5
The recursive formula for a geometric sequence is given below. What is the third term in the sequence?
f(1) = 2
f(n) = 3f(n − 1)
-
OA. 18
OB. 54
OC. 162
OD. 12
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Answers

Answer 1
f(1) = 2
f(2) = 3f(1) = 3(2) = 6
f(3) = 3f(2) = 3(6) = 18 (A)
Answer 2

[tex]\Large{ \boxed{ \tt{ \blue{A}}}}\Large{ \boxed{ \tt{ \pink{N}}}}\Large{ \boxed{ \tt{ \green{S}}}}\Large{ \boxed{ \tt{ \purple{W}}}}\Large{ \boxed{ \tt{ \red{E}}}}\Large{ \boxed{ \tt{ \pink{R}}}}[/tex]

[tex] \: \: [/tex]

A. 18

[tex] \: \: [/tex]

[tex]\Large{ \boxed{ \tt{ \blue{S}}}}\Large{ \boxed{ \tt{ \pink{O}}}}\Large{ \boxed{ \tt{ \green{L}}}}\Large{ \boxed{ \tt{ \purple{U}}}}\Large{ \boxed{ \tt{ \red{T}}}}\Large{ \boxed{ \tt{ \pink{I}}}}\Large{ \boxed{ \tt{ \blue{O}}}}\Large{ \boxed{ \tt{ \pink{N}}}}[/tex]

[tex] \: \: [/tex]

[tex] \mathtt{f(1) = 2}[/tex][tex] \tt{f(2) \: = \: 3f \: (1) \: = \: 3(2) \: = \: 6}[/tex][tex] \tt{f(3) \: = \: 3f(2) \: = \: 3(6) \: = \: 18}[/tex]

[tex]\color{pink}─────────────────────────────────────[/tex]

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Related Questions

To estimate the height of a totem pole, Jorge uses a small square of plastic. He holds the square up to his eyes and walks backward from the pole. He stops when the bottom of the pole lines up with the bottom edge of the square and the top of the pole lines up with the top edge of the square. Jorge's eye level is about 2 m from the ground. He is about 3 m from the pole. Which of the following is the best estimate of the height of the totem pole?

Answers

Answer:

6.5 meters

Step-by-step explanation:

1 (c)
Gavin goes to Joti's shop.
He is making a circular blanket.
The finished blanket will have a radius of 0.325 m
It will have ribbon all around the edge.
He thinks he will need 2.5 m of ribbon.
Gavin knows that is about 3.1416
Round to 1 decimal place and use this value to work out how much ribbon
Gavin will have left if he buys 2.5 m
[4 marks]

Answers

Answer: 0.5m

Hope this helps!

a random number is selected from a random set 2,3,4,10

Answers

The number is even or less than 12. Then the correct option is C.

The complete question is given below.

A number is selected at random from the set {2, 3, 4, … 10}. Which event, by definition, covers the entire sample space of this experiment?

a. The number is greater than 2.

b. The number is not divisible by 5.

c. The number is even or less than 12.

d. The number is neither prime nor composite.

e. The square root of the number is less than 3.

What are sets?

A set is a group of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

A number is selected at random from the set {2, 3, 4, … 10}.

2, 4, 6, 8, 10 are even, but the rest are odd (BUT note the word “or”). The rest are less than 12. YES

Then the correct option is C.

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FAST!
A right rectangular prism has a square base and a height of 2.5 meters. If the length of a side of the square base is 4 meters, what is the volume of the prism?

Answers

Ggggggghhggggggggggg

Answer:

69 there hope it helps ;)

Step-by-step explanation:

420

HELP THIS IS URGENT WILL GIVE BRANLIEST ANSWER 3 AND 6

Answers

awnser is c because i just did it

40 points please Please help me

Answers

Answer:

19.51 units = x

Step-by-step explanation:

Here is one way :

Height = 18 cos 47 = 12.276

then     cos 51 = 12.276 /  x

                 x = 12.276 / cos 51 = 19.51

What are your top 3 theorems in higher mathematics? Why do you like them the most?

Answers

My theorems include the Pythagoras theorem, midpoint theorem, and angle bisector theorem.

How to illustrate the theorem?

The Pythagoras theorem is used to find the length in a right angle.

The midpoint theorem states that the line segment in a triangle is parallel to the third side and is half the length.

The angle bisector theorem is concerned with the lengths of the two segments that the triangle side is divided into by a line which bisects the opposite angle.

I like them because they're important when solving triangle related problems.

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What are the approximate area and circumference, respectively, of a circle with a diameter of 30 inches?​

Answers

Solution:

[tex]\searrow[/tex]

Detailed explanation:

Here we need to find both the circumference and the area of a circle whose diameter is 30 in.

///\\\///\\\///\\\///\\\///\\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\////\\\\////\\\\///\\\///\\\///\\\///

                                   ⚜  Circumference

This is the formula that we use for the circumference. [tex]\large\texttt{$C=\pi d$}[/tex].

Here, C is the circumference,

[tex]\pi[/tex] is pi, *

d is the diameter

_____________

* The number pi is an irrational number. This means that no matter how hard we try, we cannot write this number as a fraction. The reason for that is: The number pi has never-ending digits after its decimal point.

To avoid getting never-ending numbers, we will use 3.14 for pi.

_____________

Alright, so now we just stick in the values.

[tex]\boldsymbol{C=3.14\cdot30}[/tex]

[tex]\boldsymbol{C=94.2\:inches}[/tex]

The circumference is successfully calculated.

///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\////\\\\///\\\///\\\///\\\//\\//\/\/\/\//\///\\//

                                            ⚜ Area

This is the formula we will use to work out the area.

[tex]---\mapsto\boldsymbol{A=\pi r^2}[/tex]

Here,

A denotes the area

[tex]\pi[/tex] denotes pi

r denotes the radius (30/2=15, because the diameter is always two times the radius)

[tex]\large\boldsymbol{\therefore,\;the\;radius\;is\;15}[/tex]

Once again, it's just a matter of sticking in the values.

[tex]---\mapsto\boldsymbol{A=3.14\cdot15^2}[/tex]

NB:

Remember the Order of Operations!

P.E.M.D.A.S.

P=Parentheses

This operation tells us to evaluate all expressions in the parentheses first, if any are present.

E=Exponents

This one tells us to evaluate all expressions with exponents, if any are present.

M=Multiplication | D=Division

Unlike the two operations above, these two are completely interchangeable.

A=Addition | S=Subtraction

Like M and D, A and S are interchangeable.

_________________

Now let's simplify... According to P.E.M.D.A.S., we should square 15 first.

[tex]---\mapsto\boldsymbol{A=3.14\cdot225}[/tex]

Now, we need to multiply.

[tex]---\mapsto\boldsymbol{A=706.5\;square\;inches}[/tex]

"If a = − 8, b = − 7, c = 6, verify that (a+b) + c = a + (b+c)."

Answers

Answer:

The commutative property of addition says that changing the order of addends does not change the sum.

(a+b)+c = a+ (b+c)

( -8 + -7) + 6 = -8 + ( -7 + 6)

-15 + 6          =   -8 + -1

-9                  =  -9

Answer:

Hence, proved (a+b) + c = a + (b+c)."

Step-by-step explanation:

first take left hand side and insert the values of a, b, and c and similarly than take right hand side.

L.H.S

(a+b)+c

(-8+(-7))+6

(-8-7)+6

-15+6

-9

R.H.S

a+(b+c)

-8+(-7+6)

-8+(-1)

-8-1

-9

hence, proved (a+b) + c = a + (b+c)."

how would i solve this problem

Answers

Answer:

30

Step-by-step explanation:

1500/50=30

Find the midpoint of the segment with the following endpoints.
(-3,-3) and (1, 2)

Answers

[tex]\left(\frac{-3+1}{2}, \frac{-3+2}{2} \right)=\boxed{\left(-1, -\frac{1}{2} \right)}[/tex]

Is equal to (0,-5) and (4,6) in the line

please i need it so badl please

The sum of the ages of Damien and Keyanna is 100 years. 10 years ago, Damien's age was 4 times Keyanna's age. How old is Damien now?

Answers

Answer:

Damien is 74 years old now

Step-by-step explanation:

Define the variables:

Let d = age of DamienLet k = age of Keyanna

Given information:

The sum of the ages of Damien and Keyanna is 100 years. 10 years ago, Damien's age was 4 times Keyanna's age.

From the given information, create 2 equations:

Equation 1:  d + k = 100

Equation 2:  d - 10 = 4(k - 10)

Rewrite Equation 1 to make k the subject:

⇒ k = 100 - d

Substitute this into Equation 2 and solve for d:

⇒ d - 10 = 4(100 - d - 10)

⇒ d - 10 = 400 - 4d - 40

⇒ d - 10 = 360 - 4d

⇒ d - 10 + 10 = 360 - 4d + 10

⇒ d = 370 - 4d

⇒ d + 4d = 370 - 4d + 4d

⇒ 5d = 370

⇒ 5d ÷ 5 = 370 ÷ 5

⇒ d = 74

Therefore, Damien is 74 years old now.

A local baseball stadium has a total of 2,497 seats, with 210 seats reserved for season ticket holders.

If x represents the number of non-reserved seat tickets sold for the upcoming game, which of the following equations can be used to find the number of seats available for the upcoming game?

y = 2,497 - 210x
B.
y = 2,287 - 210x
C.
y = 2,287 - x
D.
y = 2,497 - x

Answers

Answer:

I believe d would be the answer.

Step-by-step explanation:


A hose fills a hot tub at a rate of 5.2 gallons per minute. How many minutes will it take to fill a 600 gallon hot tub? (nearest tenth)

Answers

Answer:

115.38 is what I got when I tryed to work it out

What is the domain of the function y = StartRoot x + 6 EndRoot minus 7?

Answers

In the set of real numbers square roots are only defined for values greater than or equal to zero.
(x + 6) > = 0
x > = -6

Answer: B

Step-by-step explanation:

Edge 2023

The Pythagorean Identity states that: (sin x)^2 + (cos x)2 = 1

Given sin 0 = 2/5, find cos 0.

cos 0 = ?/?

Answers

Answer:

[tex]\cos \theta =\dfrac{\sqrt{21}}{5}[/tex]

Step-by-step explanation:

Given:

[tex]\sin \theta=\dfrac{2}{5}[/tex][tex](\sin x)^2+(\cos x)^2=1[/tex]

Substitute the given value of sin θ into the given identity and solve for cos θ:

[tex]\begin{aligned}(\sin x)^2+(\cos x)^2 & =1\\\implies (\sin \theta)^2+(\cos \theta)^2 & =1\\\left(\dfrac{2}{5}\right)^2+(\cos \theta)^2 & =1\\\left(\dfrac{2^2}{5^2}\right)+(\cos \theta)^2 & =1\\\dfrac{4}{25}+(\cos \theta)^2 & =1\\(\cos \theta)^2 & =1-\dfrac{4}{25}\\(\cos \theta)^2 & =\dfrac{21}{25}\\\cos \theta & =\sqrt{\dfrac{21}{25}}\\\cos \theta & =\dfrac{\sqrt{21}}{\sqrt{25}}\\\cos \theta & =\dfrac{\sqrt{21}}{5}\end{aligned}[/tex]

Brainliest to whoever answers :) Highly appreciated

Answers

Answer:

the answer is L

Step-by-step explanation:

rounding up to any number/decimal requires the digit before the specified digit to be 5 or greater.
rounding down requires the digit to be 4 or less.
if the estimated time to the nearest 0.01 of a second is 35.20 then the actual race time could be from 35.195 to 35.205 since any number between could be rounded to 35.20

what is -36 degrees converted
to radians

Answers

Answer:

Answer: 0.628 radian

Step-by-step explanation:

how to convert from degrees to radians?

Answer:To convert the value of the angle in degree, to its equivalent radians, we need to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.

Answer:

See below

Step-by-step explanation:

- 36  *  PI / 180 = -pi/5 radians  = -  .6283 R

Find the jacobian of the vector valued function F(v) = [3x*2y, 5xx, 9yy]

Answers

Answer:

F(v)=0

Step-by-step explanation:

F(v) = [3x*2y, 5xx, 9yy]

Calculate the product

F(v) =[tex]\frac{d}{dv\\}[/tex] [3x*2y, 5x*x, 9y*y]

The derivative of a constant is always 0

F(v) =[tex]\frac{d}{dv\\}[/tex]((6xy,5[tex]x^{2}[/tex],9[tex]y^{2}[/tex]))

f(v)=0


Which statements about the location of the point are
true? Select three options.
The point is in the first octant.
The point lies behind the yz-plane.
The x-coordinate is -3.
The y-coordinate is positive.
The point lies to the left of the xz-plane.

Answers

Answer:

Step-by-step explanation:

a car corporation produced 1560 more cars this month than last. Write a signed number to represent this month's change in the production​

Answers

Answer:

+1560

Step-by-step explanation:

Since the corporation produced 1560 more cars then the answer is simply +1560.

What is 9 lbs 6 oz converted to ounces?

Answers

Answer:

150 ounces

Step-by-step explanation:

If a person is chosen at random in this survey, what is the P(decaf or sugar)?

HELP PLS!

Answers

The value of the probability P(decaf or sugar) is 0.41

How to determine the probability?

From the table, we have:

P(decaf) = 0.05 + 0.08 + 0.09 = 0.22

P(sugar) = 0.19 + 0.08 = 0.27

P(decaf and sugar) = 0.08

The required probability is:

P = P(decaf) + P(sugar) - P(decaf and sugar)

This gives

P = 0.22 + 0.27 - 0.08

Evaluate

P = 0.41

Hence, the value of the probability P(decaf or sugar) is 0.41

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Function: one to one. Help with this math question!

Answers

The answer for f.f (x) = 25 / 4x² and g.g(x)= 4x² -28x +49.

What is a Function ?

A function is a mathematical statement used to relate a dependent and an independent variable.

It is given that

f(x) = 5/2x

g(x) = 2x - 7

It is asked to found

f.f

g.g

f.f (x) = (5/2x) * (5/2x)

= 25 / 4x²

g.g(x)= ( 2x - 7)( 2x - 7)

= 4x² -28x +49

Both the answers are in its simplified form

Therefore the answer for f.f (x) = 25 / 4x² and g.g(x)= 4x² -28x +49.

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A clothing store is having a 15% off sale on t-shirts. If you will save $3.75 on a shirt, what was the original price before the sale? Show your work.

Answers

Answer:

$25

Step-by-step explanation:

3.75 is 15% of 25.

15% × 25 = 3.75

he area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π.

Answers

Answer:

14m

Step-by-step explanation:

Area = πr²

A = 153.86m²

153.86 = 3.14 *r²

r² = 153.86/3.14

r = √49

r = 7

d = 2r

d = 2*7

d = 14

A flower garden is shaped like a circle. Its diameter is 24yd . A ring-shaped path goes around the garden. Its outer edge is a circle with diameter 30yd.

Answers

Answer:  32 bags of sand

==========================================================

Explanation:

We have two concentric circles. Think of a bulls-eye on a dart board. The inner circle is the garden itself. The outer circle is the garden plus the surrounding pathway. What we're interested in is the area of the outer ring, which is the area of the garden path only.

To find this ring area, we'll need to find the area of each circle.

A = area of the smaller circle

A = pi*r^2

A = pi*12^2

A = 144pi

Notice how I took half of the 24 yard diameter to get the radius of 12 yards.

B = area of the larger circle

B = pi*r^2

B = pi*15^2

B = 225pi

Subtract the two results

C = area of the outer ring, aka the garden path only

C = B - A

C = 225pi - 144pi

C = (225-144)pi

C = 81pi

We're told to use 3.14 in place of pi

C = 81*pi

C = 81*3.14

C = 254.34

The garden path has an area of roughly 254.34 square yards.

1 bag of sand covers 8 square yards.

So we'll need (254.34)/(8) = 31.7925 = 32 bags of sand

Multiply and remove all perfect squares from inside the square roots. Assume a is positive.

3[tex]3\sqrt{5a}*8\sqrt{35a^{2} }[/tex]









Answers

The multiplication is 120*[tex]a^{3/2}[/tex].

What is exponents and powers?

Power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and exponent denotes the number of times the same base number is multiplied.

Given:

3√(5a) * 8 √(35a²)

= 3√(5a)* 8* a *√7* √5

= 3*8*5*a *√(7a)

= 120 [tex]a^{1/2+1}[/tex]

=120*[tex]a^{3/2}[/tex]

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Answer:

[tex]120a\sqrt{7a}[/tex]

Step-by-step explanation:

It's right on khan academy

The figure below shows parallel lines cut by a transversal:

A pair of parallel lines is shown with arrowheads on each end. A transversal cuts through these two lines. An angle formed between the top parallel line and the transversal on the inner left side is marked 1. Another angle formed between the bottom parallel line and the transversal on the inner right side is marked 2.

Which statement is true about ∠1 and ∠2?

∠1 and ∠2 are congruent because they are a pair of adjacent angles.
∠1 and ∠2 are complementary because they are a pair of adjacent angles.
∠1 and ∠2 are congruent because they are a pair of alternate interior angles.
∠1 and ∠2 are complementary because they are a pair of alternate interior angles.

Answers

∠1 and ∠2 are congruent because they are a pair of alternate interior angles , Option C is the right answer.

What are Parallel Lines ?

When two lines do not meet at any point and the distance between them remains constant , then the two lines are called parallel to each other .

It is given that the parallel lines are cut by a transversal and the angles are marked

The angle 1 and angle 2 are congruent because they are pair of alternate interior angles .

Therefore Option C is the right answer.

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A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?

Answers

Answer:

51

Step-by-step explanation:

let's set the starting number as x

1. x times 2 = 2x

2. 2x- 138

3. result = 102

So, 2x-138 = 102

Now lets work backwards to solve for x.

1. 2x = 102

x = 51

So the starting number was 51.

Answer: 120

2x - 138 = 102
+138 +138
(x=the missing number)

2x =240

240\2 = 120

x=120
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