please answer this question ​

The term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.

Given,

In the question:

The quadratic sequence is :

3, 11, 25, 45, ...

To find the nth term of the quadratic sequence.

Now, According to the question;

The first term of the sequence is 3, the second term is 11, the third term is 25, and the fourth term is 45.

The difference between the first and second terms can be calculated as follows:

11-3 = 8

The difference between the second and third terms can be calculated as follows:

25-11 = 14

The difference between the third and fourth terms can be calculated as follows:

45-25 = 20

The sequence is expressed as follows:

3,3+8,11+11,25+20,...

The difference between consecutive terms expands by 6.

Use the principle of mathematical induction.

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

= 3n(n+1)

The sequence's nth term can be calculated as follows:

term = 3n(n+1) - 4n + 1

             = 3n² - n + 1

Hence, the term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.

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They won 168/11 games.

From the question, we have

Ratio = 3:8

team played = 56 games

Won = 56*3/11

=168/11

=15.27

Divide:

Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.

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Answer: 12%

Step-by-step explanation:

Answer: 12%

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

Answer: rotate 180° and translate down.

Step-by-step explanation:

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Rotating angle 1 by 180° would leave it in the position of angle 4. From there, you can translate it directly down onto angle 8. This will prove congruency.

The number of cheese produced in 2006 is 7.8 thousand

The number of cheese produced in 2014 is 9.8 thousand

The given equation that models the growth of cheese is known as an exponential equation. An exponential equation is a non-linear equation.

The given exponential equation is y = 7.1(1.03)^x

Where:

Number of cheese produced in 2006 = 7.1(1.03)^3 = 7.8 thousand

Where x = 2006 - 2003 = 3

Number of cheese produced in 2014 = 7.1(1.03)^11 = 9.8 thousand

Where x = 2014 - 2003 = 11

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The value of x when QR is a midsegment of triangle BCD is 11 units.

According to the question,

We have the following information:

QR is a midsegment of triangle BCD.

Now, we know that the length of midsegment of any triangle is equal to half of the length of side corresponding to the midsegment.

So, we have the following expression:

QR = BD/2

Putting the values of QR and BD from the figure:

x-2 = (x+7)/2

Using the cross multiplication method:

2x-4 = x+7

Moving x from the right hand side to the left hand side:

2x-x = 7+4

x = 11 units

Hence, the value of x when QR is a midsegment of triangle BCD is 11 units.

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Using the equation of the model:

a. 7.8 billions of pounds

b. 9.8 billions of pounds.

In the above problem given, the equation, y = 7.1(1.03)^x models the cheese production in the country, where:

a. 2006 after 2003 is 3 years. Substitute x = 3 into the equation, y = 7.1(1.03)^x:

y = 7.1(1.03)^3

y = 7.8

Total cheese produced in 2003 was about: 7.8 billions of pounds

b. 2014 after 2003 is 11 years. Substitute x = 11 into the equation, y = 7.1(1.03)^x:

y = 7.1(1.03)^11

y = 9.8

Total cheese that would be produced in 2014 will be about: 9.8 billions of pounds.

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A simple random sample of size n from a finite population of size n is a sample selected such that each possible sample of size the same probability of being selected.

As we know that,

A selection of participants from a population are chosen at random by the researcher using simple random sampling, a sort of probability sampling. Every person in the population has the same chance of being chosen.

So n has the same probability of being selected.

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The right question is

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size

n has a probability of 0.5 of being selected.

n has the same probability of being selected.

N and n have the same probability of being selected.

n has a probability of 0.05 of being selected.

As previously stated, a system will not be stable if its eigenvalues have any non-negative real parts, the system will be unstable if an eigenvalue has no imaginary part and is equal to zero. A trivial instance of the complex eigenvalue with a zero component exists here.

When both eigenvalues are zero, what takes place?

A zero eigenvalue implies the network being referred to is particular.The null space of the matrix is based on the eigenvectors that correspond to the zero eigenvalues.

When one eigenvalue is zero, what does this mean?

If and only if A is not invertible, then the number 0 is an eigenvalue of A.

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Answer:

Joe has 6 $5 bills and 4 $1 bills.

Step-by-step explanation:

Joe has 10 bills, $1 and $5, so:

Joe has a total of $34, so:

Substitution can be used between the two equations to achieve the answer.

Answer:

Step-by-step explanation:

330

Answer:

0.84

Step-by-step explanation:

23.35 divided by 27.65 = 0.84448462929

Rounded to the first 2 decimal places would be:

0.84

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Answer:

Step-by-step explanation:

[tex]\frac{23.35}{27.65} \approx{0.84}\\[/tex]

The constants that we have to multiply to eliminate one variable from the system are 12 and 5.

The equations are

5x+13y = 232

12x + 7y = 218

Here we can cancel both x term and y terms, lets choose x terms  and apply the elimination method

The coefficient of x in first equation is 5 and 12 in second equation

We have to make it same

Prime factorization

5 = 5×1

12 = 2×2×3

LCM (5, 12 ) = 2×2×3×5 = 60

Multiply the first equation by 12 and second equation by 5

60x + 156y = 2784

60x + 35y = 1090

Subtract equation 2 from equation 1

121y = 1694

Here we have eliminated x term

Hence, the constants that we have to multiply to eliminate one variable from the system are 12 and 5.

The complete question is:

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? 5x + 13y = 232

12x + 7y = 218

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188.4 cm²  is the surface area of the cone .

What is known as a cone?

given   r = 4 cm

           l = 15 cm

the curved surface area = πrl

                                     = 3.14 * 4 * 15

                                      = 188.4 cm²

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Answer: 76 cm2

Step-by-step explanation:

I Did it trust

The slope of the line of best fit, where x represents the average daily temperature and y represents the total ice cream sales, is of:

1.4.

The line of best fit is obtained inserting the points of data, given either in a table or in a scatter plot, in a linear regression calculator.

The format of the line of best fit is the same as of a standard linear function, as follows:

y = mx + b.

In which the parameters are given as follows:

For this problem, the points are given as follows:

(56.1, 107), (60.3, 116), (64.2, 120), (66.4, 122), (71.3, 125), (73.9, 130), (74.2, 132), (75.2, 135), (80.2, 141), (84.8, 151).

Inserting these points into a calculator, the equation is presented as follows:

y = 1.4x + 26.8.

Hence the slope of the function is of:

m = 1.4.

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Answer:

40

Step-by-step explanation:

8x4 is 32 and to find a triangle is Length x Hight devided by 2.

Answer:

Step-by-step explanation:

0.75

hope this helps

Answer:

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

[tex]x(x^{2}[/tex] + [tex]5)[/tex]

Step-by-step explanation:

[tex]Factor ( x^{3}[/tex] + [tex]5x )[/tex]

[tex]x^{3}[/tex] + [tex]5x[/tex]

= [tex]x(x^{2}[/tex] + [tex]5)[/tex]

Hope this helps! :)

M = 5 - 4i

J = 3 + 2i

J* = -3 + 2i (Conjugate)

Therefore M + J*

= (5 + -3) + (-4i + 2i)

= 2 - 2i

Answer:

D -6x + 2 = -15

Step-by-step explanation:

-4(3/2 x - 1/2) = -15

-4 × 3/2 x + (-4) × (-1/2) = -15

-6x + 2 = -15

Answer: D -6x + 2 = -15

Angle between hour hand and minutes hand is 60 degrees.

What is angle ?

An angle is a shape created by two rays or lines that have a shared termination.

Main Body:

As a clock is complete circle , total angle created by it is 360 degrees.

Numbers of hours in a clock = 12

Angle created by 1 hour = total angle / total no. of hours

                                        = 360/12

                                        = 30 degrees.

Now according to the question total hours = 2

multiplying 2 with degrees between 1 hour hand and minute hand.

Hence total angle created by hour and minute hand id 60 degrees.

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By factoring the polynomial function, G(W) = -125w² +180 we get w = 1.2.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. f(x) = anxn + anxn+1 +... + a² + a¹x + a⁰ is the formula for a polynomial. The greatest power of x in an expression is the polynomial's degree. Polynomials of degree 0, 1, 2, 3, and 4 are constant (non-zero) polynomials, linear polynomials, quadratics, cubics, and quartics, respectively.

Given,

Polynomial function,

-125w² + 180 = 0

-125w² = -180

w² = 180/125

w² = 1.44

Squaring,

w = √1.44

w = 1.2

By factoring the polynomial function, G(W) = -125w² +180 we get w = 1.2.

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If Jacqueline bought a bicycle at wholesale cost for $210 dollars. If the bicycle is normally $300 from the local bike shop, Then 30% markup the bike shop adds to the wholesale cost

Percentage, a relative value indicating hundredth parts of any quantity.

Given,

Jacqueline bought a bicycle at wholesale cost for $210 dollars.

The actual price of bicycle is normally $300 from the local bike shop.

We need to find the percent markup the bike shop adds to the wholesale cost.

For this we need to find the difference and we have to divide it by actual price

300-210/300=90/300=0.3

Now multiply 0.3 with 100 as hundredths to get the percentage value

0.3×100=30

Hence 30 percent markup the bike shop adds to the wholesale cost

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Answer: constant of proportionality

Explanation: Assuming that we have two proportional quantities; one is x and one is y. If you know whether the relationship between them is direct or inverse proportion, then the ratio of the two quantities y/x gives us a constant generally known as the constant of proportionality.

Answer:

The image point of (4,0) after the rotation of 90° counterclockwise about the origin is (-4,0)

Answer:

496,320 feet

Step-by-step explanation:

94 miles x [tex]\frac{5280 feet}{1 mile}[/tex] = 496320 feet

Ratio is always written as x/y where y can never be zero.

Grams of flour needed for every 200200200 and grams of sugar = 300300300 grams

The equation that represents how many grams of flour we need for some grams of sugar is fff = 222/333

Let’s assume fff as grams of flour and sss as grams of sugar.

So, the ratio for grams of flour:grams of sugar will be,

= fff:sss = 200200200:300300300

Hence, fff = 222/333 × sss

Ratio is a comparison between two things where it tells how much one thing contains the other thing.

Hence the answer is, Ratio is always written as x/y where y can never be zero.

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Answer:

your equation is f = 3/2s   so you're going to have to need 750 grams of flour for 500 grams of flour