What is the average rate of change of this function on the interval from x = 1 to x = 3? f(x)=10(2)x Enter your answer in the box.

Answers

Answer 1

Answer:

30

Step-by-step explanation:

The way to figure out the average rate of change is to divide the change in f(x) and divide that by the change in x. A formula for this is [tex]\frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}}[/tex]
1.) By this definition, we need to figure out our x1 and x2. We can say the x1 = 3 and x2 = 1
2.) Next, we plug it into the formula. We will get [tex]\frac{f(3)-f(1)}{3-1}[/tex].

3.) If we simplify, we will get 10(2)^3 - 10*2 divided by 2, which is equal to 10*4 - 10 = 30.


Related Questions

A population of lizards in a large region doubles every year. The number of lizards can be
modeled by the equation y = 500 * 2 ^ x where
× is the number of vears after a researcher
measures the population size . When x = - 3
-3what does the value of y represent ?

Answers

The value of y when the value of x is -3 for the equation,y = 500×2ˣ will be y=62.5.

What is the equation?

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the given equation of is, y = 500×2ˣ

We have to find the value of y when x = - 3.

y = 500×2ˣ

y=500×2⁻³

y=62.5

Thus, the value of y when the value of x is -3 for the equation,y = 500×2ˣ will be y=62.5.

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PLEASE HELP ASAP! I WILL GIVE BRAINLIEST!!!!!
Jack bought a tree to plant in his front yard. The tree grows at an approximate rate of 9 inches per year. After 4 years, the tree is 5 feet tall. Write an equation in slope-intercept form to find the height (in feet) of the tree, y, after x years. Then, find the number of years it will take the tree to reach 20 feet

Answers

The equation in slope-intercept form to find the height is y = 0.75x + 5 and the number of years it will take the tree to reach 20 feet is 24

The linear equation to find the height (in feet) of the tree

The given parameters in the question are

Growth = 9 inches per year

Length of the tree after 4 years = 5 feet

Convert inches to feet

So, we have

Growth = 0.75 feet per year

A linear equation of this scenario is represented as

Length = Growth * Number of years + Initial length

So, we have

y = Growth * x + Initial length

This gives

5 = 0.75 * 4 + Initial length

Evaluate

Initial length = 2

So, the equation is

y = 0.75x + 2

The number of years it will take the tree to reach 20 feet

This means that

y = 20

Recall that

y = 0.75x + 2

So, we have

0.75x + 2 = 20

Evaluate

0.75x = 18

Divide by 0.75

x = 24

Hence, the number of years is 24

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(x+1)+(x+4)+(x+7)+...+(x+40)=442

Answers

The value of the unknown variable x in the given sequence is; 14

What is the sum of the Arithmetic Sequence?

The formula for sum of an arithmetic sequence is;

Sₙ =ⁿ/₂(2a + (n − 1)d)

where;

a is first term

d is common difference

n is position of term

We are given the sequence as;

(x + 1) + (x + 4) + (x + 7) +...+ (x + 40) = 442

The common difference is;

x + 4 - (x + 1)

= 3

Now, to get the number of terms, we will say that the function follows the pattern;

aₙ = (x + 1) + 3n

Thus;

(x + 1) + 3n = x + 40

3n = 39

n = 13

Thus, there are n = 13 terms

Sₙ = ¹³/₂(2(x + 1) + (14 − 1)3) = 442

6.5(2x + 40) = 442

2x + 40 = 442/6.5

2x = 68 - 40

x = 28/2

x = 14

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Hello can someone please help me out? Thank you so much I’ll give brainly :)

Answers

Answer:

Step-by-step explanation:

the answer is a 28.27

Answer:

a) 28.27

Step-by-step explanation:

Formula we use,

→ πr²

Now the required area will be,

→ 3.14 × 3²

→ 3.14 × 9

→ 28.27 in²

Hence, the area is 28.27 in².

Montraie has 1 1/2 cups of yogurt to make smoothies. Each smoothie uses cup of 3/4 yogurt. How many smoothies can Montraie make with the yogurt?​

Answers

Montraie can make 2 cups of smoothies with the yogurt

How to determine the number of smoothies in the yogurt

From the question, we have the following parameters that can be used in our computation:

Cups of yogurt = 1 1/2

Each smoothie = 3/4 yogurt

Assume there exist a proportional relationship between the cups and the yogurt

The number of smoothies in the yogurt can be calculated using the following equation

Smoothies = (1 1/2)/(3/4)

Evaluate the quotient

Smoothies = 2

Hence, the cups is 2 yogurt

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How do you solve 3x2-5(-2)

Answers

Answer:

Step-by-step explanation:

you do the math

Answer:

16

Step-by-step explanation:

I'm solving this question according to PEMDAS.

3x2-5(-2)

3x2+10

6+10

16

Could you please give me brainliest for this? Thanks!

Negative and zero exponents 36 x¹⁵y²⁰/ 12 x³y⁵=

Answers

The negative and zero exponents of the given exponents will be 3 x¹⁵y²⁰ × x⁻³y⁻⁵z⁰.

What is the law of indices?

Index (indices) in Maths is the power or exponent which is raised to a number or a variable.

The mathematics of power or exponent of any number is called indices.

For example 5³ = 5²5 here we break 5³ into 5² and 5 so it is called the law of indices.

Another example could be 7² = 7³/7 here we divide to obtain power 2.

As per the given,

36 x¹⁵y²⁰/ 12 x³y⁵ = [(36/12) (x¹⁵y²⁰)/(x³y⁵)]

36 x¹⁵y²⁰/ 12 x³y⁵ = 3x¹⁵y²⁰ × x⁻³y⁻⁵z⁰

Hence "The negative and zero exponents of the given exponents will be 3 x¹⁵y²⁰ × x⁻³y⁻⁵z⁰".

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Evaluate each expression if w = 2, x = 3, y = 5, and z = 6.
1. 2w
2. y + 5
4. x+ w
7. y²
5. 3+ 4z
8. y - x
Fvaluate each evnreccion if m
n
3.9-2
6. 6y-5
Nov 30

Answers

1. 4
2. 10
4. 5
7. 25
5. 27
8. 2
3. 7
6. 25

Hope this helped:))

HELP THANKS SO MUCH!!!!!!

Answers

Answer:

.62 each

Step-by-step explanation:

Find a polynomial f(x) of degree 5 that has the following zeros.
-2, 3, 7, 0, 4
Leave answer in factored form

Answers

The polynomial f(x) of degree 5 that has the following zeros is

f(x) = (x+2) (x-3) (x-7)(x-0) (x-4).

What is meant by polynomial?

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents. In many branches of mathematics and science, polynomials are used. For instance, they are used to define polynomial functions, which show up in settings ranging from basic chemistry and physics to economics and social science. They are also used in calculus and numerical analysis to approximate other functions. Polynomial equations are used to form these functions.

The function's zeros are expressed as follows:

f(x) = (x-a)(x-b)..... where the a, b  are the zeros

f(x) = (x-(-2)) (x-3) (x -7)(x-0) ( x-4)

f(x) = (x+2) (x-3) (x-7)(x-0) (x-4)

Therefore, the polynomial f(x) of degree 5 that has the following zeros is

f(x) = (x+2) (x-3) (x-7)(x-0) (x-4)

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4) The trapezoid I'J'K'L' is a dilation of the trapezoid IJKL. What is the scale factor of the
dilation?
I
-10 -8 -6 -4
I'
~
104
8
6
4
2
2
-4
-6
-8
L'
L
J'
K'
4
6
J
K
10
10
4) Simplify your answer and write it as a proper fraction, an improper fraction, or a whole
number.

Answers

Answer:4

Step-by-step explanation:

16/4=4

The scale factor of the dilation is, 1/4.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The trapezoid I'J'K'L' is a dilation of the trapezoid IJKL.

Here, The length of IJ = 16

And, The length of I'J' = 4

Hence, The scale factor of the dilation is,

⇒ I'J' / IJ = 4 / 16

               = 1/4

Thus, The scale factor of the dilation is, 1/4.

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The cleaning service charges $15 per hour. Mr. Henrickson is hiring the cleaning service but does not want to spend more that $75. What is the maximum number of hours that he can hire the cleaning service? Write an inequality and solve.

Answers

The maximum number of hours that he can hire the cleaning service would be 5.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Consider that the number of hours for which the total cost would be the same be x

The first inequality is;

$15x > $75

Now equate equations

$15x - $75 = 0

15x = 75

x = 5

Hence, the maximum number of hours that he can hire the cleaning service would be 5.

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A recipe for a trail mix calls for 6 cups of Chex mix and 8 cups of pretzels how many cups of pretzels are needed to make 112 cups of trail mix

Answers

Answer:3/2

Step-by-step explanation: so you have the number of cups of Chex Mix in the bag is 3x = 3*9 = 27 cups and the number of cups of chocolate chips is 2x = 2*9 = 18 cups. Indeed, we see that 27 + 18 = 45 and 27/18 = 3/2 as required.

What is 4 1/4 x (-12.2)?

Answers

1235678.34235467556888665
Hope this helps you

Stanley runs, swims, and bikes every day. During these workouts, he runs at 9 mph, bikes at 16 mph, and swims at 2.5 mph. Yesterday, he ran for half an hour longer than he swam, and his biking time was twice his running time. How long did Stanley run, swim, and bike yesterday if the total distance he covered was 64 miles?
what distance did stanley swim run and bike
PLEASE HELP

Answers

The time  did Stanley run, swim, and bike yesterday if the total distance he covered was 64 miles is 1.5 hrs, 1 hrs, 3 hrs. The distance is 13.5 miles, 2.5 miles , 48 miles.

How to find the distance and time?

Let t represent the  time he ran

Let t -.5 represent  time he swam

Let 2t represent the  biking time

Hence,

9t + 2.5(t-.5) + 16(2t) = 64

9t + 2.5t - 1.25 + 32t = 64

Collect like terms

43.5t = 64 + 1.25

Divide both side by 43.5t

t = 65.25/43.5

t = 1.5 hrs (Time he ran)

So,

Time he swam

t -.5 where t is 1.5 hrs

1.5-.5 = 1 hr (Time he swam)

Biking time

2t where t is 1.5 hrs

2(1.5) = 3 hrs (biking time)

Distance of each

1.5(9) = 13.5 miles  (running)

1(2.5) = 2.5 miles   (swimming)

3(16) = 48 miles  (biking)

Total distance = 13.5 miles + 2.5 miles + 48 miles

Total distance = 64 miles

Therefore the time  is 1.5 hrs, 1 hrs, 3 hrs and the distance is 13.5 miles, 2.5 miles , 48 miles.

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Kyla finished a 100 meter race in one and three-eighths minutes. The winner of the raced finished in one-third of Kyla's time.

How many minutes did it take for the winner of the race to finish?

eight thirty-thirds
eleven twenty-fourths
one and three twenty-fourths
one and four-elevenths

Answers

11/24 many minutes did it take for the winner of the race to finish.

What is Fraction?

A fraction represents a part of a whole.

Given,

Kyla finished a 100 meter race in one and three-eighths minutes.

Kylas time is [tex]1\frac{3}{8}[/tex] minutes.

Convert mixed fraction to improper fraction.

11/8 minutes.

The winner of the raced finished in one-third of Kyla's time.

Which means 1/3 of 11/8

1/3×11/8

11/24

Hence, 11/24 many minutes did it take for the winner of the race to finish.

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If the simple interest on ​$2000 for 4 years is ​$480​, then what is the interest​ rate?

Answers

Answer: 6%

Step-by-step explanation:

R=100×480/2000×4

R=6%

Answer:

R

=

6

%

Step-by-step explanation:

The formula for Simple Interest is

S

I

=

P

R

T

100

Change the subject to be R.

R

=

100

×

S

I

P

T

Once that is done, we just need to substitute the values.

R

=

100

×

480

2000

×

4

R

=

6

%

Find the perimeter of the figure below
A. 44m
B. 48m
C. 52m
D. 46m
E. 50m
Perimeter equals ______________ meters

Answers

Answer: 50

Step-by-step explanation:

10+15+6+4+6+11= 50

Edit=

We can see that the length of one side is 10, and the width of one is 15. For the other side of the width, we can subtract 4 from 15 to get 11. For the other length, we can subtract 6 from 10 to get four. We also have to add in the 6 and 4 because they are parts of the border. (10+15+11+4+6+4)

A car travels 120 miles and one and a half hours what is the average speed for miles per hour

Answers

Answer:

80

Step-by-step explanation:

120 divided by 3 (for per half hr) is 40 and if you add 2 of the half hrs together (40+40) its 80

A survey was given to a random sample of 80 residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. Of those surveyed, 52 respondents said they were in favor of the plan. Determine a 95% confidence interval for the proportion of people who favor the tax plan, rounding values to the nearest thousandth.​

Answers

With a 95 percent confidence interval, the proportion of people who favor the tax plan is 0.546 ,0.755

How to solve for the interval

The value of n is the random sample n = 80

we have x as the number of people surveyed, = 52 respondents

Then p = x / n

p = 52 / 80

p = 0.65

From the z critical table, 95% confidence level = 1.96

we would have to use the confidence interval formula. This is given as:

[tex]p +- Z * \sqrt{\frac{p*(1-p)}{n} }[/tex]

we have to put in the values

[tex]0.65 +- 1.96 * \sqrt{\frac{0.65*(1-0.65)}{80} }[/tex]

0.65 ± 1.96 * 0.053326822

0.65 - 0.10452 , 0.65 + 0.10452

0.546 ,0.755

Therefore the proportion of persons that are in favor of this tax has been calculated as 0.546 ,0.755

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Find the value of X that makes m n

Answers

The value of x is 6 degree that makes m || n.

What is parallel lines?

Parallel lines are coplanar, straight lines in geometry that don't cross at any point. When two planes in the same three-dimensional space are parallel, they never cross. Curves that maintain a set minimum distance from one another and do not touch or intersect are said to be parallel curves.

(8) Given: m || n

We have to find the value of x that makes m || n.

The lines m and n are divides by the line l of angle 90 degree.

⇒ 16x - 6 = 90

Add 6 on both sides,

16x - 6 = 90 + 6

16x = 96

Divide both sides by 16

16x/16 = 96/16

x = 6

Hence, the value of x is 6 degree that makes m || n.

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Solve the equation 8 −7/10 c = 6−1/5 c for c. please show how you got it

Answers

The answer to C the number that’s missing is 8 I took the quiz

Answer:

the answer is 0.5

Step-by-step explanation:

Find the slope of the line that passes through all of the points
on the table.
X
2
7
12
17
y
2
-3
-8
-13


Only need the answer

Answers

Answer:

Step-by-step explanation:

so first you need to find the slope

you can draw the line on a graph and use a protractor

final answer=46 degrees

Answer:-5/-19

the answer is -5/-19 and can not be simplify

marking brainiest
:)

Answers

Answer:

Step-by-step explanation:

Which equation is perpendicular to y = 2/3 x - 4?
a. y = -3/2 x + 4
b. y= 2/3 x - 4
c. y = -2/3 x + 4
d. y = 3/2 x - 4

Answers

Answer:

Your answer is A) [tex]y=-\frac{3}{2}x-4[/tex]

Step-by-step explanation:

This is because the slope of a perpendicular line is a negative reciprocal in relation to the original line. In this example, [tex]\frac{2}{3}[/tex] is flipped to [tex]-\frac{3}{2}[/tex]

What is the product of a number and 18

Answers

Answer:

18n

Step-by-step explanation:

Product : Multiplication result

number : n

18 : 18

of a number and 18 : n*18

The product of a number and 18 is n*18, or 18n.

Is the system of equations consistent and independent, consistent and dependent, or inconsistent?

y=−3x+12y=−6x+2

Select the correct answer from the drop-down menu.


consistent and independent

Answers

The system of equation is consistent and independent because it has one unique solution.

How to solve system of equation?

If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent.

Therefore, let's solve the equation,

y = -3x + 12

y = -6x + 2

Using substitution,

-6x + 2 = -3x + 12

-6x + 3x  = 12 - 2

-3x = 10

x = - 10 / 3

y = -6(-10 / 3) + 2

y = 60 / 3 + 2

y = 20 + 2

y = 2

Therefore, the system of equation is consistent and independent.

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4x^2 + 4x =3
help pls

Answers

Answer:

x = .5, - 1.5

Step-by-step explanation:

4x^2 + 4x =3

To solve for x, we can complete the square.

4 ( x^2 + x) = 3

x^2 + x = 3/4

Take the coefficient of x, divide by 2, and square.

(1/2)^2

Then add to each side.

x^2 + x + 1/4= 3/4 +1/4

(x+1/2) ^2 = 1

Take the square root of each side.

x+1/2 = ±1

x = ±1 -1/2

x = 1-1/2  or -1-1/2

x = 1/2, -3/2

x = .5, - 1.5

Answer:

x = 1/2   or   -3/2

Step-by-step explanation:

Rewrite in Standard Form:

4x²+4x=3 ==>  4x²+4x-3=0

Identify:  a=4   b=4   c= -3

Quadratic Formula:

[tex]x=\frac{-b+\sqrt{b^2-4ac}}{2a} or \frac{-b-\sqrt{b^2-4ac}}{2a}\\ \\=\frac{-4+\sqrt{4^2-4(4)(-3)}}{2(4)} or \frac{-4-\sqrt{4^2-4(4)(-3)}}{2(4)}\\\\=\frac{-4+\sqrt{16+48}}{8} or \frac{-4-\sqrt{16+48}}{8}\\\\=\frac{-4+\sqrt{64}}{8} or \frac{-4-\sqrt{64}}{8}\\\\=\frac{-4+8}{8} or \frac{-4-8}{8}\\\\=\frac{4}{8} or \frac{-12}{8}\\\\=\frac{1}{2} or -\frac{3}{2}[/tex]

In order to accumulate enough money for a down payment on a​ house, a couple deposits $406 per month into an account paying 3% compounded monthly. If payments are made at the end of each​ period, how much money will be in the account in 6 ​years?

Answers

In 6 years, the couple will have $32,916.38 in the account.

Can anyone help me? Thank you

Answers

Answer:162

Step-by-step explanation:

1.5 ft = 18 inches

so

9 * 18 = 162

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