Given the function f(x) = x^2-6x+4, determine the average rate of change of the function over the interval 1≤x≤4.

Answers

Answer 1

Answer:

The average rate of change of f(x) over the interval 1 ≤ x ≤ 4 is -1.

Step-by-step explanation:

We are given the function:

[tex]f(x)=x^2-6x+4[/tex]

And we want to determine its average rate of change over the interval:

[tex]1\leq x\leq 4[/tex]

The average rate of change is synonymous with the slope. So, to find the average rate of change, we simply need to find the slope between the two endpoints.

Evaluate each endpoint:

[tex]f(1)=(1)^2-6(1)+4=-1[/tex]

[tex]f(4)=(4)^2-6(4)+4=-4[/tex]

So, our endpoints are (1, -1) and (4, -4).

The slope between them is:

[tex]\displaystyle m=\frac{(-4)-(-1)}{(4)-(1)}=\frac{-3}{3}=-1[/tex]

So, the average rate of change of f(x) over the interval 1 ≤ x ≤ 4 is -1.


Related Questions

help? could someone help me with this?

Answers

Answer:

A, C, And F

Step-by-step explanation:

HEEEEELLLPPPPPPP!!!!!!!!!!!!!

Answers

Answer:

E. b + u = 21

Step-by-step explanation:

b = (bicycles)

u = (unicycles)

The Question gives you the answer.

" the number of bicycles plus the number of unicycles is 21"

*put as an equation*

b + u = 21

<3 Enjoy,

    Dea

Add 6/7 + 80/9. Enter your answer below as an improper fraction in lowest terms, using the slash (/) as the fraction bar.​

Answers

Answer:

the answer is 614/63

Step-by-step explanation:

6/7 + 80/9

614/63

4x and -4x
Like or
Unlike

Answers

Answer:

unlike

Step-by-step explanation:

Which expression simplifies to 5v3?

Answers

Answer:

D.

Step-by-step explanation:

Answer:

D. V15

Step-by-step explanation:

Babatunde draws a drinking glass on graph paper using the scale shown below. The glass has a length of 888 units in the drawing.
A drinking glass on graph paper. An 8-unit long line is labeled, "height." A 2-unit long scale is labeled, "2.5 centimeters."

Answers

Answer:

Hum ty

Step-by-step explanation:

It’s 65

Solve for
32 + 2 = 73 – 1

Answers

Answer:

34 < 72

Step-by-step explanation:

32 + 2 = 73 - 1

34 = 73 - 1

34 = 72

Help me plssss I rlly need the answer to this

Answers

149___________________
72 degrees
Step by step explanation : 103-31=72

hi! please help. thank you!

Answers

Answer:

Step 6 is done by Additive Property of Equality, also known as Compatibility of Equality with Addition, which is defined by the following expression:

[tex]a = b \to a + c = b + c[/tex], [tex]\forall\,a,b, c\,\in \,\mathbb{R}[/tex]

Step-by-step explanation:

Step 6 is done by Additive Property of Equality, also known as Compatibility of Equality with Addition, which is defined by the following expression:

[tex]a = b \to a + c = b + c[/tex], [tex]\forall\,a,b, c\,\in \,\mathbb{R}[/tex]

1) [tex](7\cdot x - 3) + 3 = (2\cdot x + 7) + 3[/tex] Associative property/Compatibility with addition

2) [tex]7\cdot x + [3 + (-3)] = 2\cdot x + (7 + 3)[/tex] Associative and commutative properties/Definition of subtraction

3) [tex]7\cdot x + 0 = 2\cdot x + 10[/tex] Existence of the additive inverse/Definition of addition

4) [tex]7\cdot x = 2\cdot x + 10[/tex] Modulative property/Result

i have a geometry question.

Answers

Answer:

Step-by-step explanation:

You already have the area for your triangle. Substract that from the entire area of the rectangle.

To get the area of the rectangle, multiply the length by the height.

15*20 = 300

Now substract your triangle from that :)

Jordan wants to split up his socks and shoes into groups. If he has 6 pairs of shoes and 14 pairs of socks, how many groups must he create so he has an equal number of pairs of shoes and pairs of socks?

Answers

Answer:

i amm not sure

Step-by-step explanation:

The number of groups Jordan must create so he has an equal number of pairs of shoes and pairs of socks is 2.

What is HCF?

The highest common factor (HCF) is discovered by identifying all common factors of two integers and then picking the greatest one. For example, the common factors of 8 and 12 are 1, 2, and 4. The greatest common factor is four.

Jordan wants to split up his socks and shoes into groups. If he has 6 pairs of shoes and 14 pairs of socks. Therefore, she can divide the pair of socks and shoes only into groups of 2, because two is the HCF of 6 and 14.

Hence, the number of groups Jordan must create so he has an equal number of pairs of shoes and pairs of socks is 2.

Learn more about HCF:

https://brainly.com/question/17240111

#SPJ2

PLSSS HELP MEEE I WILL GIVE BRAINLIEST

Answers

Answer: A

Step-by-step explanation:

Need help with math!! Provided the graph with answers

Answers

I think the first one c and the second one a

please help me I only have 2 minutes left winner gets brainliest is 1 + (8r+9) and (2+8) + 8r equivalent

Answers

Answer:

Yes, this is equivalent.

Hope this helps!

I want to d!e ahahahahahaha

Answers

Answer:

dont say that-

Step-by-step explanation:

30 in.
10 in.
10 in.
30 in
20 in
Find the area of the arrow above.
square inches

Answers

Answer:

1100 Inches Squared

Step-by-step explanation:

Let the triangle on the top right be - (i)

Let the triangle on the top left be - (ii)

Let the bottom rectangle be - (iii)

1) The base of the triangle (i) = 10 + (20/2) (It is the base of the rectangle halfed + the given amount of half base of the triangle)

=> 10 + 10

=> 20 in

Base = 20 in

Height = 30 in

Area = 1/2 * 20 * 30

=> 10 * 30

=> 300 in

Triangle (i) = (ii)

So, the area of triangle (ii)

=> 300 in

Area of rectangle,

Length * Breadth

=> 20 * 30

=> 500 in

Total arrow's area = 300 + 300 + 500 (i + ii + iii)

=> 1100

Therefore the total area of the shape = 1100 in squared.

Hope it helps :)

A PlayStation 5 originally sells for $499.99. If you can only find them on eBay for $899.99, what is the percent of increase from the original price?

Answers

Answer:

There would be an 80% increase from 499.99 to 899.99.

Solve the following:
There are 500 students in school . 40% of them are boys and rest are girls. What is the percentage of girls? Also find the numbers of boys and girls in the school.​

Answers

Answer:

300 girls, 200 boys

Step-by-step explanation:

To find boys: 500 x 0.4 = 200

To find girls: 500 x 0.6 = 300

60% girls

Find the area of the shaded region

Answers

Answer:

40

Step-by-step explanation:

area of shaded region = area of whole figure - area of non shaded region

area of whole figure: The whole figure is a rectangle

The area of a rectangle can simply be calculated by multiplying the width by the length

The given width is 10ft and the given length is 8ft

Hence area of whole figure = 10 * 8 = 80ft²

Area of non shaded region: the non shaded region also creates a rectangle

Like stated previously the area of a rectangle can simply be calculated by multiplying the width by the length

The given width is 5ft and the given length is 8ft

Hence, area of non shaded region = 5 * 8 = 40ft²

Finally we can find the area of the shaded region.

We can easily do this my subtracting the area of the nonshaded region from the area of the whole figure

If we have identified that the area of the whole figure is 80 and the area of the non shaded region is 40

Then, area of shaded region = 80 - 40 = 40ft²

Can this be done within the hour plz. Ty.

Answers

ya ur can be done within the he

At a surf shop in Malibu, California, a used blue surfboard is on sale for $100. According to the salesperson, the new price represents a 20% discount from the original price. What did it sell for originally?

Answers

Answer:

$125

Step-by-step explanation:

if there was a discount of 20%, the sales price is 100 - 20 = 80% of the original price

let a = original price

this equation can be used to represent the question

a x 0.8 = 100 ]]divide both sides by 0.8

a = 100 / 0.8 = 125

For which of the funds shown would you pay the most commission on the purchase of 100 shares?
a. Green Energy
b. TJH Small-Cap
c. Upton Group
d. WHI Health​

Answers

Answer:

its A just got it right

Step-by-step explanation:

A warehouse has a height of 8 2/10 ​ meters, length of 120 meters, and width of 20 3/10 ​ meters. What is the volume of the warehouse?
pls answer fast, best question gets brainliest

Answers

Answer:

59×695÷500×56677×6626

Please help and add explanation

Answers

Answer:

y=-3x+10

Step-by-step explanation:

Since you know that the equation of the line is perpendicular to 1/3, you have to find the inverse of 1/3. You swap the denominator and numerator and make the number negative. In this case, it will be -3. Now that you know the slope is -3, you can use the equation y-y1=m(x-x1) where m is the slope. We know that the point (2,4) is in the graph so we can plug it into the equation. y-4=m(x-2). We know that the slope is -3 so we can plug it into the equation. y-4=-3(x-2). Simplify this to get y-4=-3x+6. Simplify this to get y=-3x+10. This means that the answer is y=-3x+10.

If this has helped you please mark as brainliest

Help help me please with this no links please

Answers

Answer:

N is perpendicular to M

Step-by-step explanation:

Because N and P are parallel, p is perpendicular to M, N is also perpendicular to M

PLEASE HELP
WILL GIVE BRAINLIEST

Answers

Answer:

Decimal form: 7.25

Mixed Number: 7 1/4

Step-by-step explanation:

9 3/4 = 39/4 (times 9*4 then add 3, keep the denominator).

2 1/2 = 5/2 (times 2*2 then add 1, keep the denominator).

39/4 - 5/2

29/4 (simplify)

ANSWER- 7 1/4

Answer:

7 1/4

Step-by-step explanation:

I learned this in like 5th grade lol.

EASY SYSTEM OF EQUATION

Answers

Answer:

3,7

Step-by-step explanation:

See steps below:)

The answer is (3,7).

find the area of the kite.

A. 27 square units
B. 40 square units
C. 18 square units
D. 36 square units

Answers

Answer:

36 unit^2.

Step-by-step explanation:

The area is the sum of the 2 triangles with each having base between the points (-2,4) and (-2,-4).

The base is4 - -4 = 8.

Area of a triangle = 1/2 * base * height.

Area of the kite = 1/2 * 8 * 3 + 1/2 * 8 * 6

= 12 + 24

= 36.

|(2,9)
J (79)
00 -
H(25)

Answers

Answer:

what  :(

Step-by-step explanation:

NEED HELP ASAP
THIS IS DUE TODAY

Answers

The correct answer is $
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