What is the average rate of change of the function over the interval x = 0 to x = 8?

f(x)=2x−1/3x+5
Enter your answer, as a fraction, in the box.

What Is The Average Rate Of Change Of The Function Over The Interval X = 0 To X = 8?f(x)=2x1/3x+5Enter

Answers

Answer 1
Answer:  13/145

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

Work Shown:

Plug in x = 0

[tex]f(x) = \frac{2x-1}{3x+5}\\\\f(0) = \frac{2*0-1}{3*0+5}\\\\f(0) = \frac{0-1}{0+5}\\\\f(0) = -\frac{1}{5}\\\\[/tex]

Repeat for x = 8

[tex]f(x) = \frac{2x-1}{3x+5}\\\\f(8) = \frac{2*8-1}{3*8+5}\\\\f(8) = \frac{16-1}{24+5}\\\\f(8) = \frac{15}{29}\\\\[/tex]

Now use the average rate of change formula

[tex]m = \frac{f(b)-f(a)}{b-a}\\\\m = \frac{f(8)-f(0)}{8-0}\\\\m = \frac{15/29 - (-1/5)}{8}\\\\m = \frac{15/29 + 1/5}{8}\\\\m = \frac{(15/29)*(5/5) + (1/5)*(29/29)}{8}\\\\m = \frac{75/145 + 29/145}{8}\\\\[/tex]

[tex]m=\frac{104/145}{8}\\\\m = \frac{104}{145} \div \frac{8}{1}\\\\m = \frac{104}{145} \times \frac{1}{8}\\\\m = \frac{104*1}{145*8}\\\\m = \frac{104}{1160}\\\\m = \frac{13}{145}\\\\[/tex]


Related Questions

Independent Practice


Find the number of solutions of the equation.

0 = x2 + 2x + 9


A.
3


B.
2


C.
1


D.
0

Answers

Answer:

Option D

Step-by-step explanation:

There are no real solution for the given equation

Answered by GAUTHMATH

SOMEONE HELP ME PLEASE

Answers

Answer:

1/36

Step-by-step explanation:

There are 6 possible outcomes 1,2,3,4,5,6

P(1) = number of outcomes that equal1 / total

        =1/6

Roll again

P(1) = 1/6

These are independent events so we can multiply the probabilities

P(1 roll again 1) = 1/6 * 1/6 = 1/ 36

What is the slope of the line y = 1/2-x+4?​

Answers

Answer:

1/2

Step-by-step explanation:

coefficient of x

Answer:

The answer above me is correct, the slope is 1/2.

Step-by-step explanation:

It is the coefficient of x.

25. A pizza shop offers 30% off the price of a large pizza every Tuesday
night. If the regular price is $25, what is the discounted price?

Answers

Answer:

25 -(.3*25)

25-7.50 = $17.50

Step-by-step explanation:

Answer:

17.50

Step-by-step explanation:

First find the amount of the discount

25 * 30%

25 * .3

7.5

Subtract this from the original amount

25 - 7.5

17.50

Chang has 2 shirts: a white one and a black one. He also has 2 pairs of pants, one blue and one tan. What is the probability, if Chang gets dressed in the dark, that he winds up wearing the white shirt and tan pants? Show your work.

Answers

Answer:

The probability that Chang gets dressed with a white shirt and tan pants is 25%.

Step-by-step explanation:

Given that Chang has 2 shirts, a white one and a black one, and he also has 2 pairs of pants, one blue and one tan, to determine what is the probability, if Chang gets dressed in the dark, that he winds up wearing the white shirt and tan pants the following calculation must be performed:

Each shirt = 50% chance

Each pants = 50% chance

0.50 x 0.50 = X

0.25 = X

Therefore, the probability that Chang gets dressed with a white shirt and tan pants is 25%.

Using trig to solve for missing angles

Answers

Answer:

0.9⁰

Step-by-step explanation:

let unknown angle be x

sin x=47/60

sin x=0.783333

x=sin(inverse) 0.7833333

x=0.9⁰

Find the measure of 2

Answers

Answer:

92

Step-by-step explanation:

Angle 2 and 92 are corresponding angles and corresponding angles are equal when the lines are parallel

Answer:

[tex]\angle 2=92^{\circ}[/tex]

Step-by-step explanation:

When two parallel lines are cut by a traversal, their corresponding angles are always equal. Corresponding angles can be found if you took each point of intersection and aligned them up with each other.

In this case, we see that [tex]\angle 2[/tex] and the angle marked as 92 degrees correspond with each other. Since all corresponding angles are equal, we have:

[tex]\angle 2=\boxed{92^{\circ}}[/tex]

Use the given conditions to write an equations for the line in slope- intercept form. passing through (1,-8) and (-7,8)

Answers

Answer:

y = -2x - 6

Step-by-step explanation:

Going from the first point to the second, we see x decreasing by 8 from 1 to -7 (this is the 'run') and y increasing by 16 from -8 to +8 (this is the 'rise').  Thus, the slope of the line through these two points is m = rise/run =  16/(-8) = -2.

Using the point-slope formula y - k = m(x - h) and the point (1, -8), we get:

y + 8 = -2(x - 1), or

y = -8 - 2x + 2, or

y = -2x - 6 (in slope-intercept form)

A runner covers the last straight stretch of a race in 3 s. During that time, he speeds up from 5 m/s to 11 m/s.What is the runner's acceleration in this part of the race? ​

Answers

Answer:

From first Newton's equation of motion:

[tex]{ \bf{v = u + at}}[/tex]

Substitute the variables:

[tex]{ \tt{11 = 5 + (a \times 3)}} \\ { \tt{3a = 6}} \\ { \tt{a = 2 \: {ms}^{ - 2} }}[/tex]

Acceleration is 2 ms-²

the value of [{(6to the power 2+8 to the power 2)to the power 1/2}]to the power 3​

Answers

Answer:

Step-by-step explanation:

[tex][(6^{2}+8^{2})^{\frac{1}{2}}]^{3} = [(36+64)^{\frac{1}{2}}]^{3}\\\\= [(100)^{\frac{1}{2}}]^{3}\\\\= 10^{3}\\\\= 1000[/tex]

For problems 1 - 4, write a two-column proof.

Answers

Solution given:

1:

<5=<6

<5+<4=180°[co interior angle]

Substituting value of<5

<6+<4=180°[it shows a property of co interior angle]

So

l || m

2:

<1=90°[ l is perpendicular to t]

<2=90°[m is perpendicular to t]

since

<1=<2[shows property of corresponding angle]

:.

l || m.

3:

<1=<2

<1=<3

substituting value of<1 in second one

<2=<3[which shows property of alternate Angel]

So

Segment ST || segment UV.

4:

<RSP=<PQR......[I]

<QRS+<PQR=180°.....[ii]

from equation I and ii we get

<RSP+<QRS=180°[which shows property of co interior angle ]

So

Segment PS || segment QR

These pictures are the questions given in the pdf, let's get the solutions.

1) Solution

It is given that,

→ <5 = <6

Then the co interior angles,

→ <5 + <4 = 180°

Now substituting value of <5,

→ <6 + <4 = 180°

This shows property of co interior angle.

Therefore, L ll m

2) Solution

Take it as,

→ <1 = 90°

In above eq. L is perpendicular to t.

→ <2 = 90

In above eq. m is perpendicular to t.

Then it will be,

→ <1 = <2

It shows property of corresponding angle.

Therefore, L ll m.

3) Solution

It is given that,

→ <1 = <2 and <1 = <3

Now substitute,

The value of <1 in second one,

→ <2 = <3

This shows property of alternate angle.

Therefore, ST || UV.

4) Solution

It is given that,

→ <RSP = <PQR --- (1)

→ <QRS + <PQR = 180° --- (2)

Now from the equation (1) and (2),

→ <RSP + <QRS = 180

It shows property of co interior angle.

Therefore, PS || QR.

The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r, where r is expressed as a decimal.

What is the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years?

$60
$80
$90
$100

Answers

Answer:

80

Step-by-step explanation:

I = Prt

I = 40  R = .10  T = 5

40 = P (.10)(5)

40 = P(.5)

Divide each side by .5

40/.5 = .5P/.5

80 = P

The interest over 5 years is $80.

The correct option is B.

What is the simple interest?

Simple interest is the borrowing amount added only to the principal amount.

The Formula to calculate the simple interest is;

                                                 S.I. = P x T x R / 100,

Where S.I. is simple interest, P is the principal amount, T is the time period and R is the interest rate in a year.

We can use the formula I = Prt to solve for P. We know that I = 40, r = 0.10, and t = 5. Substituting these values, we get:

40 = P(0.10)(5)

Simplifying:

40 = 0.5P

Dividing both sides by 0.5:

P = 80

Therefore, the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years is $80.

To learn more about the simple interest; https://brainly.com/question/25845758

#SPJ7

Arturo's goal is to find a job that provides an income of at least $60,000 a year. Kristen's Furniture offers him a job paying a base salary of $14,000 a year, plus a commission of 7% of his sales. Determine what Arturo's total sales will need to be for him to have a yearly income greater than or equal to $60,000.

If Arturo takes the job with Kristen's Furniture, he will need to have at least
$
in total sales to have a yearly income greater than or equal to $60,000 per year.

Answers

Answer:

He will need at least 657,142.86

Step-by-step explanation:

Determine how much commission he needs

60000-14000

46000

Commission is 7%

Let x be the sales

x*7% = 46000

x*.07 = 46000

Divide each side by .07

x = 46000/.07

x =657142.85714

Rounding to the nearest cent

x = 657,142.86

PLS DO THIS ASAP

no links

Answers

Answer:

SPEED ANSWER!!!!

DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD!!!!!!!!!!
The answer is D, 3 is the y intercept

what is the solution to this?

Answers

Answer:

x = -3,y = 2

Step-by-step explanation:

3x-2y = -13

4x-3y = -18

~~~~~~~~~~~~~~~~

9x -6y = -39

-8x+6y = 36

x = -3

-12 -3y = -18

-3y = -6

y = 2

find the perimeter of the figure

Answers

The answer is 51 you add all the sides together to find the perimeter

Answer:

72cm

Step-by-step explanation:

We have 4/6 sides. 4 of them are given, and they are 13.25cm, 7.25cm, 7.75cm, and 22.75cm.

The perimeter is found when you add all the lengths of the sides of a figure.

So far, we can add 13.25+7.25+7.75+22.75 = 51cm.

Let's call the first ungiven side A. We can see that 7.75cm + A = 13.25cm. Using this, we can figure out that A = 13.25-7.75 = 5.5cm.

We can call the second ungiven side B. We see that 7.25cm + B = 22.75cm. So, B = 22.75-7.25 = 15.5cm.

Now, let's add everything together. 51cm + A + B = Perimeter. 51cm + 5.5cm + 15.5cm = 72cm.

Hope this helps! Feel free to ask any questions if this doesn't make sense. :)

determine the equation of a line that goes through (-1,2) and (7,2)

Answers

Answer:

Step-by-step explanation:

To evaluate such, the following must be comprehended:

Slope: Rise/Run.

X-intercept: The peculiar point in which the observed linear data intersects the x-axis.

Y-intercept: The peculiar point in which the observed linear data intersects the y-axis.

To evaluate for the slope, which is defined as the agglomerate distance between two points contained within linear data, the following equation must be utilized:

m = (y2 - y1) / (x2 - x1)

Points utilized or given: (-1, 2) and (7, 2).

2 - 2 / 7 + 1 = 0/8 ==> 0

Henceforth, the slope for the particular configuration, as provided, is understood as zero (0).

Utilizing the integral of one of the points provided, as well as slope evaluated for, the following equation could be exploited:

Point-Slope Formula:

Y- y1 = m(x - x1)

Y - 2 = 0(x - 7)

Y - 2 = 0

Y = 2

Hence, the answer to the peculiar interrogate is disclosed as 2, which is identified as where the horizontal line intersects the y-axis at (0, 2).

*I hope this helps.

If one angle of a triangle is 60°and the ratio of other two is 1:3,find all the angles and the ratio of the sides.​

Answers

Answer:

30, 90

1 : √3 : 2

Step-by-step explanation:

let the smaller angle be x

hence, the other angle = 3x

180-60=4x

4x = 120

x = 120/4 = 30

other angle = 3(30) = 90

the triangle is a 30-60-90 triangle,

hence the ratio of the sides are 1:√3:2

( short leg : long leg : hypotenuse )

the numbers written in rectangles are the products of the numbers in connecting circle. Please solve it fast its urgent ​

Answers

Answer:

It is the third one

Step-by-step explanation:

c

Which table represents a linear function?
X
1
1
у
5
10
15
| | | |-
1
4
20
25
5

Answers

Answer:

x is the linear function table

Please hurry I will mark you brainliest

What is the equation of the line through the point (2, 3) with slope -2?

Answers

Answer:

y=-2x+7

Step-by-step explanation:

Try plotting the points on desmos. Then use the slope to find the y value.

Bruno is 4.5 times as old as Charles if Bruno is 27 how old is Charles

Answers

Answer:

6

Step-by-step explanation:

Bruno(B)= 4.5× Charles(C)

Answer:

Charles is 6

Step-by-step explanation:

Bruno = B

Charles = C

B = 4.5C

27 = 4.5C

----    -------

4.5     4.5

6    =   C

The answer is 6.

simplify negative 3 / 8 divided by negative 5 / 6

Answers

Answer:

9/20

Step-by-step explanation:

1. 3/8 / 5/6

2. 9/20

Answer:

[tex] \sf \: \frac{9}{20} [/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: \frac{ - 3 }{ \: 8} \div \frac{ - 5}{ \: 6} [/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: \frac{ - 3}{ \: 8} \div \frac{ - 5}{ \: 6} [/tex]

[tex] \sf \rightarrow \: \frac{ - 3}{ \: 8} \times \frac{ - 6}{ \: 5} [/tex]

[tex] \sf \rightarrow \: \frac{( - 3 \times - 6)}{(8 \times 5)} [/tex]

[tex] \sf \rightarrow \: \frac{18}{40} = \frac{9}{20} [/tex]

Hence, the answer is 9/20.

The total cost of a flower bouquet depends on the types of flowers in the arrangement. A bouquet containing 6 roses, 3 lilies, and 2 carnations costs $26.75. A bouquet containing 3 roses, 4 lilies, and 5 carnations costs $25.50. A bouquet containing 1 of each flower costs $6.75. Which system of equations represents this situation, where r represents the number of roses, l represents the number of lilies, and c represents the number of carnations?

Answers

Answer:

Roses 2.70, Lillies 2.45, Carnations 1.60

Please answer the questions down below i left a couple diffrent pictures

20 POINTS!!
Summer Learning HeadStart 7-8

Answers

Answer:

yes

yes

no

no

Step-by-step explanation:

4.

Additive inverses are the same number with different signs, one positive and one negative. they must add to zero. For example, -1 and 1 are additive inverses since they add to zero.

yes

yes

no

no

If a ramp is 17 feet long rises 8 feet above the floor and covers a horizontal distance of 15 feet what is the ratio of _____ to ____ is equal to San B.

Answers

In the given question, it is given that  ramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet.

And we have to find the value of tan B.

And tangent of any angle is equal to the ratio of vertical by horizontal. That is:

tanB=8/15

And that's the required missing ratio for tan B.

Answer:

The ratio of sin b to cos b is equal to tan B.

Step-by-step explanation:

Correct for plato

Given that x= –1/2 and y = 4 , evaluate 3x²y + xy²​

Answers

Answer:

-5

Step-by-step explanation:

3x²y + xy²​

Let x = -1/2 and y = 4

3(-1/2)^2 (4) + (-1/2) (4)^2

Exponents first

3(1/4) (4) + (-1/2) 16

Multiply

3 - 8

Subtract

-5

Answer:   [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\huge \boldsymbol {-5}[/tex]

Step-by-step explanation:                                                                                                                                                                                                                     simplify it                                                                                                                  [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \displaystyle\ \Large \boldsymbol{} 3x^2y+xy^2=xy(3x+y)[/tex]                                                                       evalute                                                                                                        [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \displaystyle\ \Large \boldsymbol{} -\frac{1}{2} \cdot 4 (-3\cdot \frac{1}{2}+4)=-2\!\!\!\!\diagup\cdot\frac{5}{2\!\!\!\!\diagup} =\boxed{-5}[/tex]                                                                                                                                                                                                                                                              

The sum of two integers is (-32). Their quotient is 7. What are the integers?

Answers

Answer:  -28 and -4

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

Explanation:

Let x and y be the two integers such that |x| > |y|. This is another way of saying that x is further away from 0 compared to y.

Their quotient being 7 means x/y = 7 which rearranges to x = 7y

The sum of the integers is -32 which allows us to say....

x+y = -32

7y+y = -32

8y = -32

y = -32/8

y = -4

Use this y value to find x

x = 7y

x = 7*(-4)

x = -28

The two integers are -28 and -4.

Let R={0, 1, 2, 3} be the range of h(x) = x - 7. The domain of h inverse is_____.

{-7, -6, -5, -4}
{7, 8, 9, 10}
{0, 1, 2, 3}

Answers

Answer:

{-7,-6,-5,-4}

Step-by-step explanation:

Answer:

thats not correct answer thats an odyssey question and i just tried the answer and its not right just wanted everybody to know

Step-by-step explanation:

Identify the domain of a radical function with an odd index.

Answers

Answer:

A odd index can go to " - infinity "

Step-by-step explanation:

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A person who is abusing the drug heroin most likelyA. abuses alcohol, marijuana, cocaine, or prescription opioid medications along with heroinB. received a prescription for heroin from a doctor at first but then started abusing it as time went onC. started using heroin before any other drugs but will progress to more serious drug abuseD. tried Fentanyl but wanted something that was not as strong to use recreationally Assume you had invested $1,000 in a lawn mower to set up a lawn mowing business for the summer. During the first week, you could choose either to mow the grounds at a housing development for $1,400 or to help paint a garage for $1,360. Each job would take one week. You cannot do both. You would incur additional costs of $160 for lawn mowing and $80 for garage painting. These costs include $60 under each alternative for transportation to the job. Prepare a schedule showing the net benefit or advantage of selecting one alternative over the other. (This is all information provided) Lawn mow bus. service Painting garage Differential Revenues $1,400 $1,360 $40Cost $160 $80 $80Net benefit in favor (40)of lawn service WILL GIVE BRAINLIEST IF RIGHT!!determine which of the following statements is true respond with true or false right angle has 2 complementary angles What is something that happens during translation Hiii please help me to balance the chemical equation: sodium + water ------> sodium hydroxide + hydrogen Find the value of x. how did john get the alcohol While rounding on your patients, you notice that one patient has a webbed neck, short stature,poor breast development and brown pigment spots (nevi) on her body. In her chart, you seekaryotype results showing 45 chromosomes. Her condition is broadly classified as: Find the total surface area of this square based pyramid. 10ft 10ft (in the image) Recurring upswings and downswings in an economy's real GDP over time are called Group of answer choices recessions. total product oscillations. business cycles. output yo-yos. in which are of study did avicenna make his main contribution Stalactites and stalagmites form as ________ precipitates out of the water evaporating in underground caves. How many tacos could you buy with your money? If you had $20 dollars would you have enough money to buy a taco for 37 students on a Tuesday? She said, "Would you like me to help you?" ( Change into indirect speech) At the beginning of the recent period, there were 960 units of product in a department, 35% completed. These units were finished and an additional 5,200 units were started and completed during the period. 880 units were still in process at the end of the period, 25% completed. Using the weighted average method, the equivalent units produced by the department were: 5. Read the passage.Spaniards arrived in New Mexico and began to farm. During this time, some of the domesticated animals they raised included dogs andturkeys: The people of this area, living in organized cities, were given the name Pueblos, meaning Townsmen, by the arriving Spaniards.Which underlined group of words is a participial phrase?O living in organized citiesO domesticated animalsO arriving SpaniardsO included dogs and turkeys Select the correct answer. This table represents a quadratic function. x y 0 -3 1 -3.75 2 -4 3 -3.75 4 -3 5 -1.75 "Money serves as a ______. A. unit of account, which means that it can be held and exchanged later for goods and services B. store of value, which is a function unique to money C. medium of exchange, which means that it is generally accepted in exchange for goods and services D. store of value because even during a period of inflation its value does not change" Which proportion correctly shows the equivalence of two fractions?A) 1995 = 5776B) 32116 = 929C) 1836 = 72144D) 1836 = 14472 PLEASE HELP!!!!No links PLZ