In a geometric sequence, g(3) = 1 and g(8) = 32. Which recursive definition produces this geometric sequence?

Answers

Answer 1

Step-by-step explanation:

a geometric sequence means every new element is created by multiplying the previous element always with the same number.

a n = a n-1 * number

a n = a1 * number^(n-1)

=> a8 (or g(8)) / a3 (or g(3)) = number^5 (5=8-3)

=> 32/1 = number^5

=>

[tex]number = \sqrt[5]{32} [/tex]

number = 2

and what is the starting a1 ?

it must satisfy e.g. a3

1 = a1 * 2^2

=> a1 = 1/4

therefore, the requested definition looks like

g(1) = 1/4

g(n) = g(n-1) * 2


Related Questions

I NEED HELPPPPP PLEASE

Answers

Answer:

66 ft^2

Step-by-step explanation:

2 x 3 = 6

5 x 12 = 60

6 + 60 = 66

Answer:

A=A1 + A2

A= (l×w) + (l×w)

A= ((12-3)×5) + (3×(5+2))

A=66 ft^2

Help help help help help help dont troll

Answers

Answer:the correct answer is C

Step-by-step explanation:

HELP PLEASEEEE I WILL MARK BRAINLIEST

Answers

Answer:

Step-by-step explanation:

we need to make two rectangles.  

one that is 13.1 Km  X  (9.3-4.2) Km

13.1 * 5.1 = 66.81

the next box is 4.2 X (13.1-8.1)

4.2*5 = 21

area total = 21 + 66.81 = 87.81[tex]Km^{2}[/tex]

You are road tripping down the California coast and you notice you need to fill up your gas tank. In CA, sales tax is 2.25%. You spend $56.00 to fill up your tank. How much are you paying in sales tax?

Answers

Answer:

$1.26

Step-by-step explanation:

So you just have to find 2.25% of 56.

To find a certain percentage of something, you multiply it. Let's write out a sentence explaining what you need to do. You have to find:

2.25% of 56

Whenever you've got a sentence like this, all you've got to do is change the word "of" to a multiplication symbol. And now you've got an expression:

2.25% × 56

Let's convert the percentage to a decimal. To do this, you simply remove the percent symbol, then move the decimal point 2 places to the left.

2.25% = 0.0225

And now you have:

0.0225 × 56

Then you just do the math! I am assuming you already know how to do decimal multiplication so I'm not going to explain the process here.

But once you multiply 0.0225 × 56, you get an answer: 1.26

Hope this was helpful to you, and don't forget to choose the Brainliest answer!

Help! Will give out brainliest

Answers

Answer:

75

Step-by-step explanation:

don't know how to explain hope this helps

it would be 75

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how do i do tangent lines?

Answers

Answer:

x = 154°

Step-by-step explanation:

The 4 interior angles of the quadrilateral sum to 360°

The angles between the tangents and the radii = 90°

Then

x = 360° - (90 + 90 + 26)° = 360° - 206° = 154°

Can somebody please help? It don't get it

Answers

Answer:  4

14 is shown... then you have 10 that is shown how much more would it take to make 14..... 4 more

10+x=14

x=4

Answer:

Equation: 14 - j = 10

j = 4

Step-by-step explanation:

Tell whether the statement is always, sometimes, or never true. Explain.

1. If x and y are supplementary angles, then y is acute.

2. If x and y are complementary angles, then x is obtuse.

Answers

Answer:

1. If x and y are supplementary angles, then y is sometimes acute because supplementary angles are angles that add up to 180 degrees. So, y can be acute while x can be obtuse, y can be obtuse while x can be acute, or both can be right angles.

2. If x and y are complementary angles, then x is never obtuse. Complementary angles are angles that add up to 90 degrees, and obtuse angles are angles over 90 degrees, so it's impossible to have an obtuse angle as a complementary angle.  

Step-by-step explanation:

Answer:

1) Sometimes

2) Never

Step-by-step explanation:

1) you could have two angles add up to 180 degrees and one of them could be less than 90

example, x = 140° and y = 40°

2) if two angles are complementary then their sum is 90° so neither angle must be less than 90°, thereby making them both acute angles

Is the ratio 15:12 equivalent to these? Explain your reasoning.

Answers

Let's simplify the ratio

[tex]\\ \sf\longmapsto 15:12[/tex]

[tex]\\ \sf\longmapsto \dfrac{15}{12}[/tex]

Cancel by 3

[tex]\\ \sf\longmapsto \dfrac{5}{4}[/tex]

[tex]\\ \sf\longmapsto 5:4[/tex]

A boat leaves the dock and travels 7 miles due south, then 24 miles due west.

How far is the boat from the dock?

A. 625 mi
B. 31 mi
C. 17 mi
D. 25 mi

Answers

Answer:

D

Step-by-step explanation:

The boat is a distance of 25 miles far away from the dock. which is the correct would be an option (D).

What is the right triangle?

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

A boat leaves the dock and travels 7 miles due south, then 24 miles due west which is given in the question.

According to Pythagoras's theorem,

In a right-angled triangle, "the square of the hypotenuse is equal to the sum of the squares of the other two sides."

perpendicular²+base²=hypotenuse²

The hypotenuse = c

Here , perpendicular = 7 and base = 24

⇒ 24² + 7² = c²

⇒ 576 + 49 = c²

⇒ 625 = c²

⇒ c² = 625

⇒ c = 25

Therefore, the boat is a distance of 25 miles far away from the dock.

Learn more about the right triangle here:

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A triangle has interior angles of 101 degrees, 65 degrees, what is the other degree?

Answers

Answer:

180 degrees - 101 degrees - 65 degrees = 14 degrees

Solve 9x + 18 = 6y - 3x for y​

Answers

Answer:

y = 2x + 3

Step-by-step explanation:

6(2x-3) - 2(2x+1)
can someone get an answer for that ASAP pls
no links :)​

Answers

Answer: 8x−20

Step-by-step explanation:

Distribute:

=(6)(2x)+(6)(−3)+(−2)(2x)+(−2)(1)

=12x+−18+−4x+−2

Combine Like Terms:

=12x+−18+−4x+−2

=(12x+−4x)+(−18+−2)

=8x+−20

Answer:

[tex]6 \times 2x = 12x\\ 6 \times - 3 = - 18 \\ - 2 \times 2x = 4x \\ - 2 \times 1 = - 2 \\ now \: add \: like \: terms \\ 12x - 4x = 8x \\ - 18 - 2 = 20 \\ \frac{ - 8x}{8} = \frac{20}{8} \\ x = 2.5 \: or \: \frac{5}{2} [/tex]

Step-by-step explanation:

brainiest please

PLEASE HELP!!!! I NEED THE ANSWERS URGENTLY!
Find each missing length. Give all answers in simplest radical form.​​

Answers

Step-by-step explanation:

here's your solution

==> by using Pythagoras theorem

==> base^2 = hypotenuse^2 - perpendicular^2

==> hypotenuse = 18 , perpendicular = 16

==> base^2 = 18^2 - 16^2

==> base^2 = 324 - 256

==> base^2 = 68

==> base = √68

==> base = 8.24

[tex]hope \: it \: helps[/tex]

PLEASE HELPP :(

Does the relationship shown in the table represent a direct or inverse variation relationship?

A: Direct, as x increases, y also increases
B: Direct, as x increases, y decreases
C: Inverse, as x increases, y also increases
D: Inverse, as x increases, y decreases ​

Answers

Step-by-step explanation:

i think

C: Inverse, as x increases, y also increases

Step-by-step explanation:

C: Inverse, as x increases, y also increases

hope it is helpful to you


Help PLEASE ILL MARK BRAINLIEST!!!
















Mario ran backwards 5 spaces then jumped up 3 spaces. How can we show this as an ordered pair?

Answers

I need points pleaseeee
(x-5, y+3)

explanation: going backwards represents subtraction on the x-axis so it would be -5 and jumping up represents increasing the y-axis so it would be +3

Find the total area round to the nearest 10th if necessary use the pi symbol on calculator

Answers

Answer:

[tex] Total \:area\approx 290.5\: ft^2 [/tex]

Step-by-step explanation:

Total area [tex] =\frac {1}{2} \pi r_1^2 +\frac {1}{2} \pi r_2^2 [/tex]

(where [tex] r_1 = 22/2 = 11 \: ft, \: \:\:r_2 = (30-22)/2 = 4 \: ft[/tex])

[tex]\therefore Total \:area=\frac {1}{2} \pi( r_1^2 + r_2^2) [/tex]

[tex]\therefore Total \:area=\frac {1}{2} \times 3.14(11^2 + 8^2) [/tex]

[tex]\therefore Total \:area=1.57(121 + 64) [/tex]

[tex]\therefore Total \:area=1.57(185) [/tex]

[tex]\therefore Total \:area=290.45\: ft^2 [/tex]

[tex]\therefore Total \:area\approx 290.5\: ft^2 [/tex]

Find the x intercepts of the graph of -6x + 5y =24. State your answers as while numbers or as improper fractions in simplest form.

Answers

Answer:

x-intercept: -4

y-intercept: 24/5

Step-by-step explanation:

Firstly you have to isolate the y:

-6x + 5y = 24

5y = 6x + 24

y = (6x +24)/5

Now, just think about the graph: when the function touch the x-axis, the value of y is equal to 0, and when the function touch the y-axis, the value of x is 0, so just put they in the function:

y = (6•0 + 24)/5

y = 24/5

0 = (6x + 24)/5

5•0 = 6x +24

0 = 6x +24

-6x = 24

x = 24/-6

x = -4

(x+1)^2 = -4
What are the solutions?

Answers

Answer:

x = 4i - 1 or

x = 4i + 1

Step-by-step explanation:

(x+1)^2 = -4

x+1 = (+-)4i

x = +-4i - 1

==>

x = 4i - 1 or

x = 4i + 1

Please help!! Thanks in advance!! NO links!!

Kallan will spin each spinner one time. What is the probability that the first spinner will land on a number greater than 7 and the second spinner will land on blue?

Answers

Answer:

probability for numbers greater than seven would be: 5/12

probability for landing on blue would be: 2/8

Step-by-step explanation

first, I counted all of the spaces, then I counted only the blue , or only the numbers over 7.

The length of rectangle PQRS is expressed as 2x+7. The width of rectangle PQRS is expressed as 3x−4. Which expression describes the area of rectangle PQRS?
A.6x^2
B.6x^2-29x-28
C.6x^2-15
D.6x^2+13x-28

Answers

Answer:

[tex]area = length \times width \\ = (2x + 7)(3x - 4) \\ = (6 {x}^{2} - 8x + 21x - 28) \\ = (6 {x}^{2} + 13x - 28) \: sq \: units[/tex]

The area of the rectangle PQRS is given by the formula D) 6x²+13x-28.

What is algebraic Expression?

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

The area of a rectangle is given by the formula:

A = l × w, where l is the length and w is the width.

In this case,

The length is 2x + 7 and the width is 3x - 4.

Therefore, the area of the rectangle is:

[tex]A = (2x + 7)(3x - 4)\\A = 6x^2 - 8x + 21x - 28\\A = 6x^2 + 13x - 28[/tex]

Therefore, the expression that describes the area of rectangle PQRS is D) 6x²+13x-28.

Learn more about algebraic Expression here:

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5 of 10
A fair dice is rolled.
Work out the probability of getting a number more than 4.
Give your answer in its simplest form.

Answers

Answer: 1/3

Step-by-step explanation:

numbers more than 4 are: 5, and 6

so 2/6 chance of rolling a number greater than 4

in simplest form this is 1/3

Answer:

number 4 are t is greater


When graphing a sine curve model using the equation Y = sin bx, the period (or wavelength) will be represented by
3
27
So be
period
Determine the equation for the sine curve that models the G# wave if the
wavelength of G# = 0.828 meters.
a.
y = sin(6.03x)
b. y = sin(0.828x)
C. y = sin(5.68x)
d. y = sin(7.59x)
Please select the best answer from the choices provided

use pic to answer

Answers

Answer:

its D, y= sin(7.59x)

Step-by-step explanation:

just took the quiz on edge

If P( 9,r ) = 3,024, what is r ?

plz plz plz... help mè

I mark it... :(​

Answers

Answer:

[tex] \frac{9i}{(9 - r)i} = 3024 \\ (9 - r)i = 9i \div 3024 = 362880 \div 3024 = 120 = \\ = 1 \times 2 \times 3 \times 4 \times 5 = 5i \\ r = 4[/tex]

how to tell the transformation of graphs?​

Answers

Identify The Parent Function. Ernest Wolfe. ...
Reflect Over X-Axis or Y-Axis. ...
Shift (Translate) Vertically or Horizontally. ...
Vertical and Horizontal Stretches/Compressions. ...
Plug in a couple of your coordinates into the parent function to double check your work.

Answer:

:D

Step-by-step explanation:

if the parent function, y=f(x) has a number added (y=f(x)+4) the graph will be translated up. If the parent function has a number subtracted, y=f(x)-4, the graph will be translated down. The image explains more simply, and there are more possible translations (shown in image)

Elena has written 3 sports books for kids. One book is about soccer, one is about baseball, and one is about basketball. Elena has sold a total of 3,017 of the books in local bookstores. She sold 3 times as many copies of the soccer book as the baseball book. She sold the same number of copies of the basketball book as the soccer book. How many copies of the soccer book has she sold?

Answers

Answer:

1293 soccer books

Step-by-step explanation:

The tricky part about questions like this is: how do I assign variables to the three types of book?

You get a clue from the sentence, "She sold 3 times as many copies of the soccer book as the baseball book."  The number of soccer books is being described by referring TO the number of baseball books.  Pick a variable and assign it to the item being REFERRED TO!

x = number of baseball books

Then  3x = number of soccer books.  The number of basketball books is the same, so 3x = number of basketball books.  Here's the list...

x = number of baseball books

3x = number of soccer books

3x = number of basketball books

The total of these is 3017, so

x + 3x + 3x = 3017

7x = 3017

x = 431

Ah!  But don't forget to look back at the question:  it asks for the number of SOCCER books!  That's 3x, so 3(431) = 1293.

Find the distance between the points

Answers

Answer:

12 hope this help

Step-by-step explanation:

The answer is 12 ,you have to count down from point B(-10,3) to point A (-10,-9)

could you help me with this maths problem please

10 - ____ = 9 1/8

i need to find the fraction taken away from 10 to get 9 1/8

Answers

Answer:

12

Step-by-step explanation:

I forgot Sorry

Answer:

The answer is 7/8.

You can simply bring 9⅛ to the left hand side

You'll have your answer .

To verify

10-7/8 = 73/8

which further simplifies to 9⅛.

Thanks

Please help I need to get this done

Answers

Answer:

48

Step-by-step explanation:

So you take 7x-92+6x+12=180

And then you get x=20

Plug in 20 for x for <LOM

And you get and you get 48

Hope this helped!!

The following two-way table shows the number of students of a school who have a cell phone and/or have a part-time job: Have Cell Phone Do Not Have Cell Phone Total Have Part time Job 40 10 50 Do Not Have Part time Job 10 40 50 Total 50 50 100 Based on the table, how many students have both a cell phone and a part-time job? (5 points) Question 14 options: 1) 10 2) 40 3) 50 4) 100

Answers

Answer:

I think it is B, so the correct answer is 40

Step-by-step explanation:

Answer:

The other guy is correct, the correct answer is B. 40.

Step-by-step explanation:

Under Students that have a cell phone and under students that have a part-time job the total amount of people is 40

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