given the function h(x)=x^2-9x+18, determine the average rate of change of the function over the interval 4<_ x <_ 11

Answers

Answer 1

To calculate average rate of change of a function f(x) over an interval between 2 points (a. f(a)) and (b, f(b)) is given by

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

The given function is [tex]h(x)= x^{2} -9x+18[/tex]

and the given interval is [tex]4\leq x\leq 11[/tex]

Now, h(b) = h(11) = [tex](11)^{2} -9(11)+18[/tex]

= [tex]121-99+18[/tex]

= [tex]40[/tex]

h(a) = h(4) = [tex](4)^{2} -9(4)+18[/tex]

= [tex]16 -36+18[/tex]

= [tex]-2[/tex]

The average rate of change between (4, -2) and (11, 40) is

= [tex]\frac{40-(-2)}{11-4}[/tex]

= [tex]\frac{40+2}{11-4}[/tex]

= [tex]\frac{42}{7}[/tex]

= [tex]42[/tex]

∴ The average rate of change between (4, -2) and (11, 40) is 42

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Related Questions

40, 24, 72/5
Find the 10th term

Answers

Answer:

0.24186

Step-by-step explanation:

40 x (3/5) = 24

24 x (3/5) = 72/5 or 14.4

Keep multiplying 3/5 or 0.6

= 0.24186

0.24186 is going to be your answer.

PLS HELP 50 PTS AND BRAINLY

Answers

Answer: Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(13×55)+(25×33)=?

Complete the multiplication and the equation becomes

515+615=?

The two fractions now have like denominators so you can add the numerators.

Then:

5+615=11/15

This fraction cannot be reduced.

Therefore:

13+25=11/15

Step-by-step explanation: hope this helps!!!!

Answer:The answer would be 11/15 mile

Step-by-step explanation:

the perimeter of a one rectangular deck is 78 feet. the length of deck can be represented as (2x 3), and its width can be represented as (3x-4). the perimeter of a second rectangular deck is 2 times the perimeter of the first deck with a length of (4x 6) and a width of (6x -1). what is the value of x of the first rectangular deck?

Answers

The value of x of the first rectangular deck is 8.

For given question,

The perimeter of a one rectangular deck is 78 feet.

The length of the first rectangular deck is  represented as (2x + 3), and its width is represented as (3x-4).

Similarly, the perimeter of a second rectangular deck is 2 times the perimeter of the first deck with a length of (4x + 6) and a width of (6x -1).

We need to find the value of x of the first rectangular deck.

Let P1 be the perimeter of the first rectangular deck.

⇒ P1 = 2 × (length + width)

⇒ 78 = 2 × [(2x + 3) + (3x - 4)]

⇒ 39 = (2x + 3x + 3 - 4)

⇒ 39 = 5x - 1

⇒ 40 = 5x

⇒ x = 40/5

⇒ x = 8

Therefore, the value of x of the first rectangular deck is 8.

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i need help if you help me it will be much helpfull thank you

Answers

Answer:

Step-by-step explanation:

Answer is D

509

-106

403

4 hundred and 3 ones

Simplify
(7y+4)(8y+2)

Answers

Answer:

56y^2+46y+8

Explanation:

Hope this helps you.

I dont know why i dont get it

Answers

Answer:

12 miles+14 miles+18 miles+12 miles+15 miles= 71 miles.    

Step-by-step explanation:

Give the full question next time alright?

A college baseball stadium has 6,925 seats. During 12 games this season, the stadium sells out and fills every seat.

How many tickets were sold for those 12 games?

Answers

The number of tickets sold during the 12 games is 83,100 tickets

How to calculate the number of tickets sold ?

The college stadium has 6,925 seats for the baseball games this season.

During the entire 12 baseball games, al the seats were filled up and tickets were sold out.

Therefore the number of tickets sold in the entire 12 games can be calculated by multiplying  6,925 by 12

= 6925 × 12

= 83,100

Hence 83,100 tickets were sold in the entire 12 games

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The latitude of the U.S. Embassy is 48° north of the equator. If the diameter of the earth is 7920 miles, how far is the U.S.
Embassy from the equator?

Answers

Answer:

use air math personal tutors to help you and help you show your work!

Step-by-step explanation:

If n+ 2 is divisible by 2 then which statement is always True?
A- n is an even number
B - n is an odd number
C- n is a prime number
D- b is equal to n + 1.

Answers

Answer:

the right answer is A

Step-by-step explanation:

the even number can be always divided by 1,2 and themselves

What is the missing value of 2/5 equals how many 15th

Answers

The number of fifteenths which are contained in 2/5 as required to be evaluated in the task content is; 6.

What is the number of fifteenths which are present in 2/5 as required in the task content?

It follows from the task content that the number of fifteenths which are contained in 2/5 as required is to be computed.

Given;

2/5.

To find;

How many fifteenths?

Hence, the number of fifteenths in 2/5 as required can be evaluated as follows;

2/5 ÷ 1/15

= 2/5 × 15/1

Multiply the numerators and denominators accordingly;

= 30/5

= 6.

Ultimately, the number of fifteenths in 2/5 is; 6.

Therefore, The number of fifteenths which are contained in 2/5 as required to be evaluated in the task content is; 6.

This concept follows from the division of fractions as in arithmetic operations.

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4x - 2x + x - 6 = 15
solve for x and show steps!​

Answers

Answer:

x = 7

Step-by-step explanation:

Let's solve the problem,

→ 4x - 2x + x - 6 = 15

→ 3x - 6 = 15

→ 3x = 15 + 6

→ x = 21/3

→ [ x = 7 ]

Thus, the value of x is 7.

Bro please help ima fail

Answers

In the picture there are 10 question.

1. Identify the 1st 10 perfect squares?

The 1st 10 perfect squares are 1,4,9,16,25,36,49,64,81 and 100.

[tex]1^{2} =1\\2^{2} =4\\3^{2} =9\\4^{2} =16\\5^{2} =25\\6^{2} =36\\7^{2} =49\\8^{2} =64\\9^{2} =81\\10^{2} =100\\[/tex]

2. What does it mean for a number to a perfect square? provide an example.

By squaring a whole number or an integer, one can create perfect squares. Let's examine an illustration to get the idea behind perfect squares. We can use a set of four and a second set of six marbles for this. Let's set the marbles in order.

See the figure(1).

With four marbles, we can create a square with two rows and two marbles in each row. We can create a rectangle with 6 marbles that has 2 rows with 3 marbles in each row. It signifies that 4 = 2[tex]\times[/tex]2 and 6 = 3[tex]\times[/tex]2 mathematically. Let's concentrate just on the square-shaped numerals. Here, 4 = 2 × 2 = [tex]2^{2}[/tex].

Square A is smaller then Square B. Square B is smaller then Square C.

The 3 Square side length are3,4.2 and[tex]5\frac{1}{2}[/tex].

complete the equation each of the square shown.

3. Square A=Area=[tex]3^{2}[/tex]=9

4. Square B= Area=[tex]4.2^{2}[/tex]=17.64

5. Square C=Area= [tex]\frac{5}{2} =\frac{25}{4}[/tex]

Find the length of the side of the square for each area is given

6.81 square inches

Area=81=[tex]s^{2}[/tex]

s=9

7. [tex]\frac{4}{25} cm[/tex]

area=[tex]\frac{4}{25} cm[/tex]=[tex]s^{2}[/tex]

s=[tex]\frac{2}{5}[/tex]

8.0.49 Square unit

area=0.49=[tex]s^{2}[/tex]

s=0.7

The graph represent the equation [tex]y=x^{2}[/tex].

9.complete the table of values to find corresponding y-values.

if x =-1.4

Substituting in the equation [tex]y=x^{2}[/tex]

Then y=[tex]-1.4^{2}[/tex]

y=1.96.

Therefore, (x,y)=(-1.4,1.96)

if x =-1

Substituting in the equation [tex]y=x^{2}[/tex]

Then y=[tex]-1^{2}[/tex]

y=1.

Therefore, (x,y)=(-1,1)

if x =0

Substituting in the equation [tex]y=x^{2}[/tex]

Then y=[tex]0^{2}[/tex]

y=0.

Therefore, (x,y)=(0,0)

if x =[tex]\frac{2}{5}[/tex]

Substituting in the equation [tex]y=x^{2}[/tex]

Then y=[tex](\frac{2}{5}) ^{2}[/tex]

y=[tex]\frac{4}{25}[/tex].

Therefore, (x,y)=([tex]\frac{2}{5}[/tex],[tex]\frac{4}{25}[/tex])

if x =2

Substituting in the equation [tex]y=x^{2}[/tex]

Then y=[tex]2^{2}[/tex]

y=4.

Therefore, (x,y)=(2,4)

10. why the graph of equation  [tex]y=x^{2}[/tex] is above x-axis.

Because the [tex]y=x^{2}\\[/tex] the x values are always positive because x as a square. So, the equation is always on x- axis or above x-axis.

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____ is the vertical distance between two or more lines or surfaces (part features) that are in horizontal planes.

Answers

Height  is the vertical distance between two or more lines or surfaces (part features) that are in horizontal planes.

What are horizontal planes?

Horizontal plane can as well be described as the plane or surface  that can be seen as the one that is parallel to the surface of the earth,  , it should be noted that this  plane is usually at the  at an angle of zero degree hence  horizontal plane.

Therefore, the plane  is perpendicular to the horizontal plane , hence Height  is the vertical distance between two or more lines or surfaces (part features) that are in horizontal planes.

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If one book is 2.5 inches wide and another is 1.754 inches wide, how much wider is the first?

Answers

the answer is 0.746. hope i answered in time

How do you divide 8 out of 5

Answers

Answer:

if you mean 8 divided by 5 then use long division which will result in 1 with a remainder or 3 or 1.6

Answer:

8/5=1.6

Step-by-step explanation:

There's no step by step for explaining this answer. Or nothing that I can think of

Nine less then a number is four

Answers

Answer: 13 (simplified)

Step-by-step explanation: 9 + 4= 13, minus 9  equals 4

Answer: Question: x-9=4

Step-by-step explanation: X is 13

Please help it would be very much helpul

Answers

x = 12.

Perpendicular lines are lines that intersect at a 90-degree angle. So, for example, line ST is perpendicular to line CD. So line ST is perpendicular to line CD.

Perpendicular lines always intersect each other, however, all intersecting lines are not always perpendicular to each other. The two main properties of perpendicular lines are: Perpendicular lines always meet or intersect each other. The angle between any two perpendicular lines is always equal to 90.

Given that

line m and n are perpendiculars

then angle ∠a = ∠b

then

5x + 20 = 7x -4

7x -5x = 20 + 4

2x = 24

x = 24/ 2

x = 12.

Hence the value of x = 12

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Paper weighs 4.9 kg for every 500 sheets, how much will 700 sheets weigh?

Answers

Answer:

6.86 kg

Step-by-step explanation:

Here ,apparently the weight and number of sheets are proportional.

Let m be the weight of 700 sheets.

[tex]\text{} \begin{matrix}500\ \text{sheets} \text{} \longrightarrow 4.9\ \text{kg} \\ 700\ \text{sheets} \text{} \longrightarrow m\ \text{kg} \end{matrix}[/tex]

coefficient of proportionality :

[tex]\text{} \text{The coefficient of proportionality is equal to :} \ \frac{700}{500} =\frac{7}{5}[/tex]

Then

[tex]\frac{m}{4.9} = \frac{7}{5}[/tex]

Then

[tex]m = \frac{7}{5} \times 4.9 =6.86 \ \text{kg}[/tex]

Evaluate v-w for the given values. v = -14; w = 7

Answers

Answer:

I believe the answer would be :

-14 - 7 = -21

Answer = -21

Marcy walked 3 7/10 miles on Saturday and Sunday she walked 0.25 more miles than she did on Saturday how many total miles did she walk over the weekend. Pls.



Help




It’s math



B

Answers

Over the weekend she walked a total distance of (4 + 5/8) miles

How many total miles did she walk over the weekend?

We know that on Saturday she walked a total of (3 + 7/10) miles (so we need to work with mixed numbers), and on Sunday she walked 0.25 of that distance.

Then the  distance that she walked on Sunday is:

D = 0.25*(3 + 7/10) miles

We can rewrite: 0.25 = 1/4

replacing that:

D = (1/4)*(3 + 7/10) mi = (3/4 + 7/40) mi

   = (30/40 + 7/40)mi = (37/40)mi

Then the total distance that she walked over the weekend is:

d = (3 + 7/10) mi +  (37/40)mi

  = (120/40 + 28/40) mi + (37/40) mi

  = (185/40)mi = (160/40 + 25/40) mi = (4  + 5/8) mi

Over the weekend she walked a total distance of (4 + 5/8) miles

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At his last track meet, kenneth ran the 400-meter dash in 54 seconds. his friend madelyn bet him that he couldn't run a whole kilometer at that pace, but kenneth is determined to prove her wrong. how many minutes would he have to run at this pace to win the bet? write your answer as a whole number, decimal, or simplified fraction. do not round.

Answers

Kenneth will have to run 2.25 minutes at the same speed to win the bet.

What is Speed?

Speed is the rate of movement of an object along a path in time.

=> [tex]Speed =\frac{Distance}{Time}[/tex]

Now,

Given:

Kenneth ran 400m in 54s.

To find: Number of minutes to maintain the speed to win the bet.

Finding:

According to the information given in the question,

The speed in minutes = [tex]\frac{400}{54}(60)[/tex] = 444.44 meter/min

Since Kenneth is determined to run at this speed for 1 km, he will have to maintain it for:

=> [tex]\frac{1000}{444.44}[/tex] = 2.25 minutes (As [tex]Speed =\frac{Distance}{Time}[/tex], => [tex]Time=\frac{Distance}{Speed}[/tex])

Hence, Kenneth will have to run 2.25 minutes at the same speed to win the bet.

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Five ounces of pretzels are put into each bag. How many bags can be made from 20 pounds of pretzels?

Answers

Each pound has 16 ounces in it.

20 pounds would be 16 x 20 ounces = 320 ounces.

If each bag has 5 ounces in it, that's 320 / 5 bags = 64 bags.

Pls give brainliest.

is -2/7 rational or irrational

Answers

Answer:

rational

Step-by-step explanation:

Rational numbers are able to be denoted as a ratio. -2/7 is a ratio, so it is rational.

Find an equation of the plane through(1,1,1) that contains the linere presented by the parametric equationsx= 2t;y= 1t;z= 2 3t:

Answers

To calculate the equation of the plane from the given information which is as follows:

The plane contains the line that is [tex]x = 2t; y = 1t; z =2-3t[/tex] which are passing through [tex](1,1,1).[/tex]

The standard formula for the equation of the plane is: [tex]a(x-x(0))+b(y-y(0))+c(z-z(0))=0.[/tex]

And the equation of the line is: [tex]\frac{(x-x(0))}{a} = \frac{(y-y(0))}{b} = \frac{(z-z(0))}{c}[/tex]

As per the given data, the value of [tex]a = b = c = 1.[/tex]

And when[tex]t=0: x=0;y=0;z=2[/tex]

Now, the final expression can be rewritten as: [tex]x=y=z-2[/tex]

And the equation of the line can be rewritten as:

[tex](x)+(y)+(z-2)=0.[/tex]

[tex]x+y+z-2 = 0[/tex]

What is the equation of the line?

To represent the set of points in an algebraic form is known as the equation of line. The set of points represent lines in the coordinate system. The parameters can be calculated and those parameters are slope and y-intercept.

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what is the value of x of triangle srq?

Answers

The value of "x" in the given figure and question is 20 units.

As per the question statement, We are given a figure in which we are supposed to find the value of x.

Before solving the question, if we observe the figure, we can conclude that this question will include the concepts of right angled triangle or specifically Pythagoras Theorem, which states that

[tex]Perpendicular^{2} + base^{2} = hypotenuse^{2}[/tex] where perpendicular, base and hypotenuse are the three sides of the right angled triangle.

In Triangle RTQ

using Pythagoras Theorem

[tex]RQ^{2} = TQ^{2} +TR^{2} \\RQ=x\\x^{2} = 16^{2} + TR^{2} \\TR^{2} = x^{2} -16^{2}[/tex]

Now considering triangle SRT

using Pythagoras Theorem

[tex]SR^{2} = RT^{2} + ST^{2} \\SR^{2} = (x^{2} -16^{2}) +9^{2}\\[/tex]

Now considering triangle RSQ

using Pythagoras Theorem

[tex]SQ^{2} = SR^{2} +RQ^{2} \\(9+16)^{2} = SR^{2} + RQ^{2} \\(9+16)^{2} = x^{2} -7^{2}+x^{2} \\ (9+16)^{2} =2x^{2} -7^{2} \\25^{2}+7^{2} = 2x^{2}[/tex]

[tex]2x^{2} =674[/tex]

[tex]x^{2} =337\\x=\sqrt{337} \\x=18.357[/tex]

Therefore x = 18.357 approx 20 units.

Pythagoras Theorem: The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs.

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Find the range of the data set: 10,18, 21, 28, 12, 20

Answers

Answer: 18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

The range is the greatest number minus the number with the least value.

28 - 10 = 18

Write an equation of the line and interpret the slope and y intercept (Will award brainiest answer)

Answers

Answer:

y=mx+by=mx+bm=slope(x,y)=a point on the lineb=the y value of the y-interceptm=slope(x,y)=a point on the lineb=the y value of the y-intercept

Step-by-step explanation:

an online shoe brand ran two conversion lift studies. test 1 resulted in the control group showing a 20% conversion rate while the test group showed a 25% conversion rate. the results were significant at 60%. test 2 resulted in a 20% conversion rate in the control group while the test group showed a 30% conversion rate. these results were 95% significant.

Answers

To boost their incremental ROAS, the marketing team plans to increase reach as much as feasible.

What is market science?

Using data to support decision-making objectively is central to marketing as a science. Knowing how to analyze data and spotting typical mistakes or misrepresentations in interpretations are key.

The analyst conclude -

Test 2's results were more trustworthy than Test 1's because Test 2 demonstrated a 10% difference in lift between the test and control groups and was conducted with a higher confidence level.When conducting randomized control trials utilizing their ads, an e-commerce company wants to know how reach affects the incremental ROAS outcomes.To compare reach and ROAS for each campaign ran in the previous year, the company compiles data on past campaign performance and builds a scatterplot. Over the past year, they have made numerous changes to their marketing strategy, including changes to targeting, bidding tactics, and optimization measures. To boost their incremental ROAS, the marketing team plans to increase reach as much as feasible.

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Analizeaza urmatoarele verbe mentionand persoana si numarul! a plecat,vei ajunge,sa mearga

Answers

Answer: I dont understand what your saying

Step-by-step explanation:

Are you speaking a diffrent language

Answer:

in English: let,will,arrive,let,go

in Romanian: lasa, va, sosi, lasa, pleca

Step-by-step explanation:

I think the language is Romanian

If lines a and b are perpendicular to line c, what word best describes how lines a and b relate to each other?
A.intersecting
B. Parallel
C. Perpendicular
D. Skew

Answers

answer:

C. Perpendicular

explanation:

perpendicular is defined as intersecting to create 90 degree angles on all four created angles.

if both lines a and b are perpendicular to line c, then they must be parallel.

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