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The function f(n)=−48⋅(-¼)^n is a geometric sequence

The recursive definition of f(n) is f(1) = 12;  f(n) = f(n - 1) . -¼

The function is given as:

f(n)=−48⋅(-¼)^n

Calculate f(1)

f(1)=−48⋅(-¼)^1

This gives

f(1) = 12

Calculate f(2)

f(2)=−48⋅(-¼)^2

This gives

f(2) = -3

Calculate the common ratio (r)

r = f(2)/f(1)

So, we have:

f = -3/12

Simplify

r = -1/4

Recall that: r = f(2)/f(1)

This gives

-1/4 = f(2)/f(1)

Make f(2) the subject

f(2) = -1/4* f(1)

Express 1 as 2 - 1

f(2) = -1/4* f(2 - 1)

Substitute 2 for n

f(n) = -1/4* f(n - 1)

Rewrite as:

f(n) = f(n - 1) . -¼

Hence, the recursive definition of f(n) is f(1) = 12;  f(n) = f(n - 1) . -¼

Read more about sequence at:

https://brainly.com/question/7882626

Answer:

13.5

Step-by-step explanation:

it rlly easy

Answer:

204 degrees is the answer

Step-by-step explanation:

.l

Answer:

119

Step-by-step explanation:

all angles in a triangle add up to 180

180-61-58=61

so missing inner angle is 61

then to solve 1:

180-61=119

Answer:

4000

Step-by-step explanation:

40 x 100

28/5 = 5.6
then round it up so it would be 6

________________________________________________________

[tex]35 + 15 = 50[/tex]

[tex]13 + 15 = 28[/tex]

________________________________________________________

It would take Kelly 37 more years to become 50, because 37 + 13 = 50

Now that we have found the number of years remaining, add her mother's age by the remaining years left, r

[tex]35 + r(37) = 72[/tex]

Answer:

she saved $340 in total

Step-by-step explanation:

(15 x 20) + 40 = s

s = savings

Maturity Value: 9,159.08

Interest: 1,359.08

Answer:

Part A) The length of rectangle is [tex]3x[/tex] [tex]cm[/tex]

Part B) The perimeter of the square is [tex]3x[/tex] [tex]cm[/tex]

Part C) [tex]20[/tex] [tex]cm[/tex]

Part D) [tex]39[/tex] [tex]cm^2[/tex]

Step-by-step explanation:

Part A) Find the length of the rectangle

we know that

The perimeter of rectangle is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]P=8x[/tex] [tex]cm[/tex]

[tex]W=x[/tex] [tex]cm[/tex]

substitute and solve for L

[tex]8x=2(L+x)[/tex]

[tex]4x=(L+x)[/tex]

[tex]L=4x-x=3x[/tex] [tex]cm[/tex]

Part B) Find the perimeter of the square

we know that

The perimeter of a square is

[tex]P=4b[/tex]

we have that

[tex]b=(1/4)L[/tex]

substitute the value of L

[tex]b=(1/4)3x=(3/4)x[/tex] [tex]cm[/tex]

Find the perimeter of the square

Part C) Find how many cm greater the rectangle's perimeter than the square's perimeter if x=4

Find the value of rectangle's perimeter

[tex]P=8x[/tex] [tex]cm[/tex] ------> [tex]P=8(4)=32[/tex] [tex]cm[/tex]

Find the value of square's perimeter

[tex]P=3x[/tex] [tex]cm[/tex] ------> [tex]P=3(4)=12[/tex] [tex]cm[/tex]

Find the difference

[tex]32[/tex] [tex]cm[/tex] [tex]-12[/tex] [tex]cm[/tex] [tex]=20[/tex] [tex]cm[/tex]

Part D) Find how many square cm greater the rectangle's area is than the square's area if x=4

Find the value of rectangle's area

[tex]A=(3x)(x)=3x^2[/tex] [tex]cm^2[/tex] ------> [tex]A=3(4^2)=48[/tex] [tex]cm^2[/tex]

Find the value of square's area

[tex]A=((3/4)x)^2[/tex] [tex]cm^2[/tex] ------> [tex]A=((3/4)(4))^2 = 9[/tex] [tex]cm^2[/tex]

Find the difference

Answer: 2(mJKL)=mJL

Step-by-step explanation: The arc angle is double the inscribed angle

Answer:

3:5

[tex]12~to~20 -- > 12:20[/tex]

[tex]\frac{12 / 4}{20 / 4} = \frac{3}{5} -- > 3:5[/tex]

________________________________________________________

The problem is now complete, time to go over what we just learned while reading this.

________________________________________________________

We learned how to find and simplify ratios in a story problem.

Related questions? Ask me in the comments box.

Answer:

2

Step-by-step explanation:

I think it's 2 if it is wrong pls correct me

Answer:The answer is D

Step-by-step explanation:

I know this because all the area of each face is equal to 10+10+52+32+40 and that is equal to 144in. squared

Answer:

D :)

Step-by-step explanation:

wait, have you smiled today? its very important:)

Answer:

about 78in^2

Step-by-step explanation:

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

A = [tex]\pi 5^{2}[/tex]

A = [tex]\pi * 25[/tex]

A = 3.14 * 25

A ≈ 78[tex]in^{2}[/tex]

The measure of angle L is 52

Step-by-step explanation:

Mathematically, in a triangle, the sum of the angles equal 180

So in this case;

J + K + L = 180

So therefore;

8x + 6 + 2x + 2 + 4x + 4 = 180

8x + 2x + 4x + 6 + 2 + 4 = 180

14x + 12 = 180

14x = 180 -12

14x = 168

x = 168/14

x = 12

So to get the measure of angel L, we simply substitute the value x in the equation for L

From the question, L = 4x + 4

So therefore L = 4(12) + 4 = 48 + 4 = 52

Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

If in ΔHIJ, m∠H = x - 1, m∠I = 2x + 5, and m∠J = 7x + 6.

The value of x is  17.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

Example:

Triangle ABC:

m∠A + m∠B + m∠C = 180

We have,

ΔHIJ

m∠H = x - 1

m∠I = 2x + 5

m∠J = 7x + 6

We know that,

The sum of the angles of the triangle is 180 degrees.

m∠H + m∠I + m∠J = 180

(x - 1) + (2x + 5) + (7x + 6) = 180

x - 1 + 2x + 5 + 7x + 6 = 180

10x + 10 = 180

Take 10 common.

10 (x + 1) = 180

Divide both sides by 10.

x + 1 = 180/10

x + 1 = 18

Subtract 1 on both sides.

x = 18 - 1

x = 17

Thus,

If in ΔHIJ,

m∠H = x - 1

m∠I = 2x + 5

m∠J = 7x + 6.

The value of x is  17.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ5

Answer:

CTRL C to copy and CTRL V to paste

Step-by-step explanation:

please mark brainliest and btw if you dont want to get plagarized use quillbot

Answer:

16.50 + 10.50p ≤ 90

Step-by-step explanation:

add the parking amount and the ticket cause per person (p) to make it less than or equal to $90 since that’s the only amount of money that could be used

Answer: is 126 degrees

Step-by-step explanation:

Step-by-step explanation:

The radius,r is 1 unit

The sum of angles is = π + π/4

5π/4

The length of the arc = (5π/4)/2π • 2πr

= 5π/4 units

Answer:

1/2

Step-by-step explanation:

I took the test and rise/run is being asked

Answer:

2⁶-1

Step-by-step explanation:

[tex] ({2}^{0} + {2}^{1} + {2}^{2} + {2}^{3}) + {2}^{4} + {2}^{5} \\ = ({2}^{4} - 1) + {2}^{4} + {2}^{5} \\ = 2( {2}^{4} ) + {2}^{5} - 1 \\ = {2}^{5} + {2}^{5} - 1 \\ = 2( {2}^{5} ) - 1 \\ = {2}^{6} - 1[/tex]

Answer:

lol, that is true she should stop drinking too much water.

But all jokes aside, the answer is A. At least one day she drank exactly 6 cups of water.

Answer:i dont think so..

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the yellow counters be represented by 'y' and black counters by 'b'.

Originally

After removing 21 counters

Taking the first ratio, equate it to b.

Now, substitute for 'b' in the second ratio.

Now, to find b :

Answer:

12

Step-by-step explanation:

Given ratio

yellow : black = 3 : 1

⇒ yellow : black = [tex]3x : x[/tex]

If 21 yellow counters are removed and the ratio becomes 5 : 4

[tex]\implies \textsf{yellow - 21: black = 5 : 4}[/tex]

[tex]\implies (3x - 21):x=5:4[/tex]

[tex]\implies \dfrac{3x - 21}{x}=\dfrac54[/tex]

[tex]\implies 4(3x - 21)=5x[/tex]

[tex]\implies 12x-84=5x[/tex]

[tex]\implies7x=84[/tex]

[tex]\implies x=12[/tex]

Substituting [tex]x=12[/tex] into the original ratio:

[tex]\implies \textsf{yellow : black} =3(12) : (12)=36:12[/tex]

So the total number of black counters = 12