The table shows values for a quadratic function.
What is the average rate of change for this function for the interval from x = 1
to x = 3?

The Table Shows Values For A Quadratic Function.What Is The Average Rate Of Change For This Function

Answers

Answer 1

The average rate of change for this function for the interval from x = 1

to x = 3 will be 8. Therefore option B is correct.

How to find the average rate of change of something?

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

where when

[tex]x = x_1, y = y_1\\and \\x = x_2, y = y_2[/tex]

The average rate of change can be calculated as;

From x=1 to x=3,

y = 2 and y = 18

Therefore, based on the table, when:

[tex]x_1 = 1 y_1 = 2 \\and \\x_2 = 3, y_2 = 18[/tex]

Then:

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\text{Average rate} = \dfrac{18 - 2}{3-1}\\\\\text{Average rate} = \dfrac{16}{2}\\\\\text{Average rate} = 8[/tex]

Therefore option B is correct.

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Related Questions

what is 1/4×2/5÷1/3 as a fraction
please help

Answers

Answer:

3/10

Step-by-step explanation:

Please give brainliest!

hope this helps :)

the first step is to multiply 1/4 and 2/5

1/4 times 2/5 = 2/20

you figure this out by multiplying the numerators and denominators.

next, we solve 2/20 ÷ 1/3

we do this by taking the reciprocal of 1/3, which is 3/1, and then multiplying the fractions

2/20 times 3/1 = 6/20

6/20 = 3/10

A 2-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 115-ft shadow. how tall is the cell phone tower?
the cell phone tower is _ ft

Answers

The height of the cell phone tower will be 138 feet.

What are ratio and proportion?

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

A 2-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 115-ft shadow.

Then the height of the cell phone tower will be

Let x be the height of the cell phone tower.

x / 2 = 115 x 12 / 20

    x = 69 x 2

    x = 138 feet

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Help and please show work!


Factor sin^8Θ + 2sin^4Θcos^4Θ + cos^8Θ

Answers

hi

Step-by-step explanation:

I

don't

know

see you in next question

9. A box contains 50 discs which are numbered 1 to 50. If one disc is drawn at random from the box. Find the probability that it bears: a 2 digit no. (ii) a perfect square no. (iii) a no. divisible by 5​

Answers

The probability that it bears a 2 digit no. is 41/50; a perfect square no is; 3/25; a no. divisible by 5​ is; 0.2

How to find the probability?

We are given;

Number of Discs in box = 50

Type of discs in box = Numbered 1 to 50

i) Number of 2 digit numbers = 41

Thus;

P(2 digit numbers) = 41/50

ii) Perfect square numbers are; 4, 9, 16, 25, 36 and 49. Thus;

P(perfect square number) = 6/50 = 3/25

iii) Numbers divisible by 5 are; 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.

Thus;

P(numbers divisible by 5) = 10/50 = 0.2

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What is the slope of the line that passes through the points (-6, 8) and (-9, 7)? Write your answer in simplest form.

Answers

Answer:

m=1/3

equation y=1/3x+10

Step-by-step explanation:

Find the rise and run.

1. -6--9=run=3

2. 8-7=rise=1

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the slope of the line that passes through (-6, 8) and (-9, 7).

[tex]\triangle~\fbox{\bf{KEY:}}[/tex] (formula for Slope)

[tex]\longmapsto\bf{\cfrac{y2-y1}{x2-x1}}[/tex]

y2 & y1 = the y-coordinates of the two points

x2 & x1 = the x-coordinates of the two points

[tex]\ddot\bigstar[/tex] Remember this...

[tex]\fbox{y2\;and\;y1\;are\;y-coordinates\;of\;the\;two\;points,\;and\;x2\;and\;x1\;are\;x-coordinates}}[/tex]

So we substitute the values and obtain:

[tex]\bf{\cfrac{7-8}{-9-(-6)}[/tex]

Simplifying:

[tex]\bf{\cfrac{-1}{-9+6}}[/tex]

Simplifying more:

[tex]\bf{\cfrac{-1}{-3}}[/tex]

Divide the top and bottom by -1:

[tex]\bf{\cfrac{1}{3}}[/tex]

There's the slope.

Hope it helps you out! :D

Ask in comments if any queries arise.

~Just a smiley person helping fellow students

En 2018 la empresa SAC-OLC fabrico 24000 ollas, si cada dia se fabricaron 80 ollas ¿cuantos dias no se trabajaron en la empresa?

Answers

Usando proporciones, hay que no se trabajaron en 65 dias durante el año de 2018 en la empresa SAC-OLC.

¿Qué es una proporción?

Una proporción es una fracción de la cantidad total, e los problemas pueden ser resolvidos con una regla de três.

En este problema, hay que se fabricaran 24000 ollas en el año de 2018, con una taja de 80 ollas al dia. Así, el número de dias trabajados es dado por:

n = 24000/80 = 300.

El año de 2018 tuvo 365 dias, así, el número de dias no trajados fue de:

365 - 300 = 65.

Puede-se aprender mas a cerca de proporciones es brainly.com/question/26950887

please help with all of question 5 ​

Answers

Volume of a right cone with base radius r cm and height h cm :

V = 1/3 π r² h cm³

Surface area :

A = (π r² + π r √(h² + r²)) cm²

Volume of a sphere with radius r cm :

V = 4/3 π r³ cm³

Surface area :

A = 4 π r² cm²

Volume of a cuboid with dimensions r cm × r cm × h cm :

V = r² h cm³

Surface area :

A = 2 r² + 4 r h

a. If the cone and sphere have the same volume, then

1/3 π r² h = 4/3 π r³   ⇒   h = 4r

b. If the area of the cuboid is 98 cm², then

2 r² + 4 r h = 98   ⇒   r (r + 2 h) = 49

c. Since h = 4r, substituting this into the equation from (b) gives

r (r + 8 r) = 9 r² = 49   ⇒   r² = 49/9   ⇒   r = 7/3

d. With r = 7/3, we have

h = 4 × 7/3 = 28/3

and so the volume of the cuboid is

V = (7/3 cm)² (28/3 cm) = 1372/27 cm³

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:

-3/2

Step-by-step explanation:

See attached image

Answer:

[tex]m=\frac{-3}{2}[/tex]

Step-by-step explanation:

m = slope
[tex]m=\frac{-4-5}{4--2}[/tex]  
[tex]m=\frac{-9}{6}[/tex]
[tex]m=\frac{-3}{2}[/tex]

Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina?

A.
The equation that represents this situation is t − 3 = 18. Tina is 21.
B.
The equation that represents this situation is t + 3 = 18. Tina is 15.
C.
The equation that represents this situation is 3 − t = 18. Tina is 21.
D.
The equation that represents this situation is -3 − t = 18. Tina is 15.

Answers

The equation which represents the situation and how old is Tina is "The equation that represents this situation is t − 3 = 18. Tina is 21".

How to write and solve equation?

Tina's age = tCole's age = t - 3Cole's age = 18

Equate Cole's age

t - 3 = 18

add 3 to both sides

t = 18 + 3

t = 21

Therefore, the equation which represents the situation and how old is Tina is "The equation that represents this situation is t − 3 = 18. Tina is 21".

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A bicyclist pedals 40 miles in 3 hours. Write the bicyclist's speed as a rate (but not a unit rate yet). Then use the dropdown menus to report the bicyclist's rate. Numerator (top of the fraction): [ Select ] [ Select ] Denominator (bottom of the fraction): [ Select ] [ Select ]

Answers

The bicyclist's speed as a rate is 40/3 miles per hour

How to determine the bicyclist's speed as a rate?

The given parameters are:

Distance = 40 milesTime = 3 hours

The rate is calculated as:

Rate = Distance/Time

Substitute known values

Rate = 40 miles/3 hours

Rewrite as:

Rate = 40/3 miles per hour

Hence, the bicyclist's speed as a rate is 40/3 miles per hour

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how to find the 3 sides

Answers

The angle of triangle are ∠A = 86, ∠B = 55, ∠C = 39. The side of the triangles are a = 0.99, b = 0.81, c = 0.62.

What is a law of sine?

Law of sines is a formula relating the length of the sides of a triangle to the angles of the triangle.

[tex]\dfrac{sin A}{a} = \dfrac{sin B}{b} = \dfrac{sin C}{c}[/tex]

We have given angles of the triangle as

∠A = 86

∠B = 55

∠C = 39

So,

[tex]\dfrac{sin 86}{a} = \dfrac{sin 55}{b} = \dfrac{sin 39}{c}[/tex]

Now,

a = 0.99

b = 0.81

c = 0.62

The side of the triangles are a = 0.99, b = 0.81, c = 0.62.

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100 points plus brainliest

Answers

Answer:

45 degrees

Step-by-step explanation:

so we know there is one 90 degree angle

and the other two angles are congruent

so the math would go like this

180-90=90

90/2= 45

(the 2 represents the two angles)

Answer:

x = 22.62°  (nearest hundredth)

Step-by-step explanation:

As this is a right triangle, we can use the cosine trigonometric ratio to find x.

[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]

where:

[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)

Given:

[tex]\theta=x[/tex]A = 12H = 13

Substitute the given values into the formula and solve for x:

[tex]\implies \cos(x)=\dfrac{12}{13}[/tex]

[tex]\implies x=\cos^{-1}\left(\dfrac{12}{13}\right)[/tex]

[tex]\implies x=22.61986495...^{\circ}[/tex]

[tex]\implies x=22.62^{\circ}\:\: \sf(nearest\:hundredth)[/tex]

The graph of a quadratic function passes through the points (0,-4) and (-2,0). what is a zero of the function

Answers

Answer:

-2

Step-by-step explanation:

the zero of the function is -2 because it's the root of the equation when y= 0

Which regular polygon has a rotation of 240 degree to carry the polygon onto itself?

Answers

The regular polygon that has a rotation of 240 degrees to carry the polygon onto itself is the equilateral triangle.

The missing part of the question

Options

Equilateral triangle

Octagon

Rectangle

Pentagon

How to determine the polygon?

A polygon that can carry itself onto itself after a rotation of 240 degrees must obey the following rule:

Angle of rotation = 360/Sides

Next, we test the options:

Option (a) equilateral triangle

Angle of rotation = 360/3

Evaluate

Angle of rotation = 120

Next, we list the multiples of 120

120, 240, 360.....

See that 120 is a factor of 240.

This means that the equilateral triangle would be rotated onto itself when rotated by 240 degrees.

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A flower bed in your yard is in the shape of a right triangle. The perpendicular sides of the bed measure 14 feet and 11 feet. Calculate the area of the flower bed.

Answers

The area of the flower bed is 77 square feet

How to determine the area?

The given parameters are:

Shape = TrianglePerpendicular sides = 14 feet and 11 feet

The area of the flower bed is calculated as:

Area = 0.5 * Product of perpendicular sides

So, we have:

Area = 0.5 * 14 * 11

Evaluate

Area = 77

Hence, the area of the flower bed is 77 square feet

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Carmen used a random number generator to simulate a survey of how many children live in the households in her town. There are 1,346 unique addresses in her town with numbers ranging from zero to five children. The results of 50 randomly generated households are shown below.

Children in 50 Households
Number of Children
Number of Households
0
5
1
11
2
13
3
10
4
9
5
2


Using a proportion, what can you infer about the number of households in her town that have more than three children?
About 242 households have more than three children.
About 269 households have more than three children.
About 296 households have more than three children.
About 565 households have more than three children.

Answers

About 296 households have more than three children. Then the correct option is C.

How to find that a given condition can be modeled by binomial distribution?

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

 

The expected value will be

E(X) = np

Carmen used a random number generator to simulate a survey of how many children live in the households in her town.

There are 1,346 unique addresses in her town with numbers ranging from zero to five children.

The results of 50 randomly generated households are shown below.

Children in 50 Households

Number of Children        Number of Households

             0                                          5

             1                                          11

             2                                        13

             3                                        10

             4                                         9

             5                                         2

Then the value of p and n will be

p = 11/50

n = 1346

Then the expected value will be

E(x) = (11/50) x 1346

E(x) = 296.12 ≈ 296

Then the correct option is C.

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Melissa rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total less than 12.

Answers

Answer:

It would be 35/36

Step-by-step explanation:

so if you did like 1+1, 1+2, 1+3....2+1,2+2, 2+3 yada yada

the only possible number combo that would equal twelve is 6+6 and there is 36 possible combos so your answer is 35/36

- a former algebra 2 student

5/8 of a number is 200. What is 7/10 of the number ?

Answers

Answer:

224

Step-by-step explanation:

Let x be the unknown number.

(5÷8)x = 200

Then

x = (8×200) ÷ 5

  = 1600 ÷ 5

  =320

……………………………

(7/10)x = (7/10)×320

           = (7×320) ÷ 10

           = 224

Answer:

= 224

Step-by-step explanation:

Hi there!, here is how we solve the problem;

To begin, the question wants us to determine

[tex] \frac{7}{10} [/tex]

of the number x (unknown).

[tex] \frac{5}{8} = 200 \\ \frac{8}{8} = x \\ ( \frac{ \frac{8}{8} \times 200 }{ \frac{5}{8} } ) \\ = \frac{8}{8} \times 200 \times \frac{8}{5} \\ = 320 \\ x = 320[/tex]

We have found our x = 320

Lets now determine

[tex] \frac{7}{10} [/tex]

Which is given by;

[tex]( \frac{7}{10} \times 320 \\ = 224[/tex]

[tex] \frac{7}{10} [/tex]

of the number is therefore 224.

= 224 <<<<<< Ans

I hope this helps.

Have a nice studies.

How many solutions are in 17x-8=3x+16

Answers

There is only one solution that satisfies the equation.
14x = 24
x = 24/14 = 12/7
17x-8=3x+16
-3x. | -3x.
———————-
14x-8=16
+8| +8
———————-
14x=24
——. ——. X=12/7 ______
14. 14. Or In decimal x=1.714285
5
Or x= 1 ——
7

H E L P M E P L I Z
In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.
23z+19=3(5z-9)+8z+46
15y+32=2(10y-7)-5y+46

Answers

The 2 equations are classified as Identities because both sides remain the same for all values of z.

How to Classify Equations?

1) We are given the equation;

23z + 19 = 3(5z - 9) + 8z + 46

Let us try z = 0

23(0) + 19 = 3(5(0) - 9) + 8(0) + 46

19 = -27 + 46

19 = 19

Let us try z = 5;

23(5) + 19 = 3(5(5) - 9) + 8(5) + 46

134 = 48 + 40 + 46

134 = 134

Thus, this is an identity as both sides remaining the same for all values of z.

2) We are given the equation;

15y + 32 = 2(10y - 7) - 5y + 46

At y = 0, we have;

15(0) + 32 = 2(10(0) - 7) - 5(0) + 46

32 = -14 + 46

32 = 32

Let us try y = 2;

15(2) + 32 = 2(10(2) - 7) - 5(2) + 46

62 = 26 - 10 + 46

62 = 62

This is an identity as both sides remaining the same for all values of z.

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1. Which is NOT a benefit of direct deposit? (1 point)

The money is available as soon as your employer makes the transfer.

You do not need to drive to the bank to make a deposit.

You can plan when you are paying bills.

You can avoid having a hold placed on when funds are available.

Answers

Answer:

d

Step-by-step explanation:

the statement "you can avoid having a hold placed on when funds are available is noat a benefit of the direct deposit

Which expression is equivalent to (x Superscript one-half Baseline y Superscript negative one-fourth Baseline z) Superscript negative 2?
StartFraction x Superscript one-half baseline Over y z squared EndFraction
StartFraction x Superscript one-half baseline Over y Superscript one-fourth Baseline z squared EndFraction
StartFraction y Superscript one-half Baseline Over x z squared EndFraction
StartFraction x z squared Over y Superscript one-half EndFraction
Submitted

Answers

By using exponent properties, we will get the simplified expression:

[tex]x^{-1}*y^{1/2}*z^2[/tex]

How to simplify the given expression?

Here we have the expression:

[tex](x^{1/2}*y^{-1/4}*z)^{-2}[/tex]

Remember the exponent properties:

[tex](a^n)^m = a^{n*m}[/tex]

And:

[tex](a*b)^n = (a^n)*(b^n)[/tex]

So using these two properties, we can rewrite:

[tex](x^{1/2})^{-2}*(y^{-1/4})^{-2}*(z)^{-2}\\\\(x^{-2*1/2})*(y^{-2*-1/4})*(z^{-2}})\\\\x^{-1}*y^{1/2}*z^2[/tex]

So we conclude that the completely simplified expression is:

[tex]x^{-1}*y^{1/2}*z^2[/tex]

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Answer:

C

Step-by-step explanation:

Distribute the -2 to the exponents of x, y, and z.

x: 1/2 * -2/1 = -2/2 = -1

y: -1/4 * -2/1 = 2/4 = 1/2

z: 1/1 * -2/1 = -2/1 = -2

Now to get a negative out of the exponents, you simply move them on the other side of the equation (If it is on top move, it to the bottom and vice versa.)

So, once you move all of the exponents you get C.

31 32 33 34
Which polynomial function could be represented by the graph below?
16
14
42
10
8-6
6 8 X
O f(x) = x³ + x² - 6x
O f(x)=x²-x² - 6x
4
1:00:00+
bocchette
ANLAT
K
C

Answers

The polynomial function that could be represented by the graph is f(x) = x³ + x² - 6x

How to determine the polynomial?

The attached graph represents the missing part of the question

From the attached graph, the x-intercepts of the graph are:

x1 = -3

x2 = 0

x3 = 2

The equation of the graph is then calculated as:

f(x) = (x - x1)(x - x2)(x - x3)

This gives

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

Expand

f(x) = x(x² + 3x - 2x - 6)

Evaluate

f(x) = x(x² + x - 6)

Expand

f(x) = x³ + x² - 6x

Hence, the polynomial function that could be represented by the graph is f(x) = x³ + x² - 6x

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PLEASE HELP ME!!!!!!!!!!!!!!!

Answers

Answer:

hypotenuse(h)^2 = 3^2 + 7^2

h^2 = 9 + 49

h = √58

h = 7.6

Find the midpoint of A and B where A has coordinates (2, 3)
and B has coordinates (8, 9).

Answers

Step-by-step explanation:

Solution,Given,Coordinates of A and B are (2,3) and(8,9) respectively. Let A(2,3)= (x1,y1) and B(8,9)=(x2,y2)Midpoint of AB(m)=?Now,using midpoint formulam= {(x1+x2)/2 ,(y1+y2)/2}or m= {(2+8)/2,(3+9)/2}.°. m=(5,6)

Answer:Mxy= [(Xa+Xb/2);(Ya+Yb/2)]

=(2+8/2);(3+9/2)

Midpoint= (5, 6)

Step-by-step explanation:

Please help me!!!! I would really appreciate it!!!

Answers

Answer:

x=-(7 [tex]\pm i\sqrt(7)[/tex])

Step-by-step explanation:

A bakery sold a total of 400 cupcakes in a day, and 43% of them were vanilla flavored. how many of the cupcakes sold that day were vanilla flavored?

Answers

The number of the cupcakes sold that day that were vanilla flavored is 172.

How do we calculate a number from a percentage?

The number of the cupcakes sold that day that were vanilla flavored can be calculated using the following formula:

Number of vanilla flavored cupcakes sold = Total number of cupcakes sold * Percentage that were vanilla flavored .............. (1)

Substituting the relevant values into equation (1), we have:

Number of vanilla flavored cupcakes sold = 400 * 43% = 172

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Express in simplest radical form.

5x√192x³+√3x5

please help!!

Answers

[tex]-5x\sqrt{192x^3} + \sqrt{3x^5}\\\\=-5x\left(192x^3 \right)^{\tfrac 12} + \left(3x^5 \right)^{\tfrac 12}\\\\=-5\cdot (192)^{\tfrac 12} \cdot x \cdot x^{\tfrac 32} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-5\left( 64 \cdot 3 \right)^{\tfrac 12} \cdot x^{1+\tfrac 32} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-5\cdot 8\cdot 3^{\tfrac 12} \cdot x^{\tfrac 15} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-40\cdot 3^{\tfrac 12} \cdot x^{\tfrac 52}+3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\[/tex]

[tex]=-39\cdot 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-39\sqrt 3 \sqrt{x^5}[/tex]

A rescue mission is being conducted using a plane to drop supplies and medical personnel. A helicopter
is also sent from the same base station to rescue wounded persons. If the plane flies 400 mph, the
helicopter flies 200 mph, and they leave at the same time, how far away is the rescue site if the
helicopter arrives 1 hour after the plane arrives?
If t represents the time that the plane flies, which of the following equations could be used to solve the
problem?
400/t = 200/(t+1)
400t = 200(t+1)
400t = 200t+1

Answers

400 miles away is the rescue site if the helicopter arrives 1 hour after the plane arrives and the expression 400t = 200(t + 1) represents the  time that the plane flies option second is correct.

What is distance?

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

We have:

A helicopter is sent from the same base station to rescue wounded persons. If the plane flies 400 mph, the helicopter flies 200 mph, and they leave at the same time.

Let's suppose the plane takes t hours

We know,

Distance = speed×time

400×t = 200(t + 1)

or

400t = 200(t + 1)

After solving we get:

t = 1 hour

Distance = 400×1 = 400 miles

Thus, 400 miles away is the rescue site if the helicopter arrives 1 hour after the plane arrives and the expression 400t = 200(t + 1) represents the  time that the plane flies option second is correct.

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Find the equation of the line shown.
y
X
0 1 2 3 4 5 6 7 8 9 10
10
987654321

Answers

Answer:

  y = 2x

Step-by-step explanation:

The graph is of a straight line through the origin. Its slope can be determined from the grid points it passes through. That slope will be the constant of proportionality for the proportion represented.

__

When the graph is a line through the origin, it is a representation of a proportion that can have the equation ...

  y = kx

where k is the constant of proportionality, also the slope of the line.

The value of k will be the y-value when x=1. Reading from the graph, we find the line goes through point (1, 2), so y = 2 when x = 1. That means k = 2 and the equation of the line is ...

  y = 2x

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