A recursive rule for a geometric sequence is
a1 = 9; an = 2/3 (an−1)

What is the iterative rule for this sequence?

A.) an = 9 • (2/3)^n
B.) an = 2/3 • 9^n
C.) an = 9 • (2/3)^n-1

Answers

Answer 1

Answer:

C. [tex]a_n=(9)(\frac{2}{3})^{n-1}[/tex]

Step-by-step explanation:

Iterative geometric sequence:

[tex]a_n=a_1x^{n-1}[/tex]

Recursive geometric sequence:

[tex]a_n=xa_{n-1}[/tex]

The equations are very similar and you only really need to rearrange it. The factor (2/3) and the first term (9) are given, so you can write the iterative equation:

[tex]a_n=(9)(\frac{2}{3})^{n-1}[/tex]

And so the answer is C.


Related Questions

Sarah has 150 marbles. Of the marbles, 2/5 are blue, 3/10 are clear, and the rest are green. What is the ratio of blue marbles to clear marbles to Green marbles in simplest form?

Answers

Answer:

4 : 3 : 3

Step-by-step explanation:

2/5 of 150 = 300/5 or 60;  therefore, there are 60 blue marbles

3/10 of 150 = 450/10 or 45;  therefore, there are 45 clear marbles

150 - (60 + 45) = number of green marbles;  there are 45 green marbles

Blue : Clear : Green ratio is 60 : 45 : 45 or 4 : 3 : 3

please help me Simplify (4m3)2.

Answers

Answer:The simplified form of (4m3)2 is 24m.Step-by-step explanation:(4m3)2=> 4 x m x 3 x 2=> 24mConclusion:

Therefore, the simplified form of (4m3)2 is 24m.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Insert two rational number between 1.3 bar and 1.4 bar​

Answers

General method:

Given numbers are 1.3 bar and 1.4 bar

1.3 bar = 1.333...1.4 bar = 1.444...

Two rational numbers between them

= 1.3222... and 1.43333...

Mean Method:

Let X = 1.333... → → →eqn(i)

since the periodicity is 1 then multiply eqn(i) with 10

⇛10×X = 1.333...×10

⇛10X = 13.333... → → →eqn(ii)

Subtract eqn(ii)-eqn(i)

10X = 13.333...

X = 1.333...

(-)

____________

9X = 12.000...

____________

⇛9X = 12

⇛X = 12/9

⇛X = 4/3

and

Let X = 1.444... → → →eqn(i)

since the periodicity is 1 then multiply eqn(i) with 10

⇛10×X = 1.444...×10

⇛10X = 14.444...→ → →eqn(ii)

Subtract eqn(ii)-eqn(i)

10X = 14.444...

X = 1.444...

(-)

____________

9X = 13.000...

____________

⇛9X = 13

⇛X = 13/9

Now we have 12/9 and 13/9

The rational number between them by mean method (a+b)/2

⇛{(12/9)+(13/9)}/2

⇛(25/9)/2

⇛25/18

and Second rational number

⇛{(12/9)+(25/18)}/2

⇛{(24+25)/18}/2

⇛(49/18)/2

⇛49/36

Answer: The two rational numbers between them are 25/18 and 49/36.

also read similar questions: INSERT TWO RATIONAL NUMBERS BETWEEN 2 AND 3. How to find them?

https://brainly.com/question/85169?referrer

For f(x) = 4 - x and g(x) = 3x² + x + 5, find the following functions.
a.
(fog)(x); b. (gof)(x); c. (fog)(3); d. (gof)(3)

Answers

Look at the attached photo for the answers.

What is the y-intercept of the line?

Answers

Answer:

1

Step-by-step explanation:

It’s either 1 or 1/2, I believe it’s 1 more though so try that :)

Andrew is half his brother's age. Three years ago, the sum of their ages was 24. How old are they each now? Please answer Fast.

Answers

Answer:

Andrew 10 and his brother 20 years old

Step-by-step explanation:

three years ago

7 and 17  add up to 24

Hope this helps

Which inequality is displayed on the number line?

Answers

Answer is B x values are greater than or equal to –2.

expain plese and txsss

Answers

(x+2)(x-16)
A = X
B= 2
C= X
D= -16

Answer:

(x-16)(x+2)

Step-by-step explanation:

-32=-16*2

-16+2=-14

How long does it take for sunlight to reach earth? Show Work!

Answers

Answer: 8.3 minutes

Step-by-step explanation:

The time t may be obtained using the speed distance equation s=d/t. Rearranged to solve for time it would be: t=s/v, where s is the distance between the Sun and Earth and v is the speed of light.

Answer: The Sun is 93 million miles away, so sunlight takes 8 and 1/3 minutes to get to us.


Light from the Sun takes about 5 and 1/2 hours to reach it and roughly the same time to return to Earth. By the time the light reaches us, it has spread out so much that the planet looks very dim, and requires a good telescope to spot. Photo of Pluto and its moon Charon, as seen with the Hubble Space Telescope in 1994.

Sunlight travels at the speed of light. Photons emitted from the surface of the Sun need to travel across the vacuum of space to reach our eyes. The short answer is that it takes sunlight an average of 8 minutes and 20 seconds to travel from the Sun to the Earth

Picture:

9. Find the slope of the line
that passes through the
following pairs of points.


a. (5, 4) and (-4,3)


B. (10, 8) and (9, 13)

Answers

Answer:

a]y= 0.11x + 3.44

b]y= 0.11x + 3.44

explanation:

y=mx+b form

Help, please! I need this done for my finals.

Answers

Answer:

First one is yes second one is yes 3 one is yes 4 one is yes and first one is a repeating decimal

Step-by-step explanation:

Also sorry if it's wrong but I tried also hope u have a great day!

A print shop at a community college in Cupertino, California, employs two different contractors to maintain its copying machines. The print shop needs to have 12 IBM, 18 Xerox, and 20 Canon copying machines serviced. Contractor A can repair 2 IBM, 1 Xerox, and 2 Canon machines at a cost of $800 per month, while Contractor B can repair 1 IBM, 3 Xerox, and 2 Canon machines at a cost of $1000 per month. What is the minimum cost to employ the contractors? Round your answer to the nearest whole number. Do not include a dollar sign or comma in your answer.

Answers

The cost to employ the contractors is $11250

The general cost to employ someone is between 1.25 and 1.40 of their real wage. This means the real wage is lower than the cost to employ that person.

Moreover, to determine the cost to employ the contractors, we need to determine their total wage:

Contractor A:  $800 (Includes the repairment of 2 IBM, 1 Xerox, and 2 Canon machines).Contractor B: $1000 (Includes the repairment of 1 IBM,  3 Xerox, and 2 Canon machines.

Total: $1800 to repair 3 IBM, 4 Xerox, and 4 Canon machinesTotal machines to be repaired: 12 IBM, 18 Xerox, 20 Canon machines.

Now, for all the machines to be repaired you will need to pay a total of $9000

$1800 x 5 = $ 9000 (Includes the repairment of 15 IBM, 20 Xerox, and 20 Canon machines, which will cover all the machines you need).

Finally, let's find out the cost using the minimum rate.

$9000 x 1.25 = $11,250

Learn more about general cost in: https://brainly.com/question/3902215

Answer:

$8800

Step-by-step explanation:

Let x be the number of months contract A is employed and let y be the number of months contractor B is employed. Since we are trying to minimize cost, our objective function represents the total cost to employ contractor A and contract B. This function is defined by

C(x,y)=800x+1000y

The first constraint is that the company needs to have 12 IBM copying machines serviced and we know that contractor A can repair 2 IBM copying machines and contractor B can repair 1 IBM copying machines. This translates into the following inequality.

2x+y≥12

The second constraint is that the company needs 18 Xerox copying machines serviced and we know that contractor A can repair 1 Xerox copy machines while contractor B can repair 3 Xerox copy machines. This translates into the following inequality.

x+3y≥18

The third constraint is that the company needs 20 Canon copying machines serviced and we know that contractor A and contractor B can repair 2 Canon copy machines each. This translates into the following inequality.

2x+2y≥20

The fact that x and y must be positive numbers is represented by the following two constraints:

x≥0,y≥0

Using all of this information, our problem is as follows.

Minimize: C(x,y)=800x+1000y

Subject to: 2x+y≥12

x+3y≥18

2x+2y≥20

x≥0

y≥0

The corner points are:

(0,12),(18,0),(2,8),(6,4)

The point (6,4) gives lowest cost: $8800

6x+3y=-3 how to graph it need answers quick

Answers

Answer:

Equation in slope intercept form: y = -2x -1

Step-by-step explanation:

First you must convert this equation from standard form to slope intercept form (y=mx+b).

Subtract 6x on both sides to get 3y = -6x - 3. Then divide by 3 on both sides to get y = -2x - 1.

Now to graph:

First we will plot the y-intercept, which will be (0,-1). The point will be on the y-axis, since that's the point in which the line will cross.

Next we will go down 2 units and over to the right 1 unit, until we get to the next point.

(Picture is attached above for your convenience⤴⤴⤴)

Hope this helps you :)

9. GIVEN: y(x + 1) = 51; y = 3 PROVE: x = 16​

Answers

Answer:

see explanation

Step-by-step explanation:

y(x + 1) = 51 ← substitute y = 3 into the equation

3(x + 1) = 51 ( divide both sides by 3 )

x + 1 = 17 ( subtract 1 from both sides )

x = 16

Answer:Below!Step-by-step explanation:

Given:

y(x + 1) = 51y = 3

What to prove: x = 16

=> y(x + 1) = 51=> 3(x + 1) = 51=> 3x + 3 = 51=> 3x = 51 - 3=> 3x = 48=> x = 16Conclusion:

We have now proved that x = 16.

Hoped this helped.

[tex]BrainiacUSer1357[/tex]

Write as an equation and solve: Eight less than the number is 31.

Answers

Step-by-step explanation:

x is the number

so, the equation is

x - 8 = 31

x = 39

Answer:

n is the number

Step-by-step explanation:

n-8=31

n = 39

hoped that helped:P

Help me please 13x55x10

Answers

The answer is 7,150.

Pls Help! Which graph A,B or C?​

Answers

Answer:

Answer=C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Parallel lines hAve no solutions

Option A omitted

Two lines intersection point gives one solution only

Option B omitted

One single line denotes to infinite solutions

Option C is correct

Jacob has 4 reams of paper. Each ream of paper has 250 sheets of paper.
He will take the paper and make booklets. Each booklet will use 8 sheets of
paper What is the greatest number of booklets Jacob can make with this
amount of paper?
A 262
B. 125
C 1,008
D. 575

Answers

Answer: 125

Explanation
250x4=1000
1000 divided by 8 = 125
Answer:125 bookletsStep-by-step explanation:

1 ream = 250 papers

=> 4 reams = 250 x 4=> 4 reams = 1000 papers.

1 booklet = 8 papers

=> 1000 ÷ 8 = x booklets=> 125 bookletsConclusion:

Therefore, with 4 reams of paper, Jacob will be able to create 125 booklets.

Hoped this helped.

[tex]-BrainiacUser1357-[/tex]

Please help! IXL math problem

Answers

Answer:

224, 755

Step-by-step explanation:

you first have to find the differnce between 177 and 47 which equals to 133.

so you have to do 94+133

and 885-133

Jessica is wrapping a gift in a rectangular box with gift wrapping paper for a birthday party. The box is 11 inches long, 8 inches wide, and 5 inches tall. How much gift wrapping paper will she need to wrap the box

Answers

Using the surface area of a rectangular prism, it is found that she will need 366 square inches of wrapping paper to wrap the box.

He wraps the box with paper outside, hence, the amount needed is the surface area.

Surface area:

The surface area of a rectangular prism of length l, width w and height h is given by:

[tex]S = 2(lw + lh + wh)[/tex]

In this problem, the dimensions of 11 inches long, 8 inches wide, and 5 inches tall mean that [tex]l = 11, w = 8, h = 5[/tex]. Hence:

[tex]S = 2[11(8) + 11(5) + 8(5)] = 366[/tex]

She will need 366 square inches of wrapping paper to wrap the box.

You can learn more about the surface area of a rectangular prism at https://brainly.com/question/1310421

Which rule was used to create the input/output?

Answers

The answer should be A i think

Answer:

B. y = -4x

Step-by-step explanation:

input x in the possible answers

y = -4x

-4(2) = 8

-4(1) = -4

-4(-3) = 12

-4(-5) = 20

Mattie Evans drove 350 miles in the same amount of time that it took a turbopropeller plane to travel 1350 miles. The speed of the plane Has 200 mph faster than
the speed of the car. Find the speed of the plane.

(Simplify )

Answers

let

d1 = 250 mi the distance that Mattie Evans drove

v1 = the speed of Mattie Evans

d2 = 1300 mi the distance the plane traveled

v2 = the speed of the plane

The speed of the plane was 190 mph faster than the speed of the car:

v2 = v1 + 190

since time = distance/speed and they both traveled the same time we have

d1/v1 = d2/v2

250/v1 = 1300/v2 cross multiply

250v2 = 1300v1 divid eboth sides by 50

5v2 = 26v1

by solving the system of equations:

v2 = v1 + 190

5v2 = 26v1

we find

v1 = 45.24 mph

v2 = 235.24 mph

Find the volume of the sphere.

Answers

Answer:

4.19

Step-by-step explanation:

v=4/3(pie x r^3)

v=4/3(pie x 1^3) = 4.18879

v=4.19

I actually need help please help quickly

Answers

Answer:

NEED MORE

Step-by-step explanation:

find measure of angle b

Answers

Answer:

9. b=120 8. b=43 11 b=84 12 b=23

Step-by-step explanation:

number 9 the angle is equals to 189 number 10 they're both the same and 11 is equal to 180, 12 the angle is equal to 90

Given that p²,q² are two roots of x²-x+16=0.
Form another equation with roots 1/p,1/q.

Answers

Answer:

  x² -3/4x +1/4 = 0

Step-by-step explanation:

Consider the two equations in factored and expanded forms:

  (x -p²)(x -q²) = x² -(p²+q²)x +p²q² = 0   ⇒   p²+q² = 1, p²q² = 16

and

  (x -1/p)(x -1/q) = x² -(1/p+1/q)x +1/(pq) = 0

Consider the squares of the sum and product of roots:

  constant term: (1/(pq))² = 1/(p²q²) = 1/16   ⇒   1/(pq) = √(1/16) = 1/4

  x-term: (1/p +1/q)² = (p +q)²/(pq)² = (p² +q² +2pq)/(p²q²)

  = (p² +q²)/(p²q²) +2/(pq)

  = 1/16 +2/√16 = 9/16   ⇒   (1/p +1/q) = √(9/16) = 3/4

Then the equation with roots 1/p and 1/q is ...

  x² -3/4x +1/4 = 0

Need help with properties if dilations homework

Answers

With a dial action, although the dilated image may get smaller or larger the angles/ slope of lines would remain the same.

Slope = change I. Y over the change in X

Slope = (5-4) /(3-2) = 1/1 = 1

Slope = 1

If the average volume flow of blood through the aorta is 8.5 × 10-5 m 3/s and the cross-sectional area of the aorta is 3.0 × 10 -4 m2, what is the average speed of blood in the aorta?

Help me:)

Answers

The average speed of blood in the aorta is 0.2833 m/s

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance  / time

From the question, to calculate the average speed:

Average speed = Volume rate / cross sectional area

Average speed = 8.5 * 10⁻⁵ / (3 * 10⁻⁴) = 0.2833 m/s

The average speed of blood in the aorta is 0.2833 m/s

Find out more on average speed at: https://brainly.com/question/680492

solve plssssssssssssssssssssssssssssssssssssssssssssss

Answers

If any questions leave a comment

Answer:

[tex]\frac{973}{324} [/tex]

Step-by-step explanation:

[tex] ( - \frac{ 27}{64} - ( - \frac{125}{8} ))\times ( \frac{2}{3} )^{4} [/tex]

[tex] ( - \frac{ 27}{64} + \frac{125}{8} ) \times \frac{16}{81} [/tex]

[tex] \frac{973}{64} \times \frac{16}{81} [/tex]

[tex] \frac{973}{4} \times \frac{1}{81} [/tex]

[tex] \frac{973}{324} [/tex]

A math book at the Victor Valley College bookstore originally cost $84 to purchase. If they sell it for $126, what is the markup rate?

Answers

The answer is 150%
Equation: 126/84= 1.5• 100= 150%
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