Which of the following is a Recursive Formula for an Arithmetic Sequence?

The Piecewise -Defined function and how it is graphed is given below..

Given the function in the attached image,

See the attached Graph for better understanding.

Learn more about Piecewise -Defined function:
https://brainly.com/question/18859540
#SPJ1

If A and B are similar matrices and v is an eigenvector of A, then v is also an eigenvector of B , similarly if u is an eigenvector of B then u is also eigenvector of A.

Suppose A and B are n×n matrices over R or C. We say A and B are similar, or that A is similar to B, if there exists a matrix P such that B =P⁻¹AP.

The eigenvalues are the roots of the

characteristic polynomial.

B =P⁻¹AP ⇔ PBP⁻¹ = A

If Av = λv , then PBP⁻¹v = λv ⇒ BP⁻¹v = P⁻¹λv

So, if v is an eigenvector of A, with eigenvalue λ, then P⁻¹v (which is non-zero since P is invertible) is an eigenvector of B with the same eigenvalue. If u is an eigenvector for B then P⁻¹v is an eigenvector for A. So, every eigenvalue of A is an eigenvalue of B and since you can interchange the roles of A and B in the previous calculations, every eigenvalue of B is an eigenvalue of A too. Hence, A and B have the same eigenvalues.

To learn more about Eigenvector and eigen values, refer:

https://brainly.com/question/14406572

#SPJ4

The circumference of the given circle is 41 cm

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

The circumference of a circle is the boundary length of the circle, it is basically the perimeter of the circle, in degree measure it can not exceed by 360°

Given that, a circle, with diameter, 13 cm, we need to find it circumference.

We know that, the circumference of a circle is given by,

Circumference of the circle = π × diameter

= 3.14 × 13

= 40.82

≈ 41 cm

Hence, the circumference of the given circle is 41 cm

Learn more about circles, click;

https://brainly.com/question/29142813

#SPJ9

Answer:

Step-by-step explanation:

30 minutes UoU

Every 10 minutes he finishes 20% of the book case.

so In 10 minutes he will have 50% done, In 20 minutes 60%, in 40 minutes 100%

Answer:

9

Step-by-step explanation:

3x^2 + 3x - 9

Substitute x = 2 into the equation.

3(2)^2 + 3(2) - 9

3(4) + 6 - 9

12 + 6 - 9

18 - 9 =

9

Answer:

the first

Step-by-step explanation:

there two lones

Answer:

2 rays that meet at an endpoint.

Step-by-step explanation:

Looking at the picture, I can see two rays (since they only point in one direction) meeting at an endpoint. As a result, that forms the figure shown the best of the 4 choices.

The length of side x is approximately 24.87, rounded to the nearest hundredth.

how can we find side of the triangle?

To find the length of side x, we can use the sine function, which relates the opposite side to an angle to the hypotenuse:

sin(11°) = opposite side/hypotenuse

Rearranging this equation, we get:

opposite side = sin(11°) * hypotenuse

We know that the hypotenuse has a length of 130, so we can substitute that in:

opposite = sin(11°) * 130

Using a calculator, we can evaluate sin(11°) to be approximately 0.1919, so we can substitute that in as well:

opposite = 0.1919 * 130

Simplifying this expression, we get:

opposite ≈ 24.87

Therefore, the length of side x is approximately 24.87, rounded to the nearest hundredth.

To know more about hypotenuse:

https://brainly.com/question/12006293

#SPJ1

The number of children in Monocity is 21,000.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

Given that population of Newtown is 45000.

The population of Villeneuve = 39000.

(a) the ratio of these populations

45000: 39000

45: 39

15: 13

(b) In Newtown, 28% of the population is below the age of twenty then it would be;

28% of 45000

28% x 45000 = 12600

(c) In Villeneuve, 16,000 people are below the age of twenty then the percentage of people in Villeneuve below the age of twenty will be;

16,000 /39000 x 100

= 41 %

(d) The population of Newtown is 125% greater than it was fifty years ago then the population of Newtown fifty years ago will be;

125% of 45000

1.25 x 45000

= 56250

Thus, 56250 + 45000  = 101250

(e) In Monocity the ratio of men: women : children is 12:13:5

Total = 45000  + 39000 = 84000

Therefore, the number of children in Monocity is

84000 = 20p

p = 4200

Then 4200 x 5 = 21,000

The number of children in Monocity is 21,000.

Learn more about the ratio here:

brainly.com/question/13419413

#SPJ2

Answer:

1222

Step-by-step explanation:

312/12 = 26

So, you have to multiply y (47) by 26

This will get you 1222

Answer:

1222

Step-by-step explanation:

12/312 = 47/x

X=1222

Applying the congruent chords theorem, the value of x is: 7.

Length of segment LP is: 6 units.

In geometry, a chord is defined as the line segment that joins two points on the circumference of a circle.

In a circle, if two chords are congruent, then they are equidistant from the center of a circle, according to the congruent chords theorem.

In the circle given, chords JK = LM = 12 units. This means both chords are congruent, therefore, they are equidistant from the center of the circle S.

According to the congruent chords theorem, NS = PS, thus:

8 = 2x - 6

8 + 6 = 2x

14 = 2x

Divide both sides by 2

14/2 = 2x/2

7 = x

x = 7

LP = 1/2(12)

LP = 6 units.

In summary, applying the congruent chords theorem, the value of x is: 7.

Length of segment LP is: 6 units.

Learn more about the congruent chords theorem on:

https://brainly.com/question/7511582

#SPJ1

The sample mean is more accurate and precise than the sample midrange because it takes all the values in the sample into consideration, while the sample midrange only takes into consideration the highest and lowest values.

The sample mean is generally preferred over the sample midrange as an estimator of the population mean because it is more accurate and provides a more precise estimate of the population mean. The sample mean is the average of all the values in the sample, and it is calculated by adding all the values in the sample and then dividing by the number of values. Mathematically, the sample mean is represented as μ = ( ΣX ) / N, where ΣX represents the sum of all the values in the sample and N is the number of values in the sample. On the other hand, the sample midrange is simply the midpoint between the highest and lowest values in the sample, and it is calculated by adding the highest and lowest values and dividing by two. The sample mean is more accurate and precise than the sample midrange because it takes all the values in the sample into consideration, while the sample midrange only takes into consideration the highest and lowest values.

Learn more about sample here:

https://brainly.com/question/15659544

#SPJ4

1. The velocity at time t , v(t) = (18t² + 3 ) m/s

2. The velocity at time t = 3 seconds = 165 m/s

3. The acceleration at time t, a(t) =( 36t )m/s²

4. The acceleration at time t = 3 seconds = 108 m/s²

The quantity that tells us how fast an object is moving anywhere along its path is the instantaneous velocity.

Instantaneous acceleration is defined as the ratio of change in velocity during a given time interval such that the time interval goes to zero.

1. s(t) = 6t³ + 3t +9

to find the velocity at time t, we differentiate s(t)

= 18t² + 3

2. at t = 3s

= 18(3)² +3

= 165 m/s²

3. v(t) = 18t² + 3

to get the acceleration at time t, we differentiate v(t)

= 36t

4. when t = 3

a = 36 × 3

= 108 m/s²

learn more about instantaneous velocity and acceleration from

https://brainly.com/question/2234298

#SPJ1

Answer:

  745

Step-by-step explanation:

You want the original number of books in the library if adding 298 children's books increased the fraction of children's books from 2/5 to 4/7.

We often like to work problems like this in terms of "ratio units." Here, we'll let x represent the number of books in a ratio unit. This means the number of children's books is originally 2x, and the total number of books is originally 5x. Then we have ...

  (2x +298)/(5x +298) = 4//7

Cross multiplying gives ...

  7(2x +298) = 4(5x +298)

  3(298) = 6x . . . . . . . . . . . . . subtract (14x+4(298))

  149 = x

  745 = 5x . . . . . . the original number of books in the library

There were 745 books in the library at first.

__

Additional comment

If we let x represent the original number of library books, then the arithmetic involves more fractions. You would have an equation like ...

  2/5x +298 = 4/7(x +298)

<95141404393>

The 9th term of this arithmetic sequence is 6.

In an Arithmetic Progression (AP), the nth term is given by the formula-

a9 = a + (n-1)d

where a = first term of the AP

d = common difference

Here, we are given that a= 10 and d = - ½

Let the 9th term of the AP be a9

Therefore, according to the formula for finding the nth term of an AP, we get-

a9 = a + (9-1)d

a9 = a + 8d

Substituting the values of a and d given in the question-

a9 = 10 + 8(-1/2)

a9 = 10 - 4

a9 = 6

Thus, the 9th term of the arithmetic sequence is 6.

Learn more about Arithmetic Progressions here-

https://brainly.com/question/6561461

#SPJ9

Las cantidades de bolitas para cada una de las tres personas son las siguientes:

Amanda: 19 bolitas

Rodrigo: 15 bolitas

Patricio: 69 bolitas

En este problema tenemos a tres personas (Amanda, Rodrigo y Patricio) que se reparten 103 bolitas, en términos algebraicos, cada persona es representada por las siguientes ecuaciones:

Amanda

x = y + 4

Rodrigo

y

Patricio

z = 2 · (x + y) + 1

Total

x + y + z = 103

A continuación, determinamos la cantidad de bolitas asociada con Rodrigo:

x + y + 2 · (x + y) + 1 = 103

3 · x + 3 · y = 102

x + y = 34

y + 4 + y = 34

2 · y = 30

y = 15

Luego, determinamos las cantidades de bolitas de Amanda y Patricio:

x = 15 + 4

x = 19

z = 2 · (19 + 15) + 1

z = 2 · 34 + 1

z = 68 + 1

z = 69

El enunciado se encuentra escrito en español y el lenguaje de la respuesta es el mismo del enunciado.

The statement is written in Spanish and the language used in the answer is the same of the statement.

Para aprender más sobre sistemas de ecuaciones lineales: https://brainly.com/question/27891414

#SPJ1

Answer:

1 degrees F

Step-by-step explanation:

-3+12-6=3

3/3 = 1

1 degrees F

:]

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

Suppose \(f(x) =8^{3x\) and \(g(x) =8^{4x\), function operations that are correct include the following:

A. (f + g)(x) = \(8^{3x} + 8^{4x}\)

B. (f × g)(x) = \(8^{7x}\)

C. (f - g)(x) = \(8^{3x} - 8^{4x}\)

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:

(f × g)(x) = \(8^{3x+ 4x}=8^{7x}\)

(f ÷ g)(x) = \(8^{3x- 4x}=8^{-x}\)

Read more on exponent here: brainly.com/question/27858496

#SPJ1

Answer:

x is first angle

y is second angle

and z is third angle

Step-by-step explanation:

This question is solved by a system of equations. We have that:x is the first angle.y is the second angle.z is the third angle.Doing this, we get that:The first angle measures 30º.The second angle measures 67º.The third angle measures 83º.The sum of the measures of the angles of a triangle is 180. This means that The sum of the measures of the second and third angles is five times the measure of the first angle.This means that:From this, the first angle can be found:The measure of the first angle is of 30º.The third angle is 16 more than the second.This means that:Since We get that the second angle is:The second angle measures 67º.For the third angle:The third angle measures 83º.

Answer:

6

Step-by-step explanation:

Changing the question into an equation format :

20/x = 10/3

Multiply x on both sides :

20 = 10x/3

Multiply both sides by 3 :

60 = 10x

Divide both sides by 10 :

6 = x

x = 6

The number must be 6, but let's check:

20/6

Simplify fraction by finding common multiple:

2

20/6 ÷ 2/2 = 10/3

Same as question so ✅

Hope this helped and have a good day

Answer:

6

Step-by-step explanation:

1. 20 / x = 10 / 3

2. Cross multiply 20 time 3 and 10 times x to get 60 = 10x

3. Divide both sides by 10

4. x=6

Answer:

sept one

Step-by-step explanation:

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

The visual depiction of numbers, such as fractions, integers, and whole numbers, spread out uniformly along a single horizontal line is known as a number line. A number line can be used as a tool for operations like addition and subtraction as well as comparison and sorting of numbers.

Given:

As from the Figure we have

-1 3/4 = -7/4 = -1.75, which is represented by point 1 on the number line.

and, 14/8 = 1.75, which is represented by point 7 on the number line.

and, 1.125, which is represented by point 6 on the number line.

and, -0.875, which is represented by point 4 on the number line.

Learn more about number line here:

https://brainly.com/question/13425491

#SPJ1

Answer:

It's long but you use Substitution!

Step-by-step explanation:

Let's solve your system by substitution.

2x+3y=3750;4x+y=4250

Rewrite equations:

4x+y=4250;2x+3y=3750

Step: Solve 4x+y=4250 for y:

4x+y = 4250

4x+y+−4x = 4250+−4x (Add -4x to both sides)

y = −4x+4250

Step: Substitute −4x+4250 for y in 2x+3y = 3750:

2x+3y=3750

2x+3(−4x+4250)=3750

−10x+12750=3750 (Simplify both sides of the equation)

−10x+12750+−12750=3750+−12750 (Add -12750 to both sides)

−10x =−9000

−10x = −9000 (Divide both sides by -10)

−10          −10

x=900

Step: Substitute 900 for x in y = −4x+4250:

y=−4x+4250

y=(−4)(900)+4250

y=650 (Simplify both sides of the equation)

Answer:

x=900 and y=650

Apply Pythagorean theorem first

\(\\ \rm\rightarrowtail b^2=11^2-10^2\)

\(\\ \rm\rightarrowtail b^2=121-100\)

\(\\ \rm\rightarrowtail b^2=21\)

\(\\ \rm\rightarrowtail b=4.2\approx 4units\)

Now

\(\\ \rm\rightarrowtail \dfrac{1}{2}(x)(10)=75\)

\(\\ \rm\rightarrowtail 5x=75\)

\(\\ \rm\rightarrowtail x=15units\)

Answer:

5:8

Step-by-step explanation:

here

Discriminant

Answer:

0 (zero)

Step-by-step explanation:

Discriminant

\(b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0\)

Given equation:  \(4k^2+8k+4=0\)

Therefore:

Substitute these values into the discriminant and solve:

\(\begin{aligned}\implies b^2-4ac & = 8^2-4(4)(4)\\& = 64 - 4(16)\\& = 64 - 64\\& = 0\end{aligned}\)

Therefore, the discriminant of the given quadratic equation is zero.

This implies that the graph of the equation has one real root.

Answer:

A = 80 in²

Steps:

A = 16 × 5

A = 80 in²

Answer:

im not completely sure but i think 80in.²