Provide a real-world situation in which it would be appropriate to use a geometric sequence or series. Be sure to explain why a series or a sequence is more appropriate

I'll do part (a) to get you started.

One possible answer to part (a) is 25,11,14,2,7,9,16

There are likely other possible answers.

The explanation is below.

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Let's say 7 is the anchor value and we want to see which values could be its next door neighbor.

To summarize this subsection, the anchor value 7 could have the neighbors 9 and 2.

So we could have 2,7,9 or 9,7,2 as a subsequence. We'll keep this in mind for later.

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Now we'll make 11 the anchor. We already checked 7 and it doesn't work.

9 doesn't work either because 11+9 = 20 isn't a perfect square

Of that list, only 14 and 25 are possible neighbors of the anchor value 11.

So we could have the subsequence 14,11,25 or 25,11,14.

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If 9 is the anchor, then,

The values 7 and 16 are possible neighbors of 9. We could have the subsequence 7,9,16 or 16,9,7

Let's go back to the subsequence 2,7,9 and tack 16 at the end to get 2,7,9,16

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If 14 is the anchor, then,

We could have the subsequence 11,14,2 or 2,14,11

Let's go with the first option and stick "11,14,2" in front of "2,7,9,16" to end up with the larger subsequence 11,14,2,7,9,16

We can then stick 25 at the front because 25+11 = 36 is a perfect square.

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So one possible sequence of values is 25,11,14,2,7,9,16

Here's the verification

Each pair of adjacent terms add up to a perfect square, so the answer is confirmed.

There are probably other solutions as well.

Side note: The video math channel "Numberphile" has a video discussing this topic in which you might be interested in. Search out "The square sum problem" with quotes (the presenter/teacher in the video is Matt Parker).

Answer:

25, 11, 14, 2, 7, 9, 16.

Step-by-step explanation:

25 + 11 = 6^2

11 + 14 = 5^2

14 + 2 = 4^2

2 + 7 = 3^2

7 + 9 = 4^2

9 + 16 = 5^2

Answer:

I think ∆5 is the correct Ans

Answer:

Hope this helps.. Have a good day

Answer:

3283m/s

Step-by-step explanation:

V=U+2at

V=35+2(28)(58)

V=35+3248

V=3283m/s

Answer:

Step-by-step explanation:

These are similar triangles. We know that because we know that all right triangles are similar. The height of the red one is 8 and the height of the blue one is 4; that means that the red one is twice the size of the blue one; likewise, the blue one is half the size of the red one. That means that ALL the measurements of these triangles exist in that ratio...even the base of the blue one. If the base of the red one is 3, and the red one is twice the size of the blue one, then the base of the blue one is 3/2 or 1.5. I can't see your choices because they are too small.

Answer:

c,  

Step-by-step explanation:

Which digit in 123.456 has highest value?

answer = 1....

Answer:

1

Step-by-step explanation:

The 1 is in the hundredth's place and it has the highest value

Answer:

x2 = 256; 16 m

Step-by-step explanation:

Let x=​  the length of the side ofthe square. So an equation tomodel this problem is x2=256.x2xx===256256⎯⎯⎯⎯⎯⎯√± 16The side of a square with an areaof 256 m2 is 16 m.

Answer:

25%

Step-by-step explanation:

4+3+5=12

3/12 ×100=25

Answer:

x = 19

Step-by-step explanation:

6x+4 + 4x - 14 = 180

10x    - 10 = 180

10 X = 190

x = 19

Answer:

84%

Step-by-step explanation:

3360/4000=.84

.84=84%

Answer:

p=2

Step-by-step explanation:

9p-10=6+p

Subtract p from each side

9p-p-10=6+p-p

8p -10 =6

Add 10 to each side

8p -10+10 =6+10

8p =16

Divide each side by 8

8p/8 = 16/8

p =2

Answer:

p = 2

Step-by-step explanation:

1. 9p - 10 = 6 + p

2. 8p - 10 = 6

3. 8p = 16

4. p = 2

Answer:

[tex]{ \tt{ {x}^{2} + {y}^{2} - 6x - 2y + 4 = 0 }} [/tex]

Center:

[tex]{ \tt{(3, \: 1)}}[/tex]

Radius:

[tex]{ \tt{radius = \sqrt{ {g}^{2} + {f}^{2} - c } }} \\ = \sqrt{36 + 4 - 4} \\ = 6 \: units[/tex]

Answer:

I say it's TRUE

Step-by-step explanation:

I hope this help you

Answer:

Step-by-step explanation:

[tex]\Large \boldsymbol{} f(x) \ \ inverse \ \ function \ \ (f(x))^{-1} \\\\ y=7x+5 \\\\x=7y+5 \\\\ y=\dfrac{x-5}{7} \ \ or \ \ f(x)^{-1}= \dfrac{x-5}{7}[/tex]

Answer:

Option 1: -10d⁴ + 17d²s - 6s²

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

(-2d² + s)(5d² - 6s)

Step 2: Expand

The step of adding it to 0.25 (or 25/100, or 1/4) is indeed not relevant. 0.25 is rational.

A rational number added to a rational number gives a rational number. A rational added to an irrational number doesn't.

so effectively the task can be reduced to "wich one of these is a rational number?"

And that's only true for A. 2/9

All others can't be represented as a discrete/finite fraction / ratio.

The sum of two rational numbers is a rational number thus option (A) is correct.

Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number.

For example, √2, and √3 are irrational numbers because they cannot be written as p/q where p and q both should be integers.

The sum of two rational numbers gives the rational number.

Since 2/9 is written in p/q where 2 and 9 both are integers thus it will be rational.

So, 2/9 + 0.25 = 2/9 + 1/4

(8 + 9)/36 = 17/36 here 17 and 36 both are integers thus it will be rational.

Hence "A rational number is the result of two rational numbers".

For more about the irrational number,

https://brainly.com/question/4031928

#SPJ2

Answer:

The answer is 12

Step-by-step explanation:

The range is the difference between the lowest and highest values. In this case, this means 142 - 130 which equals 12.

Answer:

12

Step-by-step explanation:

Range = Largest number - Smallest number

Larger number = 142 ; Smallest number = 130

142-130 = 12

Range = 12

Answer:

[tex]f(x + 3) = {(x + 3)}^{3} [/tex]

Shifted left with x-intercept at (-3,0) and the y-intercept at (0,27)

Answer:

The volume of water that will fill the spa tub is 5.9 cubic meters.

Step-by-step explanation:

Volume of water that would fill the spa tub = volume of semi sphere - (volume of the first cylinder + volume of the second cylinder)

i. volume of first cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h

where r is the radius and h is the height of the cylinder.

r = [tex]\frac{0.75}{2}[/tex] = [tex]\frac{3}{8}[/tex]

 = 0.375 m

h = 0.80 m

volume of the first cylinder = [tex]\frac{22}{7}[/tex] x [tex](\frac{3}{8} )^{2}[/tex] x 0.8

                                        = 0.3536 cubic meters

ii. volume of the cylinder underneath = [tex]\pi[/tex][tex]r^{2}[/tex]h

r = [tex]\frac{1.25}{2}[/tex] = [tex]\frac{5}{8}[/tex]

 = 0.625

h = 0.70 m

volume of the cylinder underneath = [tex]\frac{22}{7}[/tex] x [tex](\frac{5}{8}) ^{2}[/tex] x 0.7

                                                      = 0.8594 cubic meters

iii. volume of the semi sphere = [tex]\frac{2}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]

where r is the radius = 1.5 m

volume of the semi sphere = [tex]\frac{2}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](1.5)^{3}[/tex]

                                             = 7.0714 cubic meters

Thus,

volume of the water to fill the spa tub = 7.0714 - (0.3536 + 0.8594)

                                                     = 5.8584

The volume of water that will fill the spa tub is 5.9 cubic meters.

Step-by-step explanation:

here's the answer to your question

Answer:

y = 3x+4

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = 3x+4

Answer:

Value of given expression is 3⁻¹⁴

Step-by-step explanation:

Given expression:

3⁻⁸ x 3⁻⁴ x 3⁻²

Find:

Value of given expression

Computation:

⇒ 3⁻⁸ x 3⁻⁴ x 3⁻²

⇒ 3[⁻⁸⁻⁴⁻²]

⇒ 3⁻¹⁴

Value of given expression is 3⁻¹⁴

Step-by-step explanation:

gjlhcohuguo

y.krgkyfjfhcxhhhxhhxfucuchhcjvgjjgvjvkvkx

Answer:

The quotient is 4x+5  and  the remainder is -13

Step-by-step explanation:

Using synthetic division

-5        4      25   12

Bringing down the 4 and multiplying

-5        4      25   12

        ↓       -20 -25

    ----------------------

         4        5    -13

The quotient is 4x+5  and  the remainder is -13

Answer:

  4x   +5    [tex]\frac{-13}{x+5}[/tex]

Step-by-step explanation:

          .           4x   +5    [tex]\frac{-13}{x+5}[/tex]

x + 5 | 4x^2 + 25x + 12

        - 4x^2 + 20x

                         5x + 12

                         5x + 25

                               -13

9514 1404 393

Answer:

Step-by-step explanation:

1) The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (4 -(-3))/(3 -0) = 7/3

__

2) The y-intercept is the point where x=0:

  (x, y) = (0, -3) . . . . . y = -3

__

3) Then the slope-intercept equation is ...

  y = mx + b . . . . . . . line with slope m and y-intercept b

  y = 7/3x -3

Answer:

x = 3.3

Step-by-step explanation:

A equation is given to us and we need to solve out for x. The given equation is ,

[tex]\sf\longrightarrow 5^{x -2}= 8 [/tex]

Take log on both sides with base as " 10" . We have ,

[tex]\sf\longrightarrow log_{10} 5^{x-2}= log_{10}\ 8[/tex]

Simplify using the property of log , [tex]\sf log a^m = m log a [/tex] , we have ,

[tex]\sf\longrightarrow ( x -2) log_{10} 5 = log_{10} 8 [/tex]

Simplify ,

[tex]\sf\longrightarrow ( x -2 ) log_{10}5 = log_{10} 2^3[/tex]

Again simplify using the property of log ,

[tex]\sf\longrightarrow (x-2) log 5 = 3 log 2[/tex]

We know that log 5 = 0.69 and log 2 = 0.301 , on substituting this , we have ,

[tex]\sf\longrightarrow ( x - 2 ) = \dfrac{ 3\times 0.301}{0.69}[/tex]

Simplify the RHS ,

[tex]\sf\longrightarrow x - 2 = 1.30 [/tex]

Add 2 both sides ,

[tex]\sf\longrightarrow \boxed{\blue{\sf x = 3.30}}[/tex]

Hence the Value of x is 3.30 .

Answer:

its actually 3.292 because we round to the nearest thousandth and thats not even the equation you use above

Step-by-step explanation:

For this equation we use the formula log a^m=m (log a) so the equation will be written as log 5 (5^x-2) = log 5 (8). You use the base, which is 5, and use log to base 5 on both sides of the equation. Then you take the exponent " x-2" and write( x-2) log 5 (5) = log 5(8). Since log a =1, you multiply that 1 by x-2, which keeps it x-2. Making the equation x-2 = log 5 (8). Next, we use the change of the base properties with the formula log b^y= log y/ log b. The equation will be written as x-2 = log 8/ log 5, since 5 is the base it stays in the bottom or basement. We then add +2 to both sides of x-2 and log 8/ log 5. To solve this equation, you can find out what log 8 and log 5 are and divide those and add +2 to solve. So log 8 = 0.903 and log 5 = 0.698970 and divide those to get 1.29190 +2 and you get the answer rounded as 3.292. 

Answer:

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Answer: See explanation

Step-by-step explanation:

Your question isn't well written, the store contains $227 and not $277.

let c be the number of $1 bills

let f be the number of $5 bills

let t be the number of $10 bills.

Therefore, the equation will be:

1c + 5f + 10t = 227

Since there are six more $5 bills than $10 bills, therefore,

f = t+6

Also, the number of $1 bills is two more than 24 times the number of $10 bills and this will be:

c = 24t + 2

Now, we substitute the equation for f and c into the main equation and this will be:

1c + 5f + 10t = 277

1(24t + 2) + 5(t + 6) + 10t = 227

24t + 2 + 5t + 30 + 10t = 227

39t + 32 = 227

39t = 227 - 32

39t = 195

t = 195/39

t = 5

Therefore, there are 5 $10 bills

Since c = 24t + 2

c = 24(5) + 2

c = 120 + 2

c = 122

Therefore, there are 122 $1 bills

Since f = t+6

f = 5+6

f = 11

Therefore, there are 11 $5 bills.