Determine the explicit form of the function that describes the sequence below.
16, 24, 36, 54, ...

A. f(n) = 8n + 8
B. f(n) = 16(3/2)^(n - 1)
C. f(n) = 3/2(n - 1) + 16
D. f(n) = 3/2(16)^(n - 1)

Answers

Answer 1

Answer:

B. f(n) = 16(3/2)^(n - 1).

Step-by-step explanation:

You can just substitute values. For questions like these, I usually use the second or third value to try the equations, because most of the time, the people who made these problems would make them all work for the first or last values.

A: 8n + 8 = 8 * 3 + 8 = 24 + 8 = 32. 32 is not equal to 36, so you can eliminate A.

B: 16 (3/2)^ (n - 1) = 16 * (1.5)^ (3 - 1) = 16 * (1.5)^ 2 = 16 * 2.25 = 36. 36 = 36, so you can keep this choice... for now.

C: 3/2 (n - 1) + 16 = 1.5 * (3 - 1) + 16 = 1.5 * 2 + 16 = 3 + 16 = 19. 19 does not equal 36, so you can eliminate C.

D: 3/2 (16)^ (n - 1) = 1.5 * (16)^ (3 - 1) = 1.5 * 16^2 = 1.5 * 256 = 384. 384 does not equal 36, so you can eliminate D as well.

Since A, C, and D do not work, you can say that the explicit form of the function would be Choice B.

Just to be sure, you can check using all four values...

f(1) = 16 * (1.5)^0 = 16 * 1 = 16   TRUE

f(2) = 16 * (1.5)^1 = 16 * 1.5 = 24   TRUE

f(3) = 16 * (1.5)^2 = 16 * 2.25 = 36   TRUE

f(4) = 16 * (1.5)^3 = 16 * 3.375 = 54   TRUE

Since all of the values match up, you can be sure that Choice B is the right answer.

Hope this helps! :)

Answer 2

The explicit form of the function that describes the sequence is

[tex]T_n[/tex] = 16 (1.5[tex])^{n-1[/tex].

What is Explicit form?

Without expressing the other terms of the sequence, explicit formulas are always utilised to represent any term of the sequence. The word "explicit" means something that may be found directly without having to know the other phrases in the sequence. A single formula, known as the explicit formula, can be used to describe each term in a series in an individual way.

we have sequence

16, 24, 36, 54, ......

So, a = 16

r =24/16  = 1.5

So, the standard form of explicit form

[tex]T_n = a r^{n-1[/tex]

Then, [tex]T_n[/tex] = 16 (1.5[tex])^{n-1[/tex]

Learn more on geometric sequence here: brainly.com/question/24643676

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Related Questions

Which of these sets of points lie within plane w?

A.
Cand G
B.
Hand E
C.
C and E
D
A and D

Answers

Answer:

option c boo if it's for plata

Shelby has already knit 8 centimeters of scarf, and can knit 1 centimeter reach night. How many nights will Shelby have to spend knitting in order to knit a total of 47 centimeters of scarf?

Answers

Answer:

39 nights.

Step-by-step explanation:

If Shelby can knit 1 centimeter per night, the amount of centimeters = the amount of nights.

Equation:

47-8=39

39 nights.

Hope this helps! :) :)

-2n-13= - 3n - 5 pls solve!

Answers

Answer:

n = 8

Step-by-step explanation:

-2n - 13 = -3n - 5

-2n + 3n = -5 + 13

n = 8

Hope this helps. Have a nice day!

Hey Your answer is n=8

a) Change 2800 cm³ into litres.

b) Change 12.4/ into cm³.​

Answers

Answer:

[tex]\huge\boxed{a)\ 2,800cm^3=2.8l}\\\boxed{b)\ 12.4l=12,400cm^3}[/tex]

Step-by-step explanation:

[tex]1l=1dm^3\\\\1dm=10cm\to1dm^3=(10cm)^3=1,000cm^3\\\\\text{therefore}\ 1l=1,000cm^3\to1cm^3=\dfrac{1}{1,000}l=0.001l\\\\a)\ 2,800cm^3=2,800\cdot0.001l=2.8l\\\\b)\ 12.4l=12.4\cdot1,000cm^3=12,400cm^3[/tex]

Answer:

a) 2.8 liters

b) 12400 cm³

Step-by-step explanation:

1 cm³ = 1 mL

1000 mL = 1 L

a)

2800 cm³ × (1 mL)/(1 cm³) × (1 L)/(1000 mL) = 2.8 L

b)

12.4 L × (1000 mL)/(1 L) × (1 cm³)/(1 mL) = 12400 cm³

you worked 6 and three fourths hours on Monday Seven and one fourth on Tuesday eight and one fourth on wendsey seven and one fourth on Thursday seven and three fourths on Friday how many hours did you work for the week

Answers

Answer:

37.25

Step-by-step explanation:

6.75+7.25+8.25+7.25+7.75=37.25

Pls Mark as Brainliest

What is the y-intercept of the function f(x)=4 - 5x?
-5
-4
4
5

Answers

Answer:

b = 4

Step-by-step explanation:

Use the slope-intercept form  y = m x + b  to find the y-intercept  b .

Answer:

C: 4

Step-by-step explanation:

pls help me with algebra i dont get it

Answers

Answer:

(0,2)

Step-by-step explanation:

i used a graphing calculator hopefully its right

Answer:

(-7,-14)

Step-by-step explanation:

you x is decreasing by -7 so your x is -7 and your y  is decreasing by -14.

A group of students must collect at least $160 to organize a science fair. They have already collected $20. Which graph best represents the possible amounts of money the students still need to collect? (1 point) Number line graph with closed circle on 160 and shading to the right. Number line graph with closed circle on 140 and shading to the right. Number line graph with closed circle on 20 and shading to the right Number line graph with closed circle on 180 and shading to the right.

Answers

Answer:

Number line graph with closed circle on 20 and shading to the right or c

Step-by-step explanation:

This is the best answer because you start of at 20 dollars and need to continue collecting money till you have 160 dollars.

Answer:

The 3rd one

Step-by-step explanation:

You have already collected $20. You need at least $160, but having even more money would be great. You need $160, but any number to the right of 160 would be even better as your goal.

a number cube numbered 1-6 is rolled 30 times and lands on an even number 18 times. How does this frequency compare to the expected frequency based on the probability of the number cube landing on an even number?

Answers

Answer:

The frequency is 3 more than expected

Step-by-step explanation:

There are 3 favourable outcomes: {2, 4, 6}

There are 6 possible outcomes: {1, 2, 3, 4, 5, 6}

probability of the number cube landing on an even number = favourable outcomes / possible outcomes = 3/6 = 1/2

If the cube is rolled 30 times, it is expected that in 1/2*30 = 15 times landed on an even number. The frequency: 18 is 3 more than expected

Keshawn is asked to compare and contrast the domain and range for the two functions.

f(x) = 5x
g(x) = 5x

Which statements could he include in his explanation? Select two options.

Answers

Answer:

fx=5x

Step-by-step explanation:

The answer is A and E

Lindsey lives 32 blocks from the grocery store. It takes her 9 minutes to walk 12 blocks. If she continues to walk at the same rate, how long would it take her to walk 32 blocks?

Answers

Answer:    

if she countinues to walk at that rate it will take her 24 minutes to walk the 32 blocks

Step-by-step explanation:

i took the 12 blocks every 9 minutes and counted for a total of 36 blocks which would take 27 minutes then since we want to know how long it would take for her to walk 32 blocks I found how long it would take her to walk 4 blocks which is 3 minutes (12/3 = 4 9/3 =3) and i subtracted those 3 minutes from the 36 block walk giving you 24 minutes for 32 blocks

hope this helps

What are the constants in the expression below? Select three options.
12+x-3.7-8y+1/3

-8

-3.7

1/3

x

12

Answers

Answer:

12, -3.7, ⅓

(2nd, 3rd and 5th option)

Step-by-step explanation:

Constants are numbers without any variables with it.

x and y are the variables here.

-8 is the coefficient of y and hence it is not a constant.

*the value of a constant will not change

Note that the constant includes the symbol too, hence it is -3.7 and not 3.7.

Answer: 2nd 3rd and 5th option hope this helps  

Step-by-step explanation:

solving linear inequality: 2x + 4

Answers

A

2x+4>16 equals 2x> 12
x>6

Vanessa built an enclosed area in the shape of a square in her backyard for her dogs. She used an outside wall of the garage for one of the sides. She had to buy 3 yards of
fencing in order to build the other sides. What is the area of the enclosure?

Answers

3 yards/3 walls = 1 yard per wall

Area = Length * Width

Area = 1 * 1 = 1 square yard

Which expression is equivalent to −(4−3)?Which expression is equivalent to −(4−3)?

Answers

Answer: −22+3

Step-by-step explanation:

Answer:

−22+3

Step-by-step explanation:

What is the domain of the function in this table?

Answers

Answer: B

Step-by-step explanation: The domain are all x values, meaning only the x values are counted for the domain.

Answer:

B

Step-by-step explanation:

domain is all the input(x):{3,4,5,6}

the domain of a graph consists of all the input values shown on the x-axis (rule)

Another asap question need help!!!!!!

Answers

Hey there! :)

Answer:

f(x + 5/4) --> f(x) is translated 5/4 units left.

f(x) - 5/4 --> f(x) is translated 5/4 units down.

Step-by-step explanation:

Recall that a linear equation in transformations form is:

f(x) = ±a(b(x-h))+k

In this instance:

f(x + 5/4) the 'h' value is -5/4, meaning the graph is translated 5/4 units left.

f(x) - 5/4 has a 'k' value of -5/4, so the graph is translated 5/4 units down.

f(x) = x2. What is g(x)?

Answers

Answer:  C

Step-by-step explanation:

f(x) = x²

g(x) has the same vertex as   f(x) but is wider so has a vertical stretch by a factor of (1/3).

g(x) = (1/3)x²

PLEASE I NEED HELP!!. i don't know how to do this.

Answers

Answer:

∠ FGE = 52.5°

Step-by-step explanation:

The secant- secant angle is half the difference of the measures of the intercepted arcs, that is

∠ FGE = [tex]\frac{1}{2}[/tex] (arc BD - arc FE )

           = [tex]\frac{1}{2}[/tex] × (135 - 30)°

           = [tex]\frac{1}{2}[/tex] × 105°

           = 52.5°

Think of a number, multiply it by 6 and increase the product by 7. It will equal a number, multiplied by 2 and
then increased by 6. What number is it?
1
4
1
10
ent
1
8

Answers

Answer:

x = -1/4

Step-by-step explanation:

Step 1: Write out 1st equation

6x + 7

Step 2: Write out 2nd equation

2x + 6

Step 3: Set equal to each other

6x + 7 = 2x + 6

Step 4: Solve

4x + 7 = 6

4x = -1

x = -1/4

Find the equation of the exponential function represented by the table below:
HELLPPP

Answers

Answer:

y = 4 [tex](\frac{1}{2}) ^{x}[/tex]

Step-by-step explanation:

For an exponential function in the form

y = a [tex]b^{x}[/tex]

Use ordered pairs from the table to find values of a and b

Using (0, 4 ), then

4 = a [tex]b^{0}[/tex] ( [tex]b^{0}[/tex] = 1 ), thus

a = 4, so

y = 4 [tex]b^{x}[/tex]

Using (1, 2 ) , then

2 = 4 [tex]b^{1}[/tex] = 4b ( divide both sides by 4 )

b = [tex]\frac{1}{2}[/tex]

Thus exponential function is

y = 4 [tex](\frac{1}{2}) ^{x}[/tex]

Answer:

y = 4 (\frac{1}{2}) ^{x}

A rectangular prism has a length of 9 in., a width of 4 in., and a height of 1 1/2in. The prism is filled with cubes that have edge lengths of 1/2 in. How many cubes are needed to fill the rectangular prism?

Answers

Hey there! :)

Answer:

432 cubes.

Step-by-step explanation:

Volume of rectangular prism: V = l × w × h

V = 9 × 4 × 1.5

V = 54 in³

Volume of cubes: V = s³

V = 1/2³

V = 1/8 in³

Set up an equation to solve for the # of cubes needed (x):

54 = 1/8x

Divide both sides by 1/8:

54 × 8/1 = x

x = 432 cubes.

this is a sketch of the curve with equation y=f(x) the vertex of the curve is at (2,-3)

Answers

Answer:

see explanation

Step-by-step explanation:

(a)

Given f(x) then f(x) + c represents a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

f(x) + 5 represents a shift up of 5 units, thus

(2, - 3 ) → (2, - 3 + 5 ) → (2, 2 )

(b)

Given f(x) then - f(x) represents a reflection of f(x) in the x- axis

Under a reflection in the x- axis

a point (x, y ) → (x, - y ), thus

(2, - 3 ) → (2, 3 )

The vertex of the given curve is the minimum point on the curve.

The vertex of f(x) + 5 is (2,2)The vertex of -f(x) is (2,3)

The vertex is given as:

[tex]\mathbf{(x,y) = (2,-3)}[/tex]

(a) The vertex of f(x) + 5

The rule of the given transformation is:

[tex]\mathbf{(x,y) \to (x,y + 5)}[/tex]

So, we have:

[tex]\mathbf{(x,y) \to (2,-3 + 5)}[/tex]

[tex]\mathbf{(x,y) \to (2,2)}[/tex]

Hence, the vertex of f(x) + 5 is (2,2)

(b) The vertex of -f(x)

The rule of the given transformation is:

[tex]\mathbf{(x,y) \to (x,-y)}[/tex]

So, we have:

[tex]\mathbf{(x,y) \to (2,-(-3))}[/tex]

[tex]\mathbf{(x,y) \to (2,3)}[/tex]

Hence, the vertex of -f(x) is (2,3)

Read more about vertex at:

https://brainly.com/question/4088301

Create a word problem that uses rates

Answers

Answer:

Ken can walk 404040 dogs in 888 hours.

How many dogs can Ken walk in 121212 hours?

Step-by-step explanation:

answer= 60

Answer:

if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. ... When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.

Step-by-step explanation:

Calculate the heigh (x) of the tree

Answers

Answer:

87 feet

Solution,

[tex]tan \: theta = \frac{opposite}{adjacent} [/tex]

[tex]tan \: 60 = \frac{h}{50} \\ 5 \: tan \: 60 = h \\ h = 50 \: tan \: 60 \\ h = 87 \: feet[/tex]

hope this helps..

Good luck on your assignment..

These tables of value represent continuous functions. In which table do the values represent an exponential function?

Answers

Answer:

B.

Step-by-step explanation:

A goes up by 1

C goes up by 8

D goes up by 5

But B increments by 2x (2 times)

Answer:

B.

Step-by-step explanation:

A goes up by 1

C goes up by 8

D goes up by 5

But B increments by 2x (2 times)

Twice the sum of two numbers is 72 if one number is 20 then the other number is

Answers

Answer:

16

Step-by-step explanation:

20 + 16=36 36x2=72

what is a point-slope equation of the line with slope -13 that goes through the point (5,7)

Answers

Answer:

y - 7 = -13( x-5)

Step-by-step explanation:

The  point slope form of a line is

y-y1 = m(x-x1)

The slope is -13 and the point is (5,7)

y - 7 = -13( x-5)

Answer:

PoInTsSsSsSsSs

Step-by-step explanation:

Help! I'm trying to solve this for A and B, and it keeps telling me I'm wrong. The equation is:

√x(7x-4√x)=Ax^(3/2) + Bx
Where A =
and B =

Answers

Answer:

A must be 7 and B must be -4

Step-by-step explanation:

Perform the indicated multiplication, obtaining:

7x^(3/2) - 4x  =  Ax^(3/2) + Bx

Then A must be 7 and B must be -4

1 point
Ana drinks orange juice every morning. She uses a glass that holds 1/8 of the container of
orange juice. She has 7/10 of a container left in the refrigerator. How many glasses of
orange juice will she be able to have? *
Your answer

Answers

Step-by-step explanation:

Ana drinks one glass of orange juice which contain 1/8 of the container in every eight day one container of orange juice finish.So,now we should do 8*7 for the reasult.So, the answer should be 56.

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