A bouncing toy reaches a height of 64 inches at its first peak, 48 inches at its second peak, and 36 inches at its third peak. Which explicit function represents the geometric sequence of the heights of the toy?

f(x) = 48(Five-sixths) Superscript x minus 1
f(x) = 48(three-fourths) Superscript x minus 1
f(x) = 64(three-fourths) Superscript x minus 1
f(x) = 64(Five-sixths) Superscript x minus 1

Answers

Answer 1

Answer:

The correct option is;

f(x) = 64(three-fourths)Superscript x minus 1

Step-by-step explanation:

The first peak height that the bouncing toy reaches = 64 inches

The second peak height that the bouncing toy reaches = 48 inches

The third peak height that the bouncing toy reaches = 36 inches

Therefore, given that the sequence has a common ratio, r = 48/64 = 36/48 = 3/4

The first term of the sequence, a = The first peak height reached = 64

The xth term of the geometric sequence with general form, xth term = ar⁽ˣ⁻¹⁾

The xth term of the geometric sequence, f(x), is therefore, given as follows;

[tex]f(x) = 64 \times \left(\dfrac{3}{4} \right) ^{(x - 1)}[/tex]

Answer 2

The correct option is;

f(x) = 64(three-fourths)Superscript x minus 1

Step-by-step explanation:

The first peak height that the bouncing toy reaches = 64 inches

The second peak height that the bouncing toy reaches = 48 inches

The third peak height that the bouncing toy reaches = 36 inches

Therefore, given that the sequence has a common ratio, r = 48/64 = 36/48 = 3/4

The first term of the sequence, a = The first peak height reached = 64

The xth term of the geometric sequence with general form, xth term = ar⁽ˣ⁻¹⁾

The xth term of the geometric sequence, f(x), is therefore the correct answer is C


Related Questions

HELP HELP HELP FAST PLS PLS


Marc sold 500 tickets for the school play. Student tickets cost $2 and adult tickets cost $5. Marc's sales totaled $1,789. a) Write a system of equations that can be used to determine how many of each type of ticket Marc sold b) Solve the system to determine how many adult tickets and how many student tickets Marc sold.

Answers

Answer:

a) System of equations will be:  [tex]x+y=500\: and\:5x+2y=1789[/tex]

b) Number of adult tickets sold =  263

Number of students tickets sold =  237

Step-by-step explanation:

Let:

Number of adult tickets sold = x

Number of students tickets sold = y

a)

As Marc sold total 500 tickets, the expression will be: [tex]x+y=500[/tex]

Student tickets cost $2 and adult tickets cost $5. Marc's sales totalled $1,789.

The expression will be: [tex]5x+2y=1789[/tex]

So, system of equations will be:  [tex]x+y=500\: and\:5x+2y=1789[/tex]

b)

Solve the system to find value of x and y

Let:

[tex]x+y=500--eq(1)\\5x+2y=1789--eq(2)[/tex]

Multiply equation 1 by 2 and subtract

[tex]2x+2y=1000\\5x+2y=1789\\-\:\:\:-\:\:\:\:\:\:\:\:\:-\\------\\-3x=-789\\x=\frac{-789}{-3}\\x=263[/tex]

We get value of x = 263

Now finding value of y by putting value of x in eq(1)

[tex]x+y=500\\263+y=500\\y=500-263\\y=237[/tex]

We get value of y = 237

Number of adult tickets sold = x = 263

Number of students tickets sold = y = 237

Two brothers went shopping at a back to school sale where all shirts and shorts were the same price. The younger brother spent $145 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and and 7 pairs of shorts and paid a total of $125 How much did one shirt cost?

Answers

145÷14=10.357142857142857143

Daniel needs to bake cookies for a bake sale. Each cookie will cost dollars. Brandon makes 12 chocolate chip cookies and 18 sugar cookies. Create an expression that represents Taylor's total cost of the cupcakes.

Answers

Answer:

An expression that represents Taylor's total cost of the cupcakes is written as:

y = 30x

Step-by-step explanation:

We are told in the question:

Brandon makes 12 chocolate chip cookies and 18 sugar cookies.

Let us represent the total cost of cookies as y

The price of each cookies as x

Therefore,an expression that represents Taylor's total cost of the cupcakes is written as:

y = 12x + 18x

y = 30x

Can someone please help me with proofs

Answers

2) AE is congruent to ED, BE is congruent to ED (a bisector splits a segment into two congruent parts)

3) Angle AEB is congruent to angle DEC (vertical angles are congruent)

4) Triangle ABE is congruent to triangle CDE (SAS)

The table below shows that the number of miles driven by Taylor is directly proportional to the number of gallons she used.
Gallons Used /Miles Driven
42 1125.6
48 1286.4
50 1340
What is the constant of proportionality between the number of miles driven and the number of gallons used?

Answers

Answer:

24.3

Step-by-step explanation:

[tex]\frac{Gallons}{Miles} =\frac{Gallons}{Miles}[/tex]

[tex]\frac{g}{884.52} =\frac{22113}{910}[/tex]

910g = 25 x 884.52

[tex]\frac{910g}{910} =\frac{22113}{910}[/tex]

g = 24.3

This is the correct answer. Hoped this helped!

The constant of proportionality is 26.8

Calculating the number of miles driven per gallon of fuel used:

1125.6/42 = 26.8

1286.4/48 = 26.8

1340/50 = 26.8

we get 26.8 miles traveled in one gallon fuel.

if we represent gallons of fuel by x and miles traveled by y, the equation thus formed will be:

                  y = 26.8x

hence the constant of proportionality is 26.8

Learn more about constant of proportionality:

https://brainly.com/question/15525667

 

Help! Find the value of x.

Answers

Answer:

30 degrees

Step-by-step explanation:

the sum of a triangles angles needs to be 180 and since its an equilateral, all angles are the same so if each angle is 60 degrees do

60 / 2 = x

x = 30

Answer:

9

Step-by-step explanation:

You add all of the side numbers together. Think this way, area you add because area starts with an A. Hope it helps.

∠A and \angle B∠B are supplementary angles. If m\angle A=(7x+10)^{\circ}∠A=(7x+10) ∘ and m\angle B=(7x-26)^{\circ}∠B=(7x−26) ∘ , then find the measure of \angle A∠A.

Answers

Answer:

108 degrees

Step-by-step explanation:

Since angles A and B are supplementary, they both add up to 180. Angle A = 7x+10, and angle B = 7x-26. You can set up the equation A + B = 180, and then plug in angles A and B, which gives you 7x+10 + 7x-26 = 180. Then you just need to isolate x:

Combine like terms: 14x - 16 = 180

Add 16 to both sides: 14x = 196

Divide both sides by 14: x = 14

Now that you know x, you can plug it into the expression for angle A (7x+10):

A = 7(14) + 10 = 98+10 = 108

(−7.4 )+ L = 9.11

What is L ?

Answers

L = 16.51

Get variable onto one side of equation and simplify:

(−7.4 )+ L = 9.11

L = 9.11 + 7.4

L = 16.51

Answer:

L=16.51

Step-by-step explanation:

-7.4 +L=9.11                         remove unnecessary (    )

L=9.11 +7.4                           move constant (7.4) to the right change sign

L=16.51                                  add the numbers

in this previous problom,ken predicted a drop in temperture would lead to adding a negitive integer

Answers

Answer:

WOAH COOL

Step-by-step explanation:

Find the exact length of the third side. 95 n 76

Answers

Answer:

121.66

Step-by-step explanation:

To solve, use the Pythagorean Theorem, which says c² = a² + b². Enter 95 as a and 76 as b and square them both. This will give you 9025 for a, and 5776 as b. Add them to get 14,801. So, c² = 14,801. Find the square root of this to get approximately 121.66. So, the third side is about 121.66 in length.

A performing arts theater offers a group rate om season passes of $70 total for the first two passes plus $25 for each additional pass. what is the cost of 8 season passes at the group rate?​

Answers

Answer:

$220.00

Step-by-step explanation:

$70 dollars for 2

$25x6

$70+$150=$220.00

If a line has a slope of -3/8, what is the slope of any line perpendicular to that line?

Answers

Answer:

The slope of they line is 8/3 = 4

Step-by-step explanation:

When two lines are perpendicular, the product of the slope of the lines is -1

Thus, we have that;

-3/8 * m = -1

3m/8 = 1

3m = 8

m = 8/3

what’s the mean (average) for the data 12 4 16 20

Answers

Answer:

13

Step-by-step explanation:

Add all of the numbers, and divide by the amount of numbers. In this instance, all four added together numbers is 52, and divided by 4 is 13. Hope this helps!

Answer:

The answer is 13.

Step-by-step explanation: In order to find the average in a set of numbers, you must add all numbers and divide them by the numbers of numbers which you have added.

For example for your problem, I added 12 + 4 +16 +20 and I got 52. Then count the numbers which u have added. There are 4 numbers I have added. Then divide that number by the total. So it would be 52/4 and once you divide, you have your answer!

Hope this helps!

For a data set of the pulse rates for a sample of adult​ females, the lowest pulse rate is 37 beats per​ minute, the mean of the listed pulse rates is x=71.0 beats per​ minute, and their standard deviation is s=18.2 beats per minute. a. What is the difference between the pulse rate of 37 beats per minute and the mean pulse rate of the​ females? b. How many standard deviations is that​ [the difference found in part​ (a)]? c. Convert the pulse rate of 37 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between −2 and 2 to be neither significantly low nor significantly​ high, is the pulse rate of 37 beats per minute​ significant?

Answers

Answer:

See below.

Step-by-step explanation:

(a) Difference = 71 - 37 = 34 beats/minute.

(b) Number of standard deviations = 34 /18.2 = 1.868.

(c) z score = (x - m )/ s     where m = mean and s = standard deviation

= (37 - 71) / 18.2 = -1.868.

(d)  This  z score lies between -2 and 2 so  a pulse rate of 37 is not significant.

Which linear equation represents a non-proportional relationship?
A)
y = 1.5%
B)
y = x + 3
ya
D)
y=-3x

Answers

Answer:

Is there an option C?

PLS HELP ME!!!!!! !!!!!!!!!!!!!”

Answers

its D

Solution:

[tex] \sqrt{60 } = \sqrt{4 \times 15} = \sqrt{4 } \times \sqrt{15} = 2 \sqrt{15 \: } \: ans[/tex]

the answer is D! hope this helped

What is the solution set of the compound inequality
x + 1 < -2x + 11 < 3 x + 5?

Answer choices:

6/5 < x < 10/3
-1/3 < x < 2
No solution
-2 < x < 10/3

Answers

Answer:6/5<x<.10/3

Step-by-step explanation:

What percent of 65 is 13?​

Answers

Answer:

Convert the fraction to a decimal, then multiply by

100 .20%

Step-by-step explanation:

The equation 6x = 3y -12 is linear

True or False

Answers

Answer:

True :D .....................

Explain what the differences between an arithmetic and geometric sequence are? IN FULL SENTENCES. *

Answers

Answer:

An arithmetic sequence has a constant difference between each term. ... A geometric sequence has a constant ratio (multiplier) between each term. An example is: 2,4,8,16,32,… So to find the next term in the sequence we would multiply the previous term by 2.

Step-by-step explanation:

pls make me brainliest

If 66 oranges cost $15, how many oranges can be purchased for $5?

Answers

Answer:

22 oranges

Step-by-step explanation:

$15 --- 66 oranges

$5 --- [tex]\frac{5}{15}[/tex] × 66 oranges = 22 oranges

4. State what additional information is required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate

Answers

The additional information required to prove the SSS Triangle Congruence Postulate is BC = KC

How to state the additional information required?

The congruence postulate is given as:

SSS Triangle Congruence Postulate

The above means that the three sides of the triangles are congruent.

From the figure, the following side lengths are said to be congruent

AK and AB

AC and AC

For the congruence postulate of the triangle to be SSS Triangle Congruence Postulate, then the third corresponding sides must be congruent

This is represented as:

BC = KC

Hence, the additional information required to prove the SSS Triangle Congruence Postulate is BC = KC

Read more about Congruence Postulate at

https://brainly.com/question/17239468

#SPJ1

The LCM of 4, 9, and 10 is _______.

36

180

40

90

Answers

Answer:

180

Step-by-step explanation:

Multiples of 4:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188

Multiples of 9:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198

Multiples of 10:

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200

Stay safe and Merry Christmas! :)

Answer:

the answer is 180

Step-by-step explanation:

68, 302 divided by 1,000 equals what?

Answers

Answer:

68.302

Step-by-step explanation:

Answer: 68.302

Step-by-step explanation:

Do long division it helps best

Write the equation of a line parallel to x = 3 that contains (−4, 5).

Answers

Answer:

y=3x+17

Step-by-step explanation:

equation:

y-y¹=m(x-x¹)

substitute with same slope.

y-5=3(x-(-4))

y-5=3x+12

y=3x+17

The three sides of a triangle are in different colors – blue, green and red. The ratio of the length of the blue side to the length of the green side to the length of the red side is 3 : 4 : 5. The perimeter of the triangle is 240 cm. a) Fill in the blank: ___ units = 240 cm b) Fill in the blank: 1 unit = ___ cm c) What is the length of the red side of the triangle?

Answers

Answer:

The perimeter is the distance around the triangle. Given the ratio, the perimeter using the ratio is;

= 3 + 4 + 5

= 12 units

a. 12 units = 240 cm

The perimeter in centimetres is 240cm and in ratio is 12 units so they are equivalent.

b. 1 unit = 20 cm

If 12 units are to 240 cm, 1 unit is;

= 240/12

= 20 cm

c. Length of red side;

Red side has length of 5 units. 1 unit is 20 cm.

Length in cm is;

= 5 * 20

= 100 cm

Simplify, if x = 2 and y = -1: 3(y + 2)^2 + 3x

Answers

Answer:

9

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Step-by-step explanation:

Step 1: Define

3(y + 2)² + 3x

x = 2

y = -1

Step 2: Evaluate

Substitute:                    3(-1 + 2)² + 3(2)Add:                              3(1)² + 3(2)Exponents:                   3(1) + 3(2)Multiply:                        3 + 6Add:                              9

best estimate for 6,193 ÷ 48 using compatible numbers.

Answers

Answer:

1)100

2)120

3)130

Step-by-step explanation:

I think these three are correct but I am not sure so sorry guyz.

Solve the following equation for D. Be sure to take into account whether a letter is capitalized or not. fD - 7 = q^2

Answers

Answer:

[tex]\displaystyle D=\frac{q^2+7}{f}[/tex]

Step-by-step explanation:

Equation Solving

We are given the equation:

[tex]fD - 7 = q^2[/tex]

It's required to solve the equation for D. All letters must preserve their capitalization.

We must isolate the letter D by removing from the left side all the terms and coefficients that surround it.

Adding 7:

[tex]fD = q^2+7[/tex]

Dividing by f:

[tex]\mathbf{\displaystyle D=\frac{q^2+7}{f}}[/tex]

Dina can run 4 miles in 30 minutes. If she maintains this pace, how many miles can she run in 90 minutes?

Answer choices
A. 12
B. 16
C. 8
D. 15

Answers

Answer:

15minutes / 2miles = 7.5 minutes to run a single mile.

7.5minutes * 5miles = 37.5minutes

37.5minutes to run 5 miles

Step-by-step explanation:

Answer:

A. 12

Step-by-step explanation:

Set up a proportion: [tex]\frac{4}{30} = \frac{x}{90}[/tex]  Cross multiply, then divide: 4 × 90 = 360, 360 ÷ 30 = 12So, Dina can run 12 miles in 90 minutes

I hope this helps!

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There was no thought of rebellion or disobedience in her mind. She knew that, even as things were, they were far better off than they had been in the days of Jones, and that before all else it was needful to prevent the return of the human beings. Whatever happened she would remain faithful, work hard, carry out the orders that were given to her, and accept the leadership of Napoleon. But still, it was not for this that she and all the other animals had hoped and toiled. It was not for this that they had built the windmill and faced the bullets of Jones's gun. 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