A function is shown in the table at the right. Find the rate of change over the interval 1≤ x≤ 3 .

A Function Is Shown In The Table At The Right. Find The Rate Of Change Over The Interval 1 X 3 .

Answers

Answer 1

Given:

The table of values of a function.

To find:

The rate of change of the function over the interval [tex]1\leq x\leq 3[/tex].

Solution:

The rate of change of a function over the interval [a,b] is:

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

The rate of change of the given function over the interval [tex]1\leq x\leq 3[/tex] is:

[tex]m=\dfrac{f(3)-f(1)}{3-1}[/tex]

From the given table, it is clear that the value of the function is 4 at [tex]x=1[/tex] and 16 at [tex]x=3[/tex].

[tex]m=\dfrac{16-4}{2}[/tex]

[tex]m=\dfrac{12}{2}[/tex]

[tex]m=6[/tex]

Therefore, the rate of change of the given function over the interval [tex]1\leq x\leq 3[/tex] is 6.


Related Questions

I need help solving both of these 2 I’ve tried asking but nobody knows

Answers

Answer:

Step-by-step explanation:

x/7 - 13 ≥ -11

x/7 ≥ 2

x ≥ 14

m/-6 + 16 ≥ 19

m/-6 ≥ 3

m/6 ≤ -3

m ≤ -18

Answer: -18

Step by step explanation

which system of equations has infinitely many solutions?

a. 4x+2y=5 -4x-2y=1
b. -10x+y=4 10x-y=4
c. -8x+y=2 8x-y=0
d. -x+2y=6 7x-2y=12

Answers

Answer:

None, each of the four given system of equations have only one solution

Step-by-step explanation:

A system of equations have infinitely many solutions, when the equations represent the same line and therefore, the two equations are the same;

Each of the options are examined as follows;

a. 4·x + 2·y = 5...(1)

-4·x - 2·y = 1...(2)

Expressing both equations with y as the subject, we have;

The value of y in equation (1) is given as follows;

4·x + 2·y = 5

2·y = 5 - 4·x

∴ y = 5/2 - 2·x

The value of y in equation (2) is given as follows;

-4·x - 2·y = 1

-2·y = 1 + 4·x

∴ y = -1/2 - 2·x

Therefore, equation (1) and equation (2) represent the same equation and are therefore equal and have only one solution

b. -10·x + y = 4...(1)

10·x - y = 4...(2)

Therefore, we have;

Adding equation (1) to equation (2) gives;

-10·x + 10·x + y - y = 4 + 4

0 + 0 = 8

0 = 8

Given that 0 ≠ 8, equation (1) is not equal to equation (2) and the two equations have only one solution

c. -8·x + y = 2...(1)

8·x - y = 0...(2)

By examination, the values on the left hand side, LHS, of both equations are the same magnitude but opposite in sign, while the right hand side, RHS, of both equations, have different magnitude

Therefore, the two equations are different and have only one solution

d. -x + 2·y = 6...(1)

7·x - 2·y = 12...(2)

Making y the subject of both equations gives;

Equation (1)

2·y = 6 + x

y = 3 + x/2

Equation (2)

2·y = 12 - 7·x

y = 6 - 3.5·x

Therefore, the two equations are different and have only one solution

Answer:

B

Step-by-step explanation:

I'm guessing the answer is B. I know why the other person said all of them only have one solution. But, On b You wrote -10x+y=4  10x-y=4

When really it was supposed to be -10x+y=4  10x-y=-4

how many ways can a person toss a coin 14 times so that tge number of tails is between 7 and 12 inclusive​

Answers

Answer:

8 tails I think so If the answer is correct plz mark me the brainliest

please help to add this exponent:)

Question:
[tex](3.09 \times {10}^{6} ) + (5.83 \times {10}^{8} )[/tex]

Answers

Answer:

[tex]5.8609 \times {10}^{8} [/tex]

Step-by-step explanation:

[tex](3.09 \times 10^6)+(5.83 \times 10^8)[/tex]

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

[tex]5.8609 \times {10}^{8} [/tex]

Hope it is helpful...

Find the direct variation equation

Answers

Answers:

The direct variation equation is y = 5xIf x = 4, then y = 20

=================================================

Explanation:

Let's say that the letter k replaces the green box

We have the equation y = kx

Plug in (x,y) = (7,35) to get the equation 35 = k*7

Dividing both sides by 7 leads to k = 5

Therefore, the direct variation equation is y = 5x

We can check this by plugging in x = 7

y = 5x

y = 5*7

y = 35

So x = 7 leads to y = 35 as expected.

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

Do the same for x = 4

y = 5x

y = 5*4

y = 20 when x = 4

Side note: direct variation equations always go through the origin.

Answer:

20

Step-by-step explanation:

if y varies directly with x, then it takes the form y=mx

to find m, substitute in the values of x and y to get 35=m*7 and simplify to get that m=5

then the equation becomes y=5x

substitute in the value they gave for x which is 4 to get y=5*4

to get that y=20

is the relationship shown by the data linear? if so, model the data with an equation.​

Answers

Answer:

The relationship is not linear.

Hope this answer is right!!

John has 12 tissues, but they caught on fire, because his older brothers a pyromaniac.
So John has to eat his boogers. He has to do it precisely, without accidentally scratching his nose and bleeding, so he has to go slow.
How long does it take for him to eat his boogers? Sometimes, he has a friend join him, and they eat their own boogers in each others presence. How long would that take?

A. 12 minutes.
B. 20 Minutes for each person.
C. An Hour.
D All day.

Answers

Answer:

Dude wt,f? The answer is B. Obviously.

Step-by-step explanation:

COMMON SENSE

It would mean the world to me if some one can answer both questions 1 and 2 please help

Answers

Answer:

the answer to both are 1. 3.77 2.19.94

A
2
The distance AB
rounded to the
nearest tenth = [?]
-1
0
2
2
-
Hint: Use the distance formula:
d= (x2 – x1)2 + (72- y)2
Enter

Answers

Answer:

ssueuwuwiaiwaiaiiaiw

Help and explain pleaseeeeeeeee

Answers

Given:

The function is:

[tex]f(x)=\{(1,0),(2,3),(3,6)\}[/tex]

The given function is:

[tex]f(x)=1-2x[/tex]

The range of this function is [tex]\{-3,-5,-7\}[/tex].

To find:

The range of first function.

The domain of second function.

Solution:

Domain is the set of input or x-values and range is the set of output or y-values.

We have,

[tex]f(x)=\{(1,0),(2,3),(3,6)\}[/tex]

Here, the x-values are 1, 2, 3 and the y-values are 0, 3, 6.

Therefore, the range of the given function is [tex]\{0, 3, 6\}[/tex]. Hence, the correct option is C.

The given function is:

[tex]f(x)=1-2x[/tex]            ...(i)

The range of this function is [tex]\{-3,-5,-7\}[/tex].

Putting [tex]f(x)=-3[/tex] in (i), we get

[tex]-3=1-2x[/tex]

[tex]-3-1=-2x[/tex]

[tex]\dfrac{-4}{-2}=x[/tex]

[tex]2=x[/tex]

Similarly,

Putting [tex]f(x)=-5[/tex] in (i), we get

[tex]-5=1-2x[/tex]

[tex]3=x[/tex]

Putting [tex]f(x)=-7[/tex] in (i), we get

[tex]-7=1-2x[/tex]

[tex]4=x[/tex]

The domain of this function is [tex]\{2,3,4\}[/tex]. Hence, the correct option is A.

Name the marked angle in 2 different ways.

Answers

Answer:

angle TVU

Step-by-step explanation:

angle UVT

please mark as brainliest

Bianca read 5 books last month. The number of pages in each book that bianca read is listed in the box below12,106,94,100,180 what is the mean absolute deviataion of the number of pages in the 5 books bianca read?

Answers

Answer:

36.32

Step-by-step explanation:

Given the data:

X = 12,106,94,100,180

The mean absolute deviation is calculated thus :

MAD = |x - mean| / n

Where n = sample size

Mean = Σx / n = (12 + 106 + 94 + 100+ 180) / 5 = 98.4

MAD = (|12 - 98.4| + |106 - 98.4| + |94 - 98.4| + |100 - 98.4| + |180 - 98.4|) / 5

MAD = 36.32

While she was on holiday,Olga measured the temperature at the same time every day. Here are the results. Work out the median: The range of the temperatures

Answers

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the required data are not given.

I will use the following data as an illustration of how to calculate median and range.

We have:

[tex]x: 11, 13, 14, 15, 18, 20[/tex]

Calculate range

Identify the highest and the least

[tex]Highest = 20[/tex]

[tex]Least = 11[/tex]

So, the range is:

[tex]Range = Highest -Least[/tex]

[tex]Range =20-11[/tex]

[tex]Range =9[/tex]

Calculate the median

The number of data we are using is 6 (i.e. even).

So, the position of the median item is:

[tex]Median =\frac{1}{2}(n+1)[/tex]

[tex]Median =\frac{1}{2}(6+1)[/tex]

[tex]Median =\frac{1}{2}*7[/tex]

[tex]Median =3.5th[/tex]

A decimal result implies that the median is the mean of the integer values before and after the result.

In this case, the median is the mean of the item at 3rd and 4th positions.

So:

[tex]Median = \frac{14+15}{2}[/tex]

[tex]Median = \frac{29}{2}[/tex]

[tex]Median = 14.5[/tex]


7. Mandy has a total of 150 nickels and
dimes, which amount to $12. How
many
of each coin does she have?

Answers

Answer:

100 dimes and 50 nickels

Step-by-step explanation:

5×50=2.00

10×100=10.00

This is my question,i hope anyone can help me

Answers

Step-by-step explanation:

a) fg(x) = f(x²-1) = 2(x²-1) + 3

= 2x² + 1

b) gf(x) = (2x+3)² - 1

= 4x² + 12x + 9 - 1

= 4x² + 12x + 8

c) fg(2) replace the value in a)

fg(2) = 2(2²) + 1

= 9

3
If x=
)
X Х
find the value of x-2
3
2.​

Answers

Step-by-step explanation:

Answer

Open in answr app

Correct option is

B

±2

x=3+22   x1=3+221×3−223−22

=3−22

(x−21)2=x+x1−2

=3+22+3−22−2=4

So, x−x1=4=±2 Ans 

The work in an office takes 150 hours to complete every week. Each person in the office works for 32 hours a week

Answers

what’s the question? you’re just stating that the work takes 150 hours to complete every week and that each person works 32 hours a week.

mich inequalities are true?
√5 <2.3 < 56
√5 <2.4 < 56
74 < 5 5.5
√3 <3 <3
V8 <2.9
√A <4.5 < 5
Which sets of inequalities are true

Answers

Answer:

[tex](a)\ \sqrt5 <2.3 < 5.6[/tex]

[tex](b)\ \sqrt 5 <2.4 < 5.6[/tex]

[tex](e)\ \sqrt 8 <2.9[/tex]

[tex](f)\ \sqrt5 <4.5 < 5[/tex]

Step-by-step explanation:

Required

Which are true

[tex](a)\ \sqrt5 <2.3 < 5.6[/tex]

Take square root of 5

[tex]2.2 <2.3 < 56[/tex] --- This is true

[tex](b)\ \sqrt 5 <2.4 < 5.6[/tex]

Take square root of 5

[tex]2.2 <2.4 < 56[/tex]  --- This is true

[tex](c)\ 7.4 < 5 <5.5[/tex]

This is false because [tex]7.4 > 5[/tex]

[tex](d)\ \sqrt 3 <3 <3[/tex]

This is false because [tex]3 = 3[/tex] not [tex]3 < 3[/tex]

[tex](e)\ \sqrt 8 <2.9[/tex]

Take square root of 8

[tex]2.8 <2.9[/tex] --- This is true

[tex](f)\ \sqrt5 <4.5 < 5[/tex]

Take square root of 5

[tex]2.2 <4.5 < 5[/tex] --- This is true

Express 120 as the product of its prime factors.
Write the prime factors in ascending order.

Answers

Answer:

2 x 2 x 2 x 3 x 5

Step-by-step explanation:

The first and smallest prime number that can be divisible by 120 is 2; 120/2 = 60, 60/2 = 30, 30/2 = 15; and the smallest prime number divisible by 15 is 3; 15/3 = 5; and the smallest prime number divisible by 5 is 5; 5/5 = 1.

hence, we have 2 x 2 x 2 x 3 x 5 = 2³ x 3 x 5

What is the slope of the line containing (-2,5) and (4, -4)?
O A. -2
O B.
3
2
O c. 2
O D.
3
2

Answers

Answer: slope is -3/2

Step-by-step explanation:

(-2,5) (4,-4)

Use the slope formula y2-y1/x2-x1

5-(-4)/-2-4 = -3/2

Answer:

The slope of the line containing (-2,5) and (4,-4) is [tex]-\frac{3}{2}[/tex]

Step-by-step explanation:

find the area of the Shaded sector. round to the nearest hundreds place
HELP!!! ASAP​

Answers

Answer:

[tex]192.27\:\mathrm{cm^2}[/tex]

Step-by-step explanation:

The area of sector with radius [tex]r[/tex] and measure [tex]\theta[/tex] is give by [tex]A=r^2\pi\cdot \frac{\theta}{360^{\circ}}[/tex]. Since vertical angles are congruent, the two shaded sectors in the figure are congruent.

What we're given:

2 sectors of equal areaEach sector has a radius of 9 cmEach sector has a measure of 136 degrees

Therefore, the area of the shaded regions (two sectors) is:

[tex]A=2\cdot 9^2\pi\cdot \frac{136}{360}=192.2654704\approx \boxed{192.27\:\mathrm{cm^2}}[/tex]

Please help!!! I don’t know how to do this

Answers

Answer:

O C. x = 3

Step-by-step explanation:

If a line is parallel to y-axis, the equation of the line is x = constant because it is at a constant distance from y-axis. so for the given question, x = 3 is the equation of the line passing through (3,2).

Write a linear equation in one variable for each of the following situations:

a) The ages of Rahim and his father are 16 years old and p years old respectively. Rahim’s father is 29 years older than Rahim.

b) Sulaiman buys m chairs which cost RM5.90 each. He pays RM50 and receives a balance of RM20.50

Answers

Answer:

a) 16 + 29 = p

or

a) p - 16 = 29

b) is confusing

Step-by-step explanation:

What is the image point (-5,3) if it is translated 3 units right and 2 units down

Answers

Our point is at -5, 3. -5 represents its x coordinate, and 3 represents its y coordinate. 3 units right makes it -2, while 2 units down makes it 1. Final coords of the point are (-2,1).

Answer:

given point is (-5,3)

right unit means positive and down unit means negative so,

image of (-5,3)---------->(-5+3-2,3+3-2)

=>(-7+3,6-2)

=>(-4,4) ANS.

2 sin2 (π/2 sin2x)=1+cos(π×cos2x)

Answers

Answer:

3/5Step-by-step explanation:

[tex]the \: equation \: is \: equivalent \: to \\ 2 \: { \sin }^{2} (( \: \frac{\pi}{2}) \: {cos}^{2} x ) = \\ \: 2 \: {sin}^{2} (( \frac{\pi}{2} sin \: 2x \: ) \\ = {cos}^{2} x = sin \: 2x \\ = \: \cos \: x(cos \: x \: - \: 2 \: sin \: x) \: = \: 0 \\ = \: 1 - 2 \tan \: x = 0 \: as \: cos \: x \: ≠ 0 \\ x ≠ (2n + 1) \frac{\pi}{2} \\ = \tan(x) = \frac{1}{2} \\ = \cos(2x) = \frac{1 - {tan \: }^{2}x }{1 + {tan \: }^{2} \:x } = \frac{3}{5} [/tex]

HOPE IT HELPS!!!!

If it is correct mark as BRAINLIEST ✌️

For the graph of the inequality x - 2y >4, what is a value of x for a point that is on the
boundary line and the axes?
0-2
04
-4
O2

Answers

Answer:

Step-by-step explanation:

Explanation:

First, find two points on the line if you change the inequality to an equation.

For  

x

=

0

:  

0

+

2

y

=

4

2

y

=

4

2

y

2

=

4

2

y

=

2

or  

(

0

,

2

)

For  

y

=

0

:  

x

+

0

=

4

x

=

4

or  

(

4

,

0

)

We can plot these two points and draw a line through them to get the border of the inequality:

graph{(x^2+(y-2)^2-0.075)((x-4)^2+y^2-0.075)(x+2y-4)=0}

The line will be solid because the inequality operator has a "or equal to" clause in it. We can now shade the area to the right of the line because the inequality has a "great than" clause in it.

graph{(x+2y-4)>=0}

(PLEASE HELP MEE)
A Jetliner uses 3,600 gallons of fuel per hour while it is cruising, and there are 15,000 gallons of fuel in the jetliner's fuel tank when It begins to crulse. If yrepresents the amount of fuel, In thousands of gallons, remaining in the fuel tank after the Jetliner cruises for x hours, determine the graph of the solution set for this situation and the equation modeled by the graph.
((Graph options in picture))​

Answers

Answer:

"A"

Step-by-step explanation:

C & D start at 12... story starts at 15

3*3600 = 10,800 ....   15,000-10,800 = 4200

at 3 the graph has to be at 4200 (which is above 3)

note at 3 "B" is at 3 so answer has to be "A"

Which of the following is a polynomial?

Answers

I think the answer is D.

A rectangular garden has length and width as given by the expressions below.
Length: 4 - 7(3x + 4y)
Width: 3x(-2y)
Write a simplified expression for the perimeter of the rectangle.
y
ху

Answers

Answer:

8 - 42x - 56y - 12xy

Step-by-step explanation:

Length = 4 - 7(3x + 4y)

= 4 - 21x - 28y

Width = 3x(-2y)

= -6xy

Perimeter of the rectangle = 2(length + width)

= 2{(4 - 21x - 28y) + ( -6xy)}

= 2(4 - 21x - 28y - 6xy)

= 8 - 42x - 56y - 12xy

Perimeter of the rectangle = 8 - 42x - 56y - 12xy

Which system is equivalent to

Answers

Answer:

We can find the system equivalent to this one by replacing one of the equations with a multiply of itself, so:

Let’s multiply y = x-2 by 2

2y=2x-4

A system equivalent to this one is

y = -2x^2 (this remains the same)

2y= 2x-4

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