A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak.

Answers

Answer 1

Hey there!

A= value of the first term
n= the number of the term you want to find
r= common ratio
value of r is = 2/3 because 27 times 2/3 = 18 which is the second term
n = 4 since you want to find the 4th term in the sequence
Plug it in and results are
4th term = 27(2/3)^(4-1) = 8
The answer is 8

Hope this helps!

Answer 2

A sequence can be used to illustrate the difference in heights of each jump and develop a pattern from them. In this case, we have 27, 18, 12,... Assuming the pattern continues, we have the previous height divided by 3 and then subtracted from itself:
[tex]a_n=a_{n-1}-\frac{a_{n-1}}{3}[/tex]

Here:
[tex]a_4=a_3-\frac{a_3}{3}=12-\frac{12}{3}=12-4=8[/tex]

Related Questions

Simplify (x^2+5x+6)/(15xy^2)/(2x^2+7x+3)/(5x^2y)

Answers

Hi. I am attaching the step-by-step answer. I hope it helps.

Take care,
Diana

What is the justification for each step in the solution of the equation?

−2(x−1)+12=4x−6−2(x−1)+12=4x−6
Select from the drop-down menus to correctly justify each step.

−2(x−1)+12=4x−6−2(x−1)+12=4x−6 Given
−2x+2+12=4x−6−2x+2+12=4x−6
−2x+14=4x−6−2x+14=4x−6 Combine like terms.
−2x=4x−20−2x=4x−20
−6x=−20−6x=−20 Addition or Subtraction Property of Equality
x=206x=206
x=103x=103 Simplify.

Answers

Here are the following justifications:

Given: -2 (x-1) +12=4x-6

Distribute property = -2x+2+12=4x-6

Combine like terms= -2x+14=4x-6

Transpose = -2x = 4x – 20

Addition or Subtraction Property of Equality = -6x = -20

Division property of equality = x = 20/6

Simplify = x = 10/3

Answer:

Step-by-step explanation:

A red blinking light blinks every 18 seconds, while a yellow blinking light blinks every 12 seconds. If both lights start at the same time, after how many seconds will they next blink at the same time? A) 6 B) 18 C) 36 D) 54

Answers

In order to find the answer, you need to find the LCM, Least Common Multiple. The least common multiple of 18 and 12 is C. 36

Brainliest Please!!!

Simplify –2x3y × xy 2. A. –2x3y4 B. –3x4y3 C. –12x4y3 D. –2x4y3

Answers

The answer is B because you need too add like terms as well and I got -3x because you have too add all the x's together and then all the y's.

Which table represents a linear function?

Answers

C hope it helpes!

:D!!

<3333

Answer

hope it helps

Evaluate this piecewise function at x=-4 and x=4.

(Can someone show me how to solve this because i don't know what to do to solve this)

Answers

The piecewise function is
f(x) = x², x≤ -4
= x³, -4 < x ≤ 1
= √x, x > 1

To find f(-4), we note that f(x) = x², x ≤ 4, so we should use this part of the function.
f(-4) = (-4)² = 16

To find f(4), we note that f(x) = √x, x > 1, so we should use this part of the function.
f(4) = √4 = +2 or -2.
A graph of the function is shown below. It indicates that f(4) = +2 for continuity.

Answer:
f(-4) = 16
f(4) = 2.

A zebra ran at a speed of 20 feet per second. Which operation should you use to find the distance the zebra ran in 10 seconds?

Answers

you would multiply speed by time

20 feet per second times 10 seconds = 200 feet total

First, you would cross multiply the equation 20ft/1s = x/10s.
Giving you 200ft/10s.

Your answer would be, 200ft.

I hope this helps!

Add.
Joe practiced his trumpet 3/4 hour on Monday and 7/12 hour on Tuesday. How long did he practice altogether?

a. 2 hours
b. 1 1/3 hours
c. 2 2/3 hours
d. 5 1/3 hours

Answers

Problem
Joe practiced his trumpet 3/4 of an hour on Monday and 7/12 of an hour on Tuesday. How long did he practice altogether?

Result
b. 1 1/3 hours.

Solution
We need to turn the fractions into time first. This is done with division, multiplication, and addition.

Let's divide and multiply

3/4 · 60 = 45
7/12 ·60 = 35

Let's add

45 + 35 = 80

From here, 80 is 60 + 20 minutes, or 1 and 1/3

Hope this helped!

The sum of two consecutive integers is 131. What are the integers?

Answers

x, x+1
x+x+1=131
2x+1=131
2x=131-1=130
x=130÷2 = 65
the integers are 65 and 66

Answer:

The Integers are 65&66

Step-by-step explanation:

Because I got correct with these awnsers

Walter is a comic book artist. He usually draws 36 comic panels each day. How many comic panels can he draw in 2 weeks.

Answers

There would be 14 days in two weeks so you need to multiply 36 x 14 = 504 comic panels in two weeks.

answer: 36 x 14 = 504
hope this helps:D

plz give brainiest

What is the result of factoring out the gcf from the expansion (24+36)?

Answers

So the greatest common factor of 24 and 36 would be 12.

So you could say,

12(2 + 3)

Break down each of the numbers

24=2*2*2*3
36=2*2*3*3

As seen, 12(2x2x3) is the greatest common factor amongst the numbers.

12(2+3)=(24+36)

Hope I helped :)

What is the answer to the word problem a can of mixed nuts has 5 peanuts for every 2 cashews. there are 175 peanuts in the can. how many cashews are there?

Answers

175(peanuts) times 2(cashews)=answer
answer=350
hope this helps

How to simplify equations with fractional exponents?

Answers

The general form for a term with fractional exponents is given as :

[tex]a^{ \frac{m}{n} }[/tex] which can be rewritten as [tex] (\sqrt[n]{a} )^m[/tex]

for example: [tex](x + 3)^ \frac{2}{3} =( \sqrt[3]{x+3})^2 [/tex]

Final answer:

To simplify equations with fractional exponents, divide the digit term of the numerator by the digit term of the denominator and subtract the exponents of the exponential terms. Then multiply the numerators and denominators together and simplify by common factors if needed.

Explanation:

When simplifying equations with fractional exponents, we can follow these steps:

Divide the digit term of the numerator by the digit term of the denominator.Subtract the exponents of the exponential terms.Multiply the numerators and denominators together and simplify by common factors if needed.

For example, let's simplify the equation √(x³ / y²). We divide x³ by y², which gives us x/y. Then we subtract the exponents, resulting in √(x/y). Finally, we can simplify the fractional exponent by taking the square root of x/y, which gives us √(x/y).

what is the slope of the line through (-7,-8) and (0,4)

Answers

the slope of the line would 12/7

Answer:

the slope of the line is 12/7

Step-by-step explanation:

What conversion factor would you use to convert cubic decimeters to milliliters?

Answers

1 cubic decimeter equals 1000 milliliters.so 1cubic decimeter=1000milliliters. Hope i helped.

Which point is on the graph of a direct variation equation in which k = 1.8? A. (4, 0.45) B. (7.2, 4) C. (4, 7.2) D. (0.45, 4)

Answers

The answer is B (7.2, 4).

Answer: C

(4, 7.2)

Step-by-step explanation: Just took this test

Betsy, a recent retiree, requires $ 6 comma 000 6,000 per year in extra income. She has $ 60 comma 000 60,000 to invest and can invest in B-rated bonds paying 15 15% per year or in a certificate of deposit (CD) paying 5 5% per year. How much money should be invested in each to realize exactly $ 6 comma 000 6,000 in interest per year?

Answers

Let the amount she invests in the B-rated bonds be x, and the amount she invested in the certificate of deposit be y.

Then,

x + y = 60,000 . . . . . . . (1)
0.15x + 0.05y = 6,000 . (2)

Multiplying the first equation by 0.15 gives:

0.15x + 0.15y = 9,000 . (3)

Subtracting equation (2) from equation (3) gives:

0.1y = 3,000

y = 3,000 / 0.1 = 30,000

From equation (1):

x + 30,000 = 60,000

x = 60,000 - 30,000 = 30,000

Therefore, the amount of money that should be invested in each to realize exactly $6,000 in interest per year is $30,000 each.

Can we obtain a diagonal matrix by multiplying two non-diagonal matrices? give an example

Answers

Yes, we can obtain a diagonal matrix by multiplying two non diagonal matrix.

Consider the matrix multiplication below

[tex] \left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{cc}e&f\\g&h\end{array}\right] = \left[\begin{array}{cc}a e+b g&a f+b h\\c e+d g&c f+d h\end{array}\right] [/tex]

For the product to be a diagonal matrix,

a f + b h = 0 ⇒ a f = -b h
and c e + d g = 0 ⇒ c e = -d g

Consider the following sets of values

[tex]a=1, \ \ b=2, \ \ c=3, \ \ d = 4, \ \ e=\frac{1}{3}, \ \ f=-1, \ \ g=-\frac{1}{4}, \ \ h=\frac{1}{2}[/tex]

The the matrix product becomes:

[tex] \left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}\frac{1}{3}&-1\\-\frac{1}{4}&\frac{1}{2}\end{array}\right] = \left[\begin{array}{cc}\frac{1}{3}-\frac{1}{2}&-1+1\\1-1&-3+2\end{array}\right]= \left[\begin{array}{cc}-\frac{1}{6}&0\\0&-1\end{array}\right][/tex]

Thus, as can be seen we can obtain a diagonal matrix that is a product of non diagonal matrices.

Yes, we can obtain a diagonal matrix by multiplying two non-diagonal matrices. A diagonal matrix is a matrix where all the elements beyond the diagonal are zeros. This is an example.
[tex] \left[\begin{array}{ccc}1&3&4\\0&-8&-9\\0&0&- \frac{55}{8} \end{array}\right] \cdot \left[\begin{array}{ccc}1&-3&- \frac{5}{8} \\0&1&- \frac{9}{8} \\0&0&1\end{array}\right] = \left[\begin{array}{ccc}1&0&0\\0&-8&0\\0&0&- \frac{55}{8} \end{array}\right] [/tex]

The number of heads that come up when a coin, biased so that heads comes up with probability 3/4, is flipped three times.

Answers

so what's the question

eight out of ten dentists prefer crest toothpaste.what is the ratio of dentist who do not prefer crest to those who do.

Answers

It would be 2:10 or 2:8

8 do, 2 don't

so the ratio would be 2:8 which can reduce to 1:4

A factor for (f/g, i, n) could be obtained by multiplying the (p/g, i, n) factor by the _______________ factor.

Answers

Answer:

Step-by-step explanation:

good question

The factor that needs to be multiplied by the (p/g, i, n) factor to obtain the (f/g, i, n) factor is the conversion factor between the two units of measurement being used for the factor.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

In this case, the units of measurement for both factors are not specified, so it's not possible to determine the specific conversion factor needed. However, in general, if the two factors are expressing the same quantity but in different units (for example, feet and meters), then the conversion factor between those two units would be used to convert the (p/g, i, n) factor to the appropriate units before multiplying it by the (f/g, i, n) factor.

Thus,

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which of the following equations describe the graph shown below?

Answers

1) The square root of x+4 +1

Hope this helps!

The sum of three consecutive even integers is –78. What are the integers? Describe how you would use the strategy of writing an equation to solve the given problem.

Answers

3 even integers

divide -78 by 3

-78 / 3 = -26

so -24 + -26 + -28 = -78

equation would be:

n + n+2 + n+4 = -78

3n +6 = -78

3n = -84

n = -84 / 3 = -28

n +2 = -28 +2 = -26

n+4 = -28 +4 = -24

x, x+1 , x+2
x+x+1+x+2 = -78
3x+3=-78
3x=-78-3= -81
x=-81÷3 = -9

the integers are -9, -8, -7

What rule can be used to find the next term of the arithmetic sequence

Answers

are you talking about PEMDAS? if so it’s parentheses, exponents, multiply, divide, add, subtract.

How many minutes will it take to drive 82 miles with the speed of 65 miles per hou?

Answers

time = distance / speed
time|hr = 82/65 hour
but 60minutes = 1hour. so
82/65 hr = 82/65×60 minutes = 75.7 minutes

A student is attempting to simplify the expression below. Sample mathematical work is shown. Which statement best applies to the sample mathematical work?

Given xy+yx+x-3(x+y), I first apply the distributive property, which yields the expression xy + yx + x – 3x – 3y. I can then collect like terms: since x – 3x = –2x, I have the expression xy + yx – 2x – 3y as my final answer.
A.
The student failed to properly apply the distributive property.
B.
The student collected two or more terms that were not like terms.
C.
The student failed to collect all like terms.
D.
The mathematical work shown above is correct.

Answers

The answer is A) The student failed to properly apply the distributive property.

find the derivative of the given function at the indicated point f(x)=1/x a=2

Answers

Final answer:

The derivative of the function f(x) = 1/x at x = 2 is -1/4, found using the power rule of differentiation.

Explanation:

To find the derivative of the function f(x) = 1/x at the point where a = 2, we employ the power rule of differentiation. The function can be rewritten as f(x) = x-1. Applying the power rule (f'(x) = n*xn-1) to this function, the derivative is f'(x) = -1*x-2 or f'(x) = -1/x2. To find the derivative at x = 2, we simply substitute x with 2, giving us f'(2) = -1/22 = -1/4.

FM = 5y + 13, MG = 5 - 3y, FG = ? M is the midpoint of FG. Use the given information to find the missing measure or value.

Answers

5y+13=-3y+5
8y=-8
y=-1
2FM=FG
-5+13-5+13=FG
FG=16

A line is a one-dimensional shape that is straight. The length of the side FG is 16 units.

What is a line?

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

Given that FM = 5y + 13 and MG = 5 - 3y. Also, midpoint of the line FG is M, therefore, the length of the two segments FM and MG will be equal to each other.

FM = MG

5y + 13 = 5 - 3y

5y + 3y = 5 - 13

8y = -8

y = -8/8

y = -1

Now, the length of the two line segments will be,

FG = FM + MG

= 2y + 13 + 5

= 2y + 18

= 2(-1) + 18

= -2 + 18

= 16

Hence, the length of the side FG is 16 units.

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What is the probability of flipping heads with a biased coin?

Answers

That depends on what the bias of the coin is.

How can I pass the Algebra 1 EOC?

Answers

Pay attention in class, study, and don't procrastinate -- it's not worth it.

You just need to study try your beast and listening to your teacher cullarely

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