Determine if each table of data represents a quadratic function by finding the second differences. T First Difference Second Difference
I need help urgently D:

Answers

Answer 1

The data table doesn't depict a quadratic function based on the given numbers.

Describe the quadratic function?

A polynomial function with the form f(x) = ax² + bx + c, where a, b, and c are constants and an is not equal to zero, is said to be quadratic. A quadratic function's graph is a parabola, a U-shaped curve.

The parabola's shape is determined by the coefficient a, with a > 0 producing an upward-opening parabola and a 0 producing a downward-opening parabola.

In this instance, taking the first differences of the function and then taking the first differences of those differences will allow us to determine if a function is quadratic or not using second differences (the second differences). In the event where the second differences are constant, the function is quadratic. The differences in this instance aren't constant.

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Answer 2

The first table represents a quadratic function, and the second table does not represent a quadratic function.

Describe Quadratic Function?

A quadratic function is a function that can be written in the form f(x) = ax² + bx + c, where a, b, and c are constants (coefficients) and x is the variable. The graph of a quadratic function is a parabola, which is a U-shaped curve.

The coefficient a determines the shape of the parabola. If a > 0, the parabola opens upwards and has a minimum value. If a < 0, the parabola opens downwards and has a maximum value. The vertex of the parabola is the point where the parabola changes direction and is given by the formula (-b/2a, f(-b/2a)).

The coefficient b determines the position of the vertex and the direction in which the parabola opens. If b > 0, the vertex is to the left of the y-axis and the parabola opens to the right. If b < 0, the vertex is to the right of the y-axis and the parabola opens to the left.

To determine if each table of data represents a quadratic function, we need to find the second differences. If the second differences are constant, then the function is quadratic. If the second differences are not constant, then the function is not quadratic.

For the first table:

x f(x) 1st diff. 2nd diff.

2 13 2 2

4 15 7 2

6 22 12 2

8 34 17 2

10 51 22 2

12 73

The second differences are all equal to 2, so the function is quadratic.

For the second table:

x f(x) 1st diff. 2nd diff.

1 7

2 15 8

3 26 11 3

4 41 15 4

5 60 22 5

6 82 32 7

7 107 42 8

8 135 58

The second differences are not constant, so the function is not quadratic.

Therefore, the first table represents a quadratic function, and the second table does not represent a quadratic function.

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Related Questions

which fraction has an equivalent decimal value that repeats

$which fraction has an equivalent decimal value that repeats$

Answers

Answer:

The answer is 2/3

Step-by-step explanation:

2/3 = 0.6666666666... with it repeating forever

Answer:

2/3

Step-by-step explanation:

The answer you selected is correct.

The decimal form of 2/3 is 0.66666666 (it repeats forever), unlike the other three:

3/4 = 0.75

4/5= 0.80

7/8= 0.875

PLEASE HELP ASAP THANKS IN ADVANCE

Answers

Answer:

the answer to the question is "C"

(SAT PREP) Find the value of x in each of the following excersises

Answers

Answer:

The answer is 155.

Step-by-step explanation:

We can find the remaining parts of the triangle angles.

A humpback whale was 270 meters north of Billet Bay, swimming south at a constant velocity. If it swam one-third of the distance to the bay in 2 minutes, what was the whale velocity?

Answers

EXPLANATION

Let's see the facts:

-Whale swimming: 270 meters

rate [2 min]---> 1/3 distance in 2 minutes

rate will be:

[ANSWER] 270 meters * 1/3 * 1/2 minutes = 45 meters/min

Plz help I need help

Answers

Answer:

a is 4 because 4 x 16=20 i hope this help

Answer :

a + 16 = 20

a = ?

a = 20 + 16

a = 36

a = 36 ✔️

Bandhan Bank employee salary after 10 years

Answers

Answer:

- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries

I was told to put the x value in parenthesis before you square it. can you help?

Answers

We have to solve the quadratic equation.

That means that we have to find the roots of it.

The quadratic equation is:

$\begin{gathered} 2x^2-4x-12=0 \\ 2(x^2-2x-6)=0 \\ x^2-2x-6=0 \end{gathered}$

Then, we apply:

$\begin{gathered} x=\frac{-b}{2a}\pm\frac{\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-2)}{2\cdot1}\pm\frac{\sqrt[]{(-2)^2-4\cdot1\cdot(-6)}}{2\cdot1}=\frac{2}{2}\pm\frac{\sqrt[]{4+24}}{2}=1\pm\frac{\sqrt[]{28}}{2}=1\pm\sqrt[]{\frac{28}{4}} \\ x=1\pm\sqrt[]{7} \end{gathered}$$\begin{gathered} x_1=1+\sqrt[]{7}\approx1+2.6=3.6\approx4 \\ x_2=1-\sqrt[]{7}\approx1-2.6=-1.6\approx-1.5 \end{gathered}$

With the rounded values of the roots, Option B is the answer.

Measures of Variation, Standard Deviation, Population Variance, Population. Can someone help?

Answers

To solve this problem one must be aware of the concepts of standard deviation and variance of raw data.

There is a direct formulae to calculate the variance of the data,

Variance = $σ^{2} =\frac{Sigma(xi-m)^{2}}{n}$

Now here we need to verify ∑x and ∑$x^{2}$.

∑x = 21+19+15+32+27

= 114

and ∑$x^{2}$ = $21^{2} +19^{2} +15^{2} +32^{2} +27^{2}$

= 441+361+225+1024+729

= 2780

So, the given relation is true.

Now the variance of the given data by putting the values in the formulae is equal to 45.2.

And Standard deviation=$\sqrt{Variance}$

= $\sqrt{45.2}$

= 6.72

And for population α²=36.16 and deviation=6.01.

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Tonya’s dog-walking service charges a flat rate of $20 per month, plus $3 per mile that each dog is walked. Beth does not charge a monthly fee for her dog-walking service, but she charges $5 per mile that each dog is walked. Write and solve an equation to find the number of miles m for which Tonya and Beth would charge the same amount.

Answers

Answer:

Ten miles

Step-by-step explanation:

Use this inequality

20 + 3m = 5m

act of transferring information from one place, person or group to another.

Answers

Answer:

Communication

Step-by-step explanation:

Communication is a way for people to transfer information to a place, another person, or a group.

Answer: The answer is "Communication"

Step-by-step explanation: Communication is transferring info from one to another.

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 20 N acts on a certain object, the acceleration of the object is 5 /ms2. If the force is changed to 16 N, what will be the acceleration of the object? /ms2

Answers

The acceleration of the object when the force on the object changes to 16 N is 4 m/s²

What is the basic formula for force?

The second law of motion by Newton says that the force is equal to the change in momentum per change in the time. For a constant mass, force equals the mass times acceleration, i.e. F = m x a.

Given here: A force acting on an object.

We know, The formula for force states that the force is equal to mass that is multiplied by the acceleration.

Thus we have the equation as F=m.a

Now in case 1 we have

20=m×5

m=4 kg

Again in case 2 we have

16 = 4×a

a=4 ms⁻²

Hence, The acceleration of the object when the force on the object changes to 16 N is 4 m/s²

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

Answers

The expression 1 2/5 + 2 2/3 using fifteenths is 3 + 6/15 + 10/15

How to rewrite the expression using fifteenths

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

1 2/5 + 2 2/3

3 + 2/5 + 2/3

To rewrite the expression using fifteenths, we multiply the numerator and the denominator of the fractions by the same number

In this case, we use 3 and 5

So, we have

3 + 2/5 * 3/3 + 2/3 * 5/5

Evaluate the products

3 + 6/15 + 10/15

Hence, the expression using fifteenths is 3 + 6/15 + 10/15

Answers

Answer:

third one m=6 and n=-4/3

Answer:

m=-3/8 n=12

Since n is a whole number, the only whole number value for n in the possible answers is 12

A tree initially measured 18 feet tall over the next 3 1/2 years it grew to a final height of 35 1/2 feet during those 3 1/2 years what was the average yearly growth rate of the height of the tree

Answers

Answer:

35.5 minus 18 is 17.5

17.5 divided by 3.5 is 5

the average growth during the last 3 1/2 years was 5 feet, each year

Write the phrase as an expression. Six more than three times a number w. An expression for this phase is..?

Answers

Answer:

6+3x=w

Step-by-step explanation:

6 *more* more always means +

and then three *times* times always means *

so it would equal 6+3x=w

3. What is f-3) if f(x) = 2x – 11 – 5? (

Answers

$\huge{\green{\underline{\underline{\bf{\orange{ANSWER:-}}}}}}$

$\longrightarrow\tt{f(x) = 2x - 11 - 5} \\ \\ \longrightarrow\tt{f( - 3) = 2( - 3) - 11 - 5} \\ \\ \longrightarrow\tt{f( - 3) = - 6 - 11 - 5} \\ \\ \longrightarrow\tt{f( - 3) = - 22}$

f(x) = 2x−11−5

= f(−3) = 2(−3)−11−5

= f(−3) = −6−11−5

= f(−3) =−22

(4,2),(-6-6) what’s the answer

Answers

Answer:

what are we finding

Are we to derive an equation of a straight line

The table shows the derivation of sin(2x). Select the
correct reason for each step.
Reason 1 is
Reason 2 is
Reason 3 is

Answers

Answer:

Reason 1 is: Addition

Reason 2 is: Sine Sum Identity

Reason 3 is: Simplify

Step-by-step explanation:

The table shows the derivation of sin(2x). Select thecorrect reason for each step.Reason 1 isReason 2

The Reason 1, Reason 2, and Reason 3 are Addition, Sine Sum Identity, and Simplify.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

= sin2x (given)

= sin(x + x) (sine sum property)

= sinx cosx + cosx sinx

= 2sinx cosx

Thus, the Reason 1, Reason 2, and Reason 3 are Addition, Sine Sum Identity, and Simplify.

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Summarizing allows you to focus on the important information by finding the introduction, topic sentence and
conclusion.
Please select the best answer from the choices provided
True or false

Answers

True. Summarizing allows you to focus on the important information by finding the introduction, topic sentence and conclusion.

Importance of summary

Summarizing is a technique that helps to distill the main points of a text by identifying the introduction, topic sentence, and conclusion. It involves condensing the information to focus on the most important aspects and omitting unnecessary details.

This process enables the reader to grasp the core message of the text quickly and efficiently.

By summarizing, one can communicate the key ideas in a concise and clear manner, making it easier for others to understand and engage with the information presented.

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What is the quotient ? -4/2 divided by 2

Answers

Answer:

$\frac{-\frac{4}{2} }{2} =-\frac{4}{2} *\frac{1}{2} =-\frac{4}{4} =-1$

Calcular los 3/5 de los 2/3 de las 3/4 de 560

Answers

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

How to solve fractions?

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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A city survey of two neighborhoods asked residents whether they would
prefer a new playground or a dog park. The survey data are shown in the
relative frequency table.
Playground
Dog park
Total
Hill Point
0.40
0.17
0.57
Northlake 0.18
0.25
0.43
Total
0.58
0.42
1.0
What percentage of the Northlake residents surveyed want a new dog park?
A. About 60%
B. About 58%
C. 25%
D. 42%

Answers

Using the proportions given in the table, it is found that the percentage of the Northlake residents surveyed that want a new dog park is:

B. About 58%.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Multiplying a proportion by 100%, a percentage is found.

Looking at the table, 25% are Northlake residents(which is 43% of the surveyed) who want a new dog park, hence the percentage is given by:

p = 25/43 x 100% = 58%.

Hence option B is correct.

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Find the product using formula ...

formula = ( a + b ) ( a - b )

a) 1.2 × 2.8

Answers

Step-by-step explanation:

1.2 × 2.8

(2 - 0.8 )(2 + 0.8)

2² - (0.8)²

4 - 0.64

3.36

Solution:

$1.2 \times 2.8 \\ = (2 - 0.8)(2 + 0.8) \\ = {(2)}^{2} - {(0.8)}^{2} \\ = 4 - 0.64 \\ = 3.36$

Answer:

3.36

Hope it helps.

Do comment if you have any query

The American Population is living longer. Along with the longevity of life comes additional challenges with both medical and Psychiatric problems. Your patient is about to be discharged from a short-tern rehab center. You overhear the daughter confiding in the nursing student that she cannot handle her mother and will be looking for a Memory care unit to put her mother in. You also hear the student nurse who was raised in a foreign country state, " I would NEVER put my mother in a home. I would take care of her woth my two sisters junti she dies.

what considerations might you make withthis students. Address the cultural differneces in elder care and adress the conself od "Role Strain" in caring for special populations.

Answers

Cultural sensitivity is crucial in elder care. Cultural beliefs impact elderly care. A foreign-raised nursing student desires to care for her mother and sisters until her mother's passing.

What is the cultural Strain?

Consider cultural values: Students from certain backgrounds may see caring for their elderly parents as a moral duty. Respecting elder beliefs is critical in discussing care options. Have open, non-judgmental communication with the nursing student. Show empathy and listen to her perspective.

Educate the nursing student about caring for a loved one with medical and psychiatric problems. Explain physical, emotional, and financial consequences, including effects on relationships and responsibilities.

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This year you earned $75,500. Last year you earned $72,400. What was the rate of change on your earnings since last year

Answers

Answer:

4.28%

Step-by-step explanation:

We Know

Last year you earned $72,400

This year you earned $75,500

What was the rate of change in your earnings since last year?

We Take

(75,500 ÷ 72,400) x 100 ≈ 104.28%

Then We Take

104.28 - 100 = 4.28%

So, the earning increased by about 4.28%.

A farmer has 30 boxes of eggs. There are 6 eggs in each box. Write, as a ratio, the number of eggs in three boxes to the total number of eggs Give your answer in its simplest form.

Answers

Answer:

1:10

Step-by-step explanation:

30 boxes = 180 eggs

3 boxes = 18 eggs

18:180 = 1:10

Using the numbers 4.3, -1.07, and -2.971, write an expression containing both addition and subtraction that simplified to a positive number.

Answers

Answer:

4.3 + (-1.07)+(-2.971)

Step-by-step explanation:

4.3 + (-1.07)+(-2.971)

4.3 -1.07-2.971

4.3 - 4.041= 0.259

True or false
-y = -112 + 4; (0, -4)

Answers

Answer:

False

Step-by-step explanation:

m.
x-intercept =
1/2
and y-intercept = 3
Write an equation for the line in point-slope form and in slope-intercept form

Answers

Answer:

slope intercept form: y= -6x+3

point slope form: y-0= -6(x -1/2)

Step-by-step explanation:

point slope form: y - y1 = m(x - x1)

substitute the values y-0=-6(x-1/2)

slope intercept form:

find the slope using two given points

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

= (3 - 0) / (0 - 1/2)

= 3 / (-1/2)

= -6

substitute into equation

y= -6x+3

{x|x + 1 ≥ 3 and x − 6 ≤ −1}

Write the solution using interval notation

Answers

Solution down below.

{x|x + 1 3 and x 6 1}Write the solution using interval notation

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Determine if each table of data represents a quadratic function by finding the second differences. T First Difference Second DifferenceI need help urgently D:​

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Determine if each table of data represents a quadratic function by finding the second differences. T First Difference Second Difference
I need help urgently D: