Mathematics College

Find the first four terms of the sequence given by the following.
4,=(-1)".31%, n=1, 2, 3, ...

Answers

Answer 1

Answer:

The first term of the sequence is:

a₁ = -3a₂ = 12a₃ = -27a₄ = 48

Step-by-step explanation:

Given the sequence

aₙ = (-1)ⁿ · 3n²

substituting n = 1 to determine the first term

a₁ = (-1)¹ · 3(1)²

Applying the exponent rule: [tex]a^1=a[/tex]

a₁ = -1 · 3(1)

a₁ = -1 · 3

a₁ = -3

substituting n = 2 to determine the 2nd term

a₂ = (-1)² · 3(2)²

a₂ = 1 · 3(4)

a₂ = 12

substituting n = 3 to determine the 3rd term

a₃ = (-1)³ · 3(3)²

a₃ = -1 · 3(9)

a₃ = -1 · 27

a₃ = -27

substituting n = 4 to determine the 4th term

a₄ = (-1)⁴ · 3(4)²

a₄ = 1 · 3(16)

a₄ = 1 · 48

a₄ = 48

Therefore, the first term of the sequence is:

a₁ = -3a₂ = 12a₃ = -27a₄ = 48

Related Questions

A sweater that is regularly priced at $25 is on sale for 25% off.

What is the amount of the discount?

What is the sale price?

What is the total price of the sweater including the 6.5% sales tax?

need help now plz

Answers

Answer:

Discount = 6.25

Sale Price = 18.75

6.5% tax = 1.21875

Final price = 19.96875 = 19.97

Step-by-step explanation:

25 x .25 = discount

25 - 6.25 = sale price

18.75 × 0.065 = tax

18.75 + 1.21875 = final price

what is the equation in point-slope form of the line passing through (2,5) and (-1,8)?

Answers

Answer:

y=-1x+7

Step-by-step explanation:

I NEED HELP PLEASE ASAP

Answers

Answer:

Answer choice C is correct

Step-by-step explanation:

What is the value of x?
Enter your answer in the box.
x =

Answers

Answer:

Step-by-step explanation:

The two triangles are similar and therefore we can set up a proportion

9/(9 + 72) = (3x - 20)/(3x - 20 + 56) Combine like terms on the right

9/(81) = (3x - 20)/(3x + 36) Cross multiply

9(3x + 36) = 81 (3x - 20) Remove the brackets.

27x + 324 +1620 = 243x Add 1620 to both sides

27x + 324 + 1620 = 243x Subtract 27x from both

1944 = 216x divide both sides by 216

x = 9

If you feel comfortable canceling the size of the numbers can be reduced.

9/81 = 1/9

1/9 = (3x - 20)/(3x + 36)

3x + 36 = 9(3x - 20)

3x + 36 = 27x - 180

36 + 180 = 24x

216 = 24x

216/24 = x

x = 9

There is another cancelation possible, but this is simple enough.

If w is 15 when z is 9, and w varies directly with z, what is the value for z when w is 5?

Answers

Answer:

3 cuh

Step-by-step explanation:

15/3 = 5 9/3= 3

A: The perimeter of a rectangular garden is 376 m. If the length of the garden is 99 m, what is its width?

B: The area of a rectangular window is 7007 cm If the width of the window is 77 cm, what is his length?

Answers

Answer:

A) the width is 89

B) if area is 7007, the length is 91

Step-by-step explanation:

Answer:

A: 89 m

B: 91 m

Step-by-step explanation:

A: P=2(L+W)

P=2L+2W

P=2(99)+2W

2W=376-198=178

W=178/2=89m

B: A=L×W

7007=L×77

L=7007/77=91

L=9l m

Find the vertex angle of the figure below B = 40 egrees

Answers

Step-by-step explanation:

it's an Equilateral triangle

the base angels are equal

A=100°

B=40°

C=40°

The required vertex angle will be 100° in the given figure.

What is an Isosceles Triangle?

An Isosceles Triangle is defined as a triangle with two sides of equal length is an isosceles triangle.

The triangle given in the figure is an Isosceles triangle.

It is given that side AB is equal to side AC.

So ∠B = ∠C = 40°

Now we know that the sum of angles of a triangle is equal to 180°. So here in this triangle ABC. These are the sum of these three angles will be equal to 180.

As per the given figure,

∠A + ∠B +∠C = 180°

∵ ∠B = ∠C = 40°

∠A + 40° +40° = 180°

∠A + 80° = 180°

∠A = 180° - 80°

∠A = 100°

Therefore, the required vertex angle will be 100° in the given figure.

Learn more about Isosceles Triangle here:

brainly.com/question/2456591

#SPJ5

An angle measures 24º more than the measure of its complementary angle. What is the
measure of each angle?
What are the two angles please hurry

Answers

Answer:

33, 57

(not 100% sure this is correct)

Step-by-step explanation:

90= x +(24 +x)

(drag 90, plus the x's and drag the 24)

90 = 2x + 24

(Subtract 24 from 24 and 90 from 24)

66 = 2x

(Divide both by two)

33 = x

(now use x and plus it by 24)

24 + x = 57

plz answer the question step by step

Answers

Answer: x = 59°, y = 114°.

Step-by-step explanation:

The sum of the opposite angles of a quadrilateral in a circle is 180°.

y = 180° - 121° = 59°

The two angles being adjacent makes a total angle of 180° on the straight line.

x = 180° - (180°-114°) = 180° - 66° = 114°

What is the volume of this aquarium

Answers

Answer:

You can also divide the number of cubic inches by 231 to get the volume in gallons. For example, let's calculate the volume of a rectangular tank that is 20″ long, 12″ wide, and 10″ high.

Step-by-step explanation:

Elsie bought a video game for 85$. if the store charges 170% of its cost for the game, how much is the store's profit?

Answers

Answer: $59.5

170/100 * 85 = 144.5

144.5 - 85 = 59.5

If that is wrong my next guess is $144.50

PLS PLS HELP!!!! Write and solve an inequality to find the possible values or x if the area of the
rectangle is < 56 feet squared.
2 ft
(3x + 4) ft

Answers

Answer:

width=2 ft, length=(3x+4)ft

Area of Rectangle=width x length

=2ft . (3x+4)ft

=6x+8 ft sq

Area of Rectangle <56 ft sq

6x+8 ft sq <56 ft sq

6x < 56 ft sq - 8 ft sq

6x < 48 ft sq Substeracting 8 on both sides

6x/6 < 48 ft sq/6 Dividing by 6 on both sides

x < 8 ft sq

Step-by-step explanation:

The time required to empty a tank varies as inversely as the rate of pumping. If a pump can empty a tank in 45 min at the rate of 600 kl/min, how long will it take the pump to empty the same tank at the rate of 1000 kl/min?

Answers

okk

Step-by-step explanation:

hii

Jack

from

United State

America

Answer:

27 minutes.

Step-by-step explanation:

R = k/t

Substituting given info

600 = k/45

k = 45 * 600 = 27000

So the relation is S = 27000/t

So if R = 1000

1000 = 27000/t

t = 27000/ 1000

t = 27.

A graph showing a proportional relationship will...

Answers

I would choose b i hope you get it right

I’ll pay you if you help me

Answers

Answer: help you with what?

Step-by-step explanation:.-.

Haha. No need of money. But ask the question..

waiting..

Addie increased the amount of chocolate chips she used for the cookie recipe by 45%. The original recipe used 28 ounces of chocolate chips. How many ounces of chocolate chips will Addie use for her recipe?

Answers

Answer:

10%of 28=2.8

40%=2.8 ×4=11.2

5%(half of 10%)=1.4

then you add 40%and 5% which is 11.2+1.4=12.6

(on a calculator you can work percentage by doing 45 percentage button×the amount)

then you add 28 ounces(original)+(increase) which is 12.6=

40.6

Addie will use 40.6 ounces of chocolate for her recipe

Answer:

Step-by-step explanation:

10%of 28=2.8

40%=2.8 ×4=11.2

5%(half of 10%)=1.4

then you add 40%and 5% which is 11.2+1.4=12.6

(on a calculator you can work percentage by doing 45 percentage button×the amount)

then you add 28 ounces(original)+(increase) which is 12.6=

40.6

Addie will use 40.6 ounces of chocolate for her recipe

1. A worker in a company work 7 hours in a day, there are 22 working days in a month other than working hours each worker works 8 extra hours in a month, how many hours a worker is working in a full month?

Answers

Answer: A worker is working 162 hours in a month.

Step-by-step explanation:

Working hours per day = 7

Total working days = 22

Extra hours per month = 8

Total hours a worker works in a month = (Working hours per day) x (Total working days) +(Extra hours per month)

Total hours works in month = = 7 x22+8

= 154+8

= 162 hours

Hence, a worker is working 162 hours in a month.

Cuatro amigos están en un equipo de baloncesto. Durante un juego, cada amigo llevaba un registro de cuántos tiros intentaron y cuántos de esos intentos hicieron. ¿Qué amigo tuvo el mejor récord en cuanto al número de disparos realizados?

Henry acerto 0.45 de sus tiros
Allison hizo 4/15 de sus tiros
Arthur acerto 8/20 de sus tiros
Trevor fallo el 58% de sus tiros

Answers

Answer:

Allison tuvo el mejor récord

Step-by-step explanation:

Use the line of best fit to determine the y-value when the x-value is 7.

A. 25
B. 37
C.53
D.42

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Maria correctly answered 16 of the 20 questions. What fraction of the questions did she answer correctly?

Answers

16/20
Simplified to 8/10
Again simplified to 4/5.

Ql. What is the slope-intercept equation of the line y-intercept=(0,1), slope =3/4

Answers

Answer:

y = 3/4x + 1

Step-by-step explanation:

would y=x be proportional or nonproportional?

Answers

Nonproportional! Hope that helps!

Nonproporcional for sure

Is the following equation true or false? Explain your reasoning.

(x + 8)2 = x2 + 64

Answers

Answer:

False

Step-by-step explanation:

(R/s)(3) = ? Please hurry

Answers

Maybe this is what your looking for.

Lynda has $32.00 to spend at the grocery store on boxes of macaroni and cheese. The cost is $3 per box. In addition, her mom told her to buy some oranges that will cost $5. Which equation will let Lynda know how many total boxes of macaroni and cheese,m, she can buy?
A.32 = 5m + 3
B.32 = 3m + 5
C.32 = 3(m - 2) - 5
D.32 = 3(m - 2) + 5

Answers

Answer:

B. 32 = 3m + 5

Step-by-step explanation:

Total money to spent = $32Cost of macaroni and cheese = $3 per boxNumber of boxes = mCost of oranges = $5

Cost of macaroni and cheeses: 3m

Required equation is:

32 = 3m + 5

Correct option is B

Which choice is equivalent to the product below?
..
Someone pls help

Answers

Answer:

Answer B

Step-by-step explanation:

√2 * √8 * √4

√8 = √(2*2*2)

√8 = 2√2

√4=2

√2* 2√2 *2

2*2*2

can someone help me with this?

Answers

Answer:

Step-by-step explanation:

51 ÷ 3 = 17

204 ÷ 17 = 12

hope this helps

True or false? 3a+15b is divisible by 3 for any values of a and b.

Answers

Answer:

true

Step-by-step explanation:

its TRUE :)

Answer:

False

Step-by-step explanation:

Take a=-1 and b=-1/7

-3+-15/7=-36/7 which is not divisible by 3. There are several other examples which I don't even need to prove

Vector B has x, y, and z components of 3, 7.2,
and 4.5 units, respectively.
Calculate the magnitude of B

Answers

Answer:

[tex]\approx 9.0\:\mathrm{units}[/tex]

Step-by-step explanation:

The magnitude of 3D vector [tex]\vec{v}[/tex] can be given by the following:

[tex]| \overline{v}| =\sqrt{{v_x}^2+{v_y}^2+{v_z}^2}[/tex]

Plugging in given values, we have:

[tex]| \overline{v}|=\sqrt{3^2+7.2^2+4.5^2},\\| \overline{v}| \approx \fbox{$9.0\:\mathrm{units}$}[/tex].

PLZ HELP Write an algebraic expression for the following phrase. the product of five and k

Answers

Answer:

Step-by-step explanation:

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Find the first four terms of the sequence given by the following. 4,=(-1)".31%, n=1, 2, 3, ...

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Find the first four terms of the sequence given by the following.
4,=(-1)".31%, n=1, 2, 3, ...