The nth term of a sequence is 3n squared -1. The nth term of a different sequence is 30 - n squared. Find the only number that is in both of these sequences

Answers

Answer 1

The number that belongs to both sequences is 26.

The formula known as the nth term allows us to locate any term in a series. The letter "n" stands for "number."

By changing the term number's value, we can create a series that uses the nth term (n).

To find the 10th term we would follow the formula for the sequence but substitute 10 instead of ‘n‘; to find the 50th term we would substitute 50 instead of n.

We have two sequences, let's call one as A and the other as B.

The n-th term of sequence A is written as:

aₙ = 3*n^2 - 1

the nth term of sequence B is written as:

bₙ = 30 - n^2

We want to find a term that belongs to both sequences, (it can be for different integers, we can use n for sequence A and x for sequence B)

Then we want to find:

aₙ = bₓ

where n and x are integer numbers.

Then we will heave:

3*n^2 - 1 = 30 - x^2

To find the pair, we could isolate one of the variables, then input different integers in the other variable and see if the outcome is also an integer.

Let's isolate n.

3*n^2 = 30 - x^2 + 1

3*n^2 = 31 - x^2

n^2 = (31 - x^2)/3

n = √(  (31 - x^2)/3)

Now let's input different values for x, and see if the outcome is also an integer, notice that x is in a negative term inside a square root, then we have only a few values of x such that the equation can be true.

Then let's start with x = 1.

n(1) = √(  (31 - 1^2)/3) = √(30/3) = √10

We know that √10 is not an integer.

now with x = 2,

n(2) = √(  (31 - 2^2)/3)  = √( (31 - 4)/3) = √(27/3) = √9 = 3

then if x = 2, we have n = 3.

Both of them are integers, then we get:

a₂ = 3*(3)^2 - 1 = 27 - 1 = 26

b₃ = 30 - 2^2 = 30 - 4 = 26

Therefore, The number that belongs to both sequences is 26.

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Related Questions

I am pretty sure its C but I might be wrong

Answers

Answer: I think it’s A

Step-by-step explanation:

But go for it

simply the following
a) 2(y-1)/3-3(y-2)/4=1
b) 3x=44/5=2x+6

Answers

The simplified value of x is 44 / 15 or 7 / 5 and value of y is -2

What is simplification?

Simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Given that, simply the following

a) 2(y-1)/3-3(y-2)/4=1

b) 3x=44/5=2x+6

1) 2(y-1) / 3 - 3(y-2) / 4 = 1

Multiplying by 12 to both sides,

8(y-1) - 9(y-2) = 12

8y-8 - 9y+18 = 12

-y + 10 = 12

y = -2

2) 3x = 44 / 5 = 2x+6

3x = 44 / 5

Multiplying by 5 to both sides,

15x = 44

x = 44 / 15

or,

44 / 5 = 2x + 6

Multiplying by 5 to both sides,

44 = 10x + 30

14 = 10x

x = 7 / 5

Hence, the simplified value of x is 44 / 15 or 7 / 5 and value of y is -2

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have to find x, y, and z,, someone help pls !!

Answers

1) To find y, you should use the pythagorean theorem
30^2 = 24^2 + y^2
So y = 18

(a) On the axes provided, sketch a slope field for the given differential equation at the 9 points indicated.

Answers

A slope field for the given differential equation dy/dx = xy/2 at the 9 points indicated is shown below.

We know that a slope field represents the slope of a differential equation at certain vertical and horizontal intervals on the coordinate plane.

First we construct a table which contains the values of slope.

Consider given differential equation dy/dx = xy/2

where -1 ≤ x ≤ 1,

1 ≤ y ≤ 3

Let the slope be m

so, dy/dx = m

For x = -1, y = 1

m = (-1 × 1)/2

   = -1/2

For x = -1, y = 2

m = (-1 × 2)/2

   = -1

For x = -1, y = 3

m = (-1 × 3)/2

   = -3/2

For x = 0, y = 1

m = (0 × 1)/2

   = 0

For x = 0, y =2

m = (0 × 2)/2

   = 0

For x = 0, y = 3

m = (0 × 1)/2

   = 0

For x = 1, y = 1

m = (1 × 1)/2

   = 1/2

For x = 1, y = 2

m = (1 × 2)/2

   = 1

For x = 1, y = 3

m = (1 × 3)/2

   = 3/2

So, the table is:

x/y     1  2    3

-1     -1/2   -1      -3/2

0     0   0   0

1       1/2     1      3/2

Therefore, the slope field is as shown below.

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what is the value of z?

420

60

440

240​

Answers

The correct answer is 60

you and three friends spent $35 on tickets at the movies. Write and solve an equantion to find the price p of one ticket

Answers

Answer:

35/4=8.75

Step-by-step explanation:

You and your 3 friends add up to 4 people so you do 35 divided by 4 and get 8.75

Answer:

Step-by-step explanation:

35/3 = p

p = 11.67 per person

What is a coordinate plane example?

Answers

A coordinate plane is a two-dimensional surface formed by two number lines

What is coordinate system?In a plane, a Cartesian coordinate system is a system of coordinates that designates each point uniquely by a pair of numerical coordinates, which are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length. Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is the name given to one horizontal number line. The y-axis is the name given to the other number line, which is vertical. At a place known as the origin, the two axes collide. The coordinate plane allows us to graph points, lines, and more. The plane that houses the x- and y-axes is known as the xy-plane, while the y- and z-axes are housed in the yz-plane and the x- and z-axes are housed in the xz-plane.

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You're working late one night and notice that the hard drive on your new computer is very active even though you aren't doing anything on the computer and it isn't connected to the Internet. What is the most likely suspect?

Answers

Answer:

The most likely suspect for the hard drive being very active even though the computer is not being used and is not connected to the Internet is malware. Malware is a type of software that is designed to cause harm to a computer system, and it can often run in the background without the user's knowledge.

The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
v (t)=20,000 (0.86)'
Find the value of the car after 4 years and after 10 years.
Round your answers to the nearest dollar as necessary.
Value after 4 years:
Value after 10 years:

Answers

Answer:

4 years: $10,94010 years: $4,426

Step-by-step explanation:

Given the value function v(t) = 20000·0.86^t, you want the value after 4 years and 10 years.

Evaluation

Put the value of t in the formula where t is, and do the arithmetic.

The attached calculator output tells us ...

  value after 4 years: $10,940

  value after 10 years: $4,426

__

Additional comment

When you are asked to do the same evaluation with different numbers, it is convenient to process them as a list, or using a spreadsheet.

To prepare for a bake-off, Luis used 590 grams of flour each day for 3 weeks. How many kilograms did Luis use in those 3 weeks? 1 g = 0.001 kg Solve this on paper. Then check your answer on Zearn. Luis used kilograms of flour in 3 weeks.

Answers

Answer: [tex]12.39\ kg[/tex]

Step-by-step explanation:

Given

Luis used 590 gm of flour each day

If he continues to use it for 3 weeks

A week has 7 days; so 3 weeks have 21 days

The flour used in 21 days

[tex]\Rightarrow 21\times 590\\\Rightarrow 12,390\ g\ \text{or}\ 12.39\ kg[/tex]

Thus, [tex]12.39\ kg[/tex] of flour is used in 3 weeks

The domain of y = √√√x-5-1 is
DONE
3 of 8
P
10
1000
098
7
6
5
4
3
12
y
2
19
Ð
6
8x

Answers

The function domain is X≥5  Or in interval notation [5, ∞)

What is Domain definition?The domain of a function is the set of input or argument values for which the function is real and definedThe domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limitedIn mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by {\displaystyle \operatorname {dom} } or {\displaystyle \operatorname {dom} f}, where f is the functionFind non-negative values for radicals x≥5solve x-5≥0:x≥5 function domain is X≥5  Or in interval notation [5, ∞)

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Angle W measures 36°. What is the angle measure of angle y? (Angle Includes x, y, w, z and is in the shape of an X?) SO confused.

Answers

Answer:

The angle measure of angle y is 36°. [ Because vertically opposite angles are equal]

Ethan wants to purchase a rectangular lot at a lake resort. He drew the layout of the lot on a coordinate plane, where the x- and y- values represent the length, in yards. The center of the lot is located at (0,0). The northeast corner of the lot is located at (16.5, 13.5). The southeast corner of the lot is located at (16.5, -13.5). The northwest corner of the lot is located at (-16.5, 13.5). The southwest corner of the lot is located at (-16.5, -13.5). What is the area of the rectangular lot?

a) 120 square yards

b) 1,782 square yards

c) 445.5 square yards

d) 891 square yards​

Answers

C) 445.5 square yards

Marion compared the y-intercept of the function f(x) shown in the table below to the y-intercept of the function g(x) graphed below
What is the distance between the y-intercept of f(x) and g(x)

Answers

Answer:

difference is 12 units

Step-by-step explanation:

line shown has a y-intercept of -4

now find y-intercept of f(x) by first finding its slope:

(-2,0) and (2,-32)

m = (0+32)/(-2-2)

m = 32/-4

m = -8 (slope)

Now find the y-intercept (or 'b') from substituting into 'y=mx+b':

0 = (-2)(-8) + b

0 = 16 + b

-16 = b (y-intercept)

-16 - (-4) = -12

numbers divisible by 5

please give me at least 6

Answers

Answer:

5,10,25,30,35,30,35,40...

Step-by-step explanation:

Multiples of 5

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

5,10,15,20,25,30,35,40,45.....

Step-by-step explanation:

just multiply 5 by consecutive natural numbers

plz mark as brainliest

2sinx^2 =sin x+3
Solve for the solutions

Answers

Answer:

x = 3/2 π    (270°)

Step-by-step explanation

2sin²x =sin x+3

2sin²x - sin x - 3 = 0

(sin x + 1) (2sin x - 3) = 0

-1 ≤ sin x ≤ 1

sin x = -1

x = 3/2 π    (270°)   or -π/2 + 2kπ (k = ..., -1, 0 , 1, ...)

We need to assume the sample was randomly selected because we are making inferences about ___________. a)unknown statistic b) unknown parameter c) means

Answers

We need to assume the sample was randomly selected because we are making inferences about means. Means refers to the average of a sample of data points, which can be used to estimate the value of an unknown population parameter.

If the sample was not randomly selected, then our estimates of the population parameter could be biased or inaccurate. This is because the sample may not be representative of the population as a whole, which could lead to incorrect estimates of the population parameter.

In order to make valid inferences about a population, it is essential to use random sampling. This is because random sampling ensures that the sample is representative of the population as a whole, meaning that the estimates of the population parameter that you obtain from the sample will be unbiased and accurate. If the sample is not randomly selected, then there is a risk that the sample is not representative of the population, which could lead to incorrect estimates of the population parameter.

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The diameter of a circular pond 63 m. Find the cost of fencing the edge of the pond if the fence costs $12 per meter.

Answers

Answer:

$2,373.84

Step-by-step explanation:

The formula for circumference is C = (pi)(diameter)

C = (3.14)(63)

C = 197.82 m

then multiply that by the cost of fence/m

197.82 x 12 = $2,373.84

What is the domain of the function y=3[x?
-0 O 0 0 0 01

Answers

It is the second one. No cap

The domain of the function y = 3[x] is (-∞, ∞), which means that the function is defined for all values of x.

What is a function?

A relation is a function if it has only One y-value for each x-value.

The function y = 3[x] is a piecewise function where [x] denotes the greatest integer function or the floor function, which returns the largest integer less than or equal to x.

The domain of the function is the set of all real numbers for which the function is defined.

As the greatest integer function is defined for all real numbers, the domain of the function y = 3[x] is also all real numbers.

Therefore, the domain of the function y = 3[x] is (-∞, ∞), which means that the function is defined for all values of x.

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work out the areas of these compound shapes ? Pls step by step

Answers

Answer:

Step-by-step explanation:

7+5+2=14

What does r equal?
Answer: r = ________

Answers

Answer:

[tex]r=\sqrt{\frac{3V}{\pi h} }[/tex]

Step-by-step explanation:

[tex]V=\frac{1}{3} \pi r^2h[/tex]

Lets solve for [tex]r[/tex].

Multiply both sides of the equation by 3.

[tex]3V=\pi r^2h[/tex]

Divide both sides of the equation by [tex]\pi h[/tex].

[tex]\frac{3V}{\pi h} =r^2[/tex]

Take the square root of both sides.

[tex]\sqrt{\frac{3V}{\pi h} } =r[/tex]

Simplify 10 1/2(1 1/7x+2/3)+5 5/6(2 2/5x+4 2/7)​

Answers

Answer:

26x+32

Step-by-step explanation:

Dariu ha a 40-ounce port drink. He drink 18 ounce. Enter the percentage of ounce Dariu ha left of hi port drink

Answers

The percentage of ounce Dariu has left of his port drink is 55%.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

It is given that Dariu ha a 40-ounce port drink.

He drank 18-ounce port drink.

First calculate what percentage of port drink Dariu drank.

The equation is -

= (18/40) × 100

= 45%

So, Dariu drank 45% of the port Drink.

Now, subtract the percentage Dariu drank from the 100% (40 Ounce) drink Dariu had -

100 - 45 = 55

Therefore, Dariu has 55% drink left.

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please help me with this

Answers

9514 1404 393

Answer:

  51.63 m²

Step-by-step explanation:

The relevant area formulas are ...

  A = πr² . . . . . area of a full circle of radius r

  A = LW . . . .  area of a rectangle of length L and width W

  A = 1/2bh . . . area of a triangle with base b and height h

__

The figure area is the sum of the areas of 1/2 a circle of radius 3 m, a rectangle with base 6 m and height 5 m, and a triangle with base 3 m and height 5 m. Using the above formulas, we find the area to be ...

  A = (1/2)(3.14)(3 m)² +(6 m)(5 m) + 1/2(3 m)(5 m)

  A = (14.13 +30 +7.5) m² = 51.63 m²

The area of the figure is about 51.63 m².

Ill mark brainly if its correct. :) a,b,c, or d. answer quick please

Answers

Answer:

d.

Step-by-step explanation:

The following table displays the number of sofas sold in a furniture store during certain months of the year.
Furniture Store Sofa Sales
January 255
February 234
March 263
April 229
May 248

Based on these data, which statement is correct?

A. There are outliers.

B. The mean best describes the data.

C. The median best describes the data.

D. The measure of variability that best describes the data is the IQR, 27.5.

Answers

I think answer should be d. Please give me brainlest let me know if it’s correct or not okay thanks bye

Construct a quadratic polynomial whose zeroes are negatives of the zeroes of the

polynomial x


x2 − x − 12.

Answers

Given:

The given quadratic polynomial is :

[tex]x^2-x-12[/tex]

To find:

The quadratic polynomial whose zeroes are negatives of the zeroes of the given polynomial.

Solution:

We have,

[tex]x^2-x-12[/tex]

Equate the polynomial with 0 to find the zeroes.

[tex]x^2-x-12=0[/tex]

Splitting the middle term, we get

[tex]x^2-4x+3x-12=0[/tex]

[tex]x(x-4)+3(x-4)=0[/tex]

[tex](x+3)(x-4)=0[/tex]

[tex]x=-3,4[/tex]

The zeroes of the given polynomial are -3 and 4.

The zeroes of a quadratic polynomial are negatives of the zeroes of the given polynomial. So, the zeroes of the required polynomial are 3 and -4.

A quadratic polynomial is defined as:

[tex]x^2-(\text{Sum of zeroes})x+\text{Product of zeroes}[/tex]

[tex]x^2-(3+(-4))x+(3)(-4)[/tex]

[tex]x^2-(-1)x+(-12)[/tex]

[tex]x^2+x-12[/tex]

Therefore, the required polynomial is [tex]x^2+x-12[/tex].

I’m not sure what it could be?

Answers

Answer:

B

Step-by-step explanation:

If x equals 1/4 then it must be B because:

All the sections are divided into fourths so 1/4 plus 3/4 is 1.

A flag pole and a building stand on the same horizontal level. From the point p at the bottom of a building the angle of the top T of the flagpole is 65°. From the point Q of the building the angle of elevation of the point T is 25°. If the building is 20m high. calvulate the distance PT, The heigt of the flagpole,The distance QT​

Answers

Answer:

PT is approximately 28.2 m

The height of the flagpole is approximately 25.56 m

QT is approximately 13.15 m

Step-by-step explanation:

Part A

From the attached drawing of the building and the flagpole, we have;

∠TQP = 25° + 90° = 115°

∠TPQ = 90° - 65° = 25°

∴ ∠QTP = 180° - (115° + 25°) = 40°

By sine rule, we have;

[tex]\dfrac{\overline {QT}}{sin(\angle TPQ)} = \dfrac{\overline {PT}}{sin(\angle TQP)} = \dfrac{\overline {QP}}{sin(\angle QTP)}[/tex]

[tex]\therefore \overline {PT} = sin(\angle TQP) \times \dfrac{\overline {QP}}{sin(\angle QTP)}[/tex]

∴ PT = sin(115°) × 20 m/(sin(40°)) = 28.1992924 ≈ 28.2

PT ≈ 28.2 m

Part B

The height of the flagpole, Ta = PT × sin(∠TPa)

∴ Ta ≈ 28.2 × sin(65°) ≈ 25.56

The height of the flagpole, Ta ≈ 25.56 m

Part C

[tex]\overline {QT} = sin(\angle TPQ) \times \dfrac{\overline {QP}}{sin(\angle QTP)}[/tex]

The distance QT= sin(25°) × 20 m/(sin(40°)) ≈ 13.15

QT ≈ 13.15 m

At her birthday party, Sam is serving a slice of cake to each attendee. Of each attendee receives 2 slices, there will be 20 slices left. If 5 attendees do not receive any slices and the rest receive 5 slices each, there will be no cake left. How many attendees were at the party

Answers

On solving the provided question, we can say that by having the equation 15 attendees were at the party

What is equation?

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

let x = number of attendees

[tex]2x[/tex] + 20 = number of slices 5(x-5) = [tex]2x[/tex] - 20

[tex]5x[/tex] - 25 = [tex]2x[/tex] + 20

[tex]3x[/tex] = 45

[tex]x[/tex] = 15

[tex]2x[/tex] + 20 = 50 slices

15 attendees

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