Given the function f(x)=-x^2-5x+12f(x)=−x 2 −5x+12, determine the average rate of change of the function over the interval -5\le x \le 4−5≤x≤4.

Answers

Answer 1

Given:

The function is

[tex]f(x)=-x^2-5x+12[/tex]

To find:

The average rate of change of the function over the interval −5 ≤ x ≤ 4.

Solution:

The average rate of change of a function f(x) over the interval [a,b] is

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

Putting x=-5 in the given function, we get

[tex]f(-5)=-(-5)^2-5(-5)+12[/tex]

[tex]f(-5)=-25+25+12[/tex]

[tex]f(-5)=12[/tex]

Putting x=4 in the given function, we get

[tex]f(4)=-(4)^2-5(4)+12[/tex]

[tex]f(4)=-16-20+12[/tex]

[tex]f(4)=-24[/tex]

Now, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is

[tex]m=\dfrac{f(4)-f(-5)}{4-(-5)}[/tex]

[tex]m=\dfrac{-24-12}{4+5}[/tex]

[tex]m=\dfrac{-36}{9}[/tex]

[tex]m=-4[/tex]

Therefore, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is -4.


Related Questions

which linear any qualities could represent the given table of values

Answers

B is correct cause it was a lot of things to do and it was hard for me to do

Can anyone help me pls???

Answers

Answer:

It's

Step-by-step explanation:

9a-3b

because 3×3a is 9a and 3×-b is -3b hope this helps

Answer:

8) A   9) B

Step-by-step explanation:

For question 8 just combine like terms, combine the numbers that have the same variables. Number 9, distribute the 3 to the rest of the equation.

Hope this helped :)

Which of the following constants can be added to x ^2 - x to form a perfect square trinomial?
1/4
1/2
1

urgent

Answers

Answer:

Its 1/4 boys dont worry i got you

Step-by-step explanation:

What’s the answer and can someone please explain it?

Answers

(10^4)^2
=10^4*2
=10^8

add x³-2x²y+4xy²-y³,2x³-5xy²+3x²y-4y³​

Answers

Step-by-step explanation:

the answer is x times (x^2 +xy-y^2 - x^2 y^32)

Can somebody plz help answer these questions correclty (like what the letters=) thanks :D

WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DD

Answers

6. P=4
7. M=7
8. N=13
9: Z= 5
10. X= 4
11. Y= 9

Answer:

6. p = 4

7. m = 7

8. n = 13

9. z = 5

10. x = 4

11. y = 9

Step-by-step explanation:

You can divide the solution by the number next to the letters/variables.

For example, to find 9p = 36 you can do 36 ÷ 9 which equals 4.

To double check, you can multiply your quotient by the divisor.

So to check if p = 4, you can do 9 x 4 which equals 36, therefore it is the solution.

PLEASE HELP ASAP?!?
What are the sine, cosine, and tangent ratios for

Answers

i’m going to assume that T is the reference angle.
sine = 8/17
cosine = 15/17
tangent = 8/15

Explain how to find the distance between 1.5 and any point, n, on a number line.​

Answers

Do you have a picture

A model of a famous statue is 3 1/2 inches tall. The actual statue is 5 1/4 feet tall. What is the ratio of the height of the model to the height of the actual statue in simplest form?

Answers

Given:

A model of a famous statue is [tex]3\dfrac{1}{2}[/tex] inches tall. The actual statue is [tex]5\dfrac{1}{4}[/tex] feet tall.

To find:

The the ratio of the height of the model to the height of the actual statue in simplest form.

Solution:

We have,

Height of the model = [tex]3\dfrac{1}{2}[/tex] inches

Height of the actual statue = [tex]5\dfrac{1}{4}[/tex] feet.

Now, the ratio of the height of the model to the height of the actual statue is:

[tex]\text{Ratio}=\dfrac{\text{Height of model}}{\text{Height of actual statue}}[/tex]

[tex]\text{Ratio}=\dfrac{3\dfrac{1}{2}\ in.}{5\dfrac{1}{4}\ ft}[/tex]

[tex]\text{Ratio}=\dfrac{\dfrac{3(2)+1}{2}\ in.}{\dfrac{5(4)+1}{4}\ ft}[/tex]

[tex]\text{Ratio}=\dfrac{\dfrac{7}{2}\ in.}{\dfrac{21}{4}\ ft}[/tex]

We know that 1 ft = 12 in.

[tex]\text{Ratio}=\dfrac{\dfrac{7}{2}\ in.}{\dfrac{21}{4}\times 12\ in.}[/tex]

[tex]\text{Ratio}=\dfrac{\dfrac{7}{2}\ in.}{21\times 3\ in.}[/tex]

[tex]\text{Ratio}=\dfrac{7}{2\times 21\times 3}[/tex]

[tex]\text{Ratio}=\dfrac{1}{2\times 3\times 3}[/tex]

[tex]\text{Ratio}=\dfrac{1}{18}[/tex]

Therefore, the ratio of the height of the model to the height of the actual statue in simplest form is [tex]\dfrac{1}{18}[/tex].

6. A piece of carpet is 240cm long.
Mr Jones cuts it into three pieces in the ratio 1 : 2 : 5
Work out the length of the longest piece of carpet.

Answers

Answer:

150 cm.

Step-by-step explanation:

The number of parts = 1 + 2 + 5 = 8 so:

the largest part = 5/8 * 240

= 5 * 30

= 150 cm.

y=2x2+3 is this a linear or nonlinear function

Answers

Answer:

y=7

Step-by-step explanation:

2x2=4 +3 =7 y

Answer
Nonlinear
Explanation
When you graph the equation there is not a constant slope and is curved so therefore it’s is nonlinear

Rob is saving to buy a new MP3 player. For every $11 he earns babysitting, he save $5. On Saturday, Rob earned $33 babysitting. How much money did he save?

Answers

Answer:

15

Step-by-step explanation:

if every $11 dollars he save $5, and sense he made $33 ( he done three babysitting)

11-5= 5 (does that three times) [5+5+5} when you add the three five , u should have 15 dollars.

so he save 15 dollars.

i don't understand this! can someone help me

Answers

Answer:

oh dang i hated doing these when i was in sixth grade lol umm  55?????

Step-by-step explanation:

use equivalent expression 20a+18+16a

Answers

Answer:

36a+18

Step-by-step explanation:

20a+16a=36a

18 does not have a "like term", so just leave it.

Write an equation, in standard form, using the following given info: M = 10
and it passes through the point (6,2) *
-10x + y = -58
-10x + y = 58. -10x - y = -58
10x + y = -58

Answers

Given:

m = 10

The line passes through the point (6,2).

To find:

The equation of line in the standard form.

Solution:

If a line passes through the point [tex](x_1,y_1)[/tex] with slope m, then the equation of line is

[tex]y-y_1=m(x-x_1)[/tex]

The line passes through the point (6,2) and m = 10. So, the equation of line is

[tex]y-2=10(x-6)[/tex]

[tex]y-2=10x-60[/tex]

[tex]y-10x=-60+2[/tex]

[tex]-10x+y=-58[/tex]

Therefore, the correct option is A.

-2x - y = 1
-6x=3y+3


Answers

Answer: All Real Number

Step-by-step explanation:

This is a system of equation, and generally, there are three ways to solve:

eliminationsubstitutionaugmented matrix

Here, we are going to use elimination

------------------------------------------------------------------------------------

Given

-2x-y=1

-6x=3y+3

Put them in the same order

-2x-y=1

-6x-3y=3

Multiply 3 on both sides for the first equation

-6x-3y=3

-6x-3y=3

We subtract the first equation from the second equation

0=0

The answer will be All Real Numbers, which means any real number will fit this equation. In the graphing method, these two equations will overlap each other.

Hope this helps!! :)

Please let me know if you have any questions

Factor the expression
27 - 9x + 15y

Answers

Simple,

factor out a 3...

3(9-3x+5y)

Thus, your answer

Answer:

-3(3x-5y-9)

Step-by-step explanation:

Consider sample data with x = 12 and s = 3. (a) Compute the coefficient of variation. % (b) Compute a 75% Chebyshev interval around the sample mean. Lower Limit Upper Limit

Answers

Answer: a) 25%

b) 75% Chebyshev interval around the sample mean=(6,18)

Step-by-step explanation:

Given: Sample mean: [tex]\overline{x}=12[/tex]

Sample standard deviation: s= 3

a) Coefficient of variation = [tex]\dfrac{s}{\overline{x}}\times100[/tex]

[tex]\\\\=\dfrac{3}{12}\times100\%=\dfrac{100\%}{4}\\\\=25\%[/tex]

b) According to the Chebychev's theorem,

75% of the population lies within 2 standard deviations from the sample mean.

i.e. 75% Chebyshev interval around the sample mean. = [tex](\overline{x}-2s,\ \overline{x}+2s)[/tex]

[tex]=(12-2(3),\ 12+2(3))\\\\=(6, 18)[/tex]

Hence, the 75% Chebyshev interval around the sample mean=(6,18)

yesterday the temperature was 7 degrees fahrenheit . Today the temperature is 0 degrees fahrenheit . What was the change in the temperature from yesterday to today?

Answers

Answer:

-7

Step-by-step explanation:

HOPE THIS HELPS

7+
2-
3+
3-
-
7+
1-
4

Answers

Answer:-15

Step-by-step explanation:

Answer:

umm... thirteen....

13

(3) need help plz Asap

Answers

Answer:

brainlist plzz

Step-by-step explanation:

D....................................

911÷406 con operaciones​

Answers

Answer:

2.24384236453

Step-by-step explanation:

division/división

Answer:

Step-by-step explanation:

2.24384236453 divicion y divicion

5x+3y-z-4x-3y-z help please ​

Answers

The simplified version of this x-2z

Step-by-step explanation:

You need to start by combining like terms. You can start with the terms that have the variable x in them. By combining those terms, the equation becomes x+3y-z-3y-z.

From here, you can combine the terms 3y and -3y, which bring the equation to x-z-z.

From here, combine the terms with the variable z. This would bring the equation down too x-2z, your final answer.

How many terms are in this expression? d + 8c + 7 ​

Answers

Answer:

2

Step-by-step explanation:

⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️

Answers

Answer: lol why so expensive.

Consider the function p(t) show.identify the intervals on which the function appears to be in increasing

Answers

Answer:A

Step-by-step explanation:

Function 1 is defined by the equation p= --3/2r - 5. function 2 is defined by the following table. Which function has a greater y-intercept. A: Function 1 B: Function 2 C: The functions have the same y-intercept.

Answers

0-5. Here’s your answer

The y-intercept of function  1 is -5.

The y-intercept of function 2 is -5.

Option C is the correct answer.

What is a function?

function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Consider the function to be in the form of p = mr + c

Where x is the y-intercept.

Function 1.

p = (-3/2)r - 5 _______(1)
y-intercept = -5

Function 2.
Let p = mr + c

Take two pairs from the table.

(0, -5) and (1, -6.5)

m = (-6.5 + 5) / (1 - 0) = -1.5

(0, -5) = (r, p)

-5 = -1.5 x 0 + c

c = -5

Now,

p = -5x - 5 ______(2)

y-intercept = -5

From (1 ) and (2)

Both have the same y-intercept.

Thus,

Function 1 and Function 2 have the same y-intercept.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ2

what is the answer to 1/2d+6

Answers

Answer:

Step-by-step explanation:

What you gave, is an expression. There is no answer. The only thing that can be done is factor out the 1/2

[tex]\frac{1}{2}(d+12)[/tex]

Please I don’t understand I need help thank you

Answers

Answer:

Step-by-step explanation:

Is there anybody here good at medical terminology??? pls I need help on one of my questions.

Answers

Answer:

I could try.

Step-by-step explanation:

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