Find (f+g)(x)

Answers

Answer:

[tex]x^{2}[/tex]-2x+10

Step-by-step explanation:

Work out the circumference of this circle with radius 7.5cm
Take pi to be 3.142​

Answers

Answer in terms of pi: 15pi cm
Explanation:
C = 2 x pi x r
C = 2 x pi x 7.5
C = 15 pi

Answer: 47.12cm (rounded to 2dp)
Explanation:
C = 2 x pi x r
C = 2 x pi x 7.5
C = 15 pi
C = 47.1238898
C = 47.12 (2 dp)

Answer:

15pi cm or 47.12

Step-by-step explanation:

Radius= 7.5cm

7.5 x 2 = 15

diameter= 15cm

circumference = pi x diameter

circumference= pi x 15

=15pi cm or 47.12

Which expression is equivalent to 4(3x + 2y) + 5(2x – 4y)?
A 222 - 12y
B 14.2 - 9y C 22x – 2y D 172 4y

Answers

Answer:

22x-12y

❤❤

hope its helpful ❤❤❤❤

THANK YOU.

Suppose that at Northside High, the number of hours per week that seniors spend on homework is approximately Normally distributed with a mean of 18.6 and a standard deviation of 6. We take a random sample of 36 seniors. What is the mean and standard deviation of the sampling distribution for the 36 students?

Answers

Answer:

The mean and standard deviation of the sampling distribution for the 36 students will be:

Mean = 18.6

Standard deviation = 6

Step-by-step explanation:

The mean and standard deviation of the sampling distribution is equal to the population mean and standard deviation respectively.  The only difference is that the population mean and standard deviation are parameters or fixed values calculated from every individual in the population, while the sample mean and standard deviation are statistics.  Statistics are calculated from only some of the individuals in a population.  They are meant to represent or approximate the population parameters.

Which line has a slope of -1/2?

Answers

Line d passes through (-4,0) and (0,-2) .
Slope = (-2-0)/(0-(-4)) = -½

Find x. Round to the nearest tenth.

Answers

By knowing all sides of triangle and applying the formula of the law of the cosines we conclude that the missing angle X is approximately 117.9°.

How to find the missing angle

In this question we have a triangle with three known side lengths but all missing angles, we can determine the missing angle by using the law of cosines. If we know that x = 90 ft, y = 55 ft and and z = 50 ft, then the missing angle X is:

90² = 55² + 50² - 2 · 55 · 50 · cos X      (1)

X ≈ 117.916°

To learn more on law of the cosines: https://brainly.com/question/17289163

#SPJ1

y = -20 + 4 If z = 3.5, then y= y=-11 liz = -1, then y (Write your answer as a de z+y=1 lfz=0 then y 21 - y=5 l z= 4 then y PLEASE DETERMINE. THE VALUE OF X​

Answers

Answer/Step-by-step explanation:

If in the value of x into each given equation to find y:

✔️x = 3.5,

y = -2(3.5) + 4

y = -7 + 4

y = -3

✔️x = -1,

y = ½(-1) + 11 = -½ + 11

y = (-1 + 22)/2 = 21/2

y = 10.5

✔️x = 0

0 + y = 1

y = 1

✔️x = 4,

2(4) - y = 5

8 - y = 5

-y = 5 - 8

-y = -3

Divide both sides by -1

y = 3

I aperciate if u can help me fast

Answers

Answer:

30

Step-by-step explanation:

cos ^-¹ (20/23) = angle

angle = 29.59

round up = 30

hope it helps

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