Q1: The first three stages of a pattern are shown below. Each stage of the pattern is made up of small squares. Each small square has an area of one square unit. Stage 1 Stage 2 (a) Draw the next two stages of the pattern. (b) The perimeter of Stage 1 of the pattern is four units. The perimeter of Stage 3 Stage 2 of the pattern is 12 units. Find a general formula for the perimeter of Stage n of the pattern, where # EN. (c) Find a general formula for the area of Stage n of the pattern, where E N. (d) What kind of sequence (arithmetic, quadratic, geometric, or none of these) do the areas follow? Justify your answer.​

Q1: The First Three Stages Of A Pattern Are Shown Below. Each Stage Of The Pattern Is Made Up Of Small

Answers

Answer 1

9514 1404 393

Answer:

  a) see attached for the drawings

  b) p = 8n -4

  c) a(n) = 4n(n -3) +13  for n > 1; a(1) = 1

  d) none

Step-by-step explanation:

a) The overall dimensions of the next two stages of the pattern will be 7×7 and 9×9. Excluding the 4 "ears", the central squares are 5×5 and 7×7. The drawings are shown in the attachment.

__

b) The sequence of perimeter values is ...

  4, 12, 20, 28, 36, ...

This is an arithmetic sequence with a common difference of 8. A suitable formula for the perimeter p of stage n is ...

  p = 8n -4

__

c) The sequence of area values is ...

  1, 5, 13, 29, 53, ...

The first differences are ...

  4, 8, 16, 24, ...

and the second differences are ...

  4, 8, 8, ...

At no level are the differences "common", so this sequence cannot be described by a polynomial function. After the first one, the second differences are common, so the sequence after the first term can be described by a quadratic function.

The function describing the sequence must be defined in two parts:

  [tex]a(n)=\begin{cases}1&\text{ for $n = 1$}\\4n(n-3)+13&\text{ for $n>1$}\end{cases}[/tex]

__

d) Because the function must be piecewise defined, the area sequence is not any of the types of sequences listed. After the first term, it is a quadratic sequence.

_____

Additional comment

The leading coefficient of the quadratic formula for the area sequence is half the second difference. When 4n² is subtracted from the sequence of areas, the remaining arithmetic sequence has a common difference of -12. In order to bring the total of these quadratic and arithmetic sequences up to the correct area value, 13 must be added. This formula would give a(1) = a(2) = 5, which is not the correct value for a(1). Hence, that must be defined separately.

Q1: The First Three Stages Of A Pattern Are Shown Below. Each Stage Of The Pattern Is Made Up Of Small

Related Questions

. The temperature fell 13°c on each of the first 2 days of the week. It rose 7°c on each of
the next 3 days and fell 9°c on each of the last 2 days. If the temperature was originally
34% what was the final temperature?

Answers

Answer:

The final temperature was 9 degrees.

Step-by-step explanation:

You can first multiply 13x2, 7x2, and 9x2. Then you subtract 26 and 18 from 34. then add 14

Help please and happy Halloween

Answers

Answer:

every time x goes up 1, y goes up 2

So the constant rate of change is 2

Step-by-step explanation:

let me know if I'm wrong

Answer:

Step-by-step explanation:

on the x side of the table it is adding 2 for every number.  

On they y side of the tables it is adding 4 for every number.

It is asking for rate of change for each table not all together.

So I geuss  x=2, y=4

A
Learning Task 3. Inside each wet and subsets, write at least 5 amples of
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Interpers
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Rational
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Solve the following word problem.

1. Mikey worked on her mathematics homework for hour and her science
homework for 7/8 hour. How long did she spend in all doing homework?

2. There are 60 students in a class. Three-fourths of them are girls. How many
boys are there?

3. One day in Baguio, the temperature went from - 2 °C to 8°C. What is the
change in temperature?

4. The elevation of Mt. Everest is 29 028 ft. The elevation of the Dead Sea is -485
ft. Find the difference in the elevation between Mt. Everest and the Dead Sea
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5. Angie cleans of the yard. Alex cleans of the remaining. What fraction of
the yard is left unclean?
3

Matinong sagot po please​

Answers

The following questions are related to problems on simple fraction and arithmetic. Hence, the solutions to the questions are as follows :

1.)

Time on mathematics = 1 hour

Time on science homework = 7/8 hours

Total time spent = (1 + 7/8) = [tex] 1 \frac{7}{8}[/tex]

2.)

Total number of students = 60

Fraction of girls = 3/4

Fraction of boys = 1 - 3/4 = 1/4

Number of boys = 1/4 × 60 = 15 boys

3.)

Initial temperature = - 2°C

Final temperature = 8°C

Change in temperature = Final temperature - Initial temperature

Change in temperature = (8 - (-2)) = 8 + 2 = 10°C

4.)

Elevation of everest = 20028 feets

Elevation of dead sea = - 485 feets

Difference in elevation = (20028 - (-485)) = 20513 feets

5.)

Question is missing key values.

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Using the graph of y = f(x) to the right, and given that the zero of the function is x=20, find the following.

Answers

Answer:

3.5

Step-by-step explanation:

the 4.1 m of concrete is made into the shape of a cylinder. The base has radios 0.5 metres. work out the height of the cylinder ( photo attached)

Answers

Answer:

5.2 metres

Step-by-step explanation:

v = pi. r^2 . h

4.1 = 3.1416 × 0.25 * h

h = 5.22 m

Veggie’s Market sells 5 avocados for $2.30 and 3 tomatoes for $2.97. Martina buys 2 avocados and 1 tomato. What is the total cost of her veggies?

Answers

Answer:

$1.91

Step-by-step explanation:

$2.30 / 5 = $0.46

$2.97 / 3 = $0.99

2 * $0.46 + $0.99 = $1.91

Answer:

1.91

Step-by-step explanation:

divide 2.30 by 5 and u get 0.47 and she bought 2 avocados so 0.47 plus 0.47 is 0.92 and 2.97 divided by 3 is 0.99 so 0.99 plus 0.92 is 1.91 dollars

Which graph shows that ice cream sales increase when temperatures increase

Answers

Answer:

.hh

Step-by-step explanation:

jj

Answer:

B

Step-by-step explanation:

You can see the scatter plot increase as temperature increases

Is this relation a function? Justify your answer.

Answers

Answer:

Yes

Step-by-step explanation:

(I can only read the graph).

Since for each dot, a vertical line drawn through it only intersects that dot, we conclude that the relation is a function.

In what quadrant will the reflection of (7,7) be located in​

Answers

Answer:

the first quadrant is positive, and positive so it would be the first quadrant

 

Step-by-step explanation:

–27y • (–z) what is the answer

Answers

Step-by-step explanation:

27yz

that is the answer

brainiest please

Hello!

The answer is 27yz.

Why?

Because if we multiply a negative times a negative, we always get a positive number.

Hope this helps you!

~Just a joyful teen

[tex]SilentNature\\(GraceRosalia)[/tex]

Anything would help :))

Answers

The first one is 3 if that helps

Step-by-step explanation:

1.

x = number

x/4 = x/3 - 1

x/3 - x/4 = 1

4x/12 - 3x/12 = 1

x/12 = 1

x = 12

2.

the numerator is the top (it gives the number of the parts of the whole that are combined in the fraction).

the denominator is the bottom (it says in how many and therefore how small parts we split the whole).

x = numerator

y= denominator

fraction is x/y

y = x + 2

(x+3)/(y+3) = 23

x + 3 = 23(y + 3) = 23y + 69

x = 23y + 66

now we use the first equation (y = x + 2) and substitute it into the last equation :

x = 23(x + 2) + 66 = 23x + 46 + 66 = 23x + 112

x = -112/22 = -56/11

y = -68/22 = -34/11

the original fraction is

x/y = -56/11 / -34/11 = -56/11 × -11/34 = 56/34 = 28/17

3.

in 1 hour the large pipe has done 1/3 of the work. and the small pipe 1/6 of the work.

so, in total in 1 hour we get (1/3 + 1/6) done.

what factor do we need to multiply (1/3 + 1/6) to get 1/1 (the whole work) ?

x(1/3 + 1/6) = 1

x(2/6 + 1/6) = 1

x(3/6) = 1

x × 1/2 = 1

x = 2

it takes both pipes together 2 hours to empty the pool.

4.

very similar to 3.

we are just using days instead of hours.

in 1 day Erwin gets 1/2 of the work done and Ana 1/5 of the work. so, together, 1/2 + 1/5 of the total work in one day.

so, how many days to get 1/1 (the whole work) done ?

x(1/2 + 1/5) = 1

x(5/10 + 2/10) = 1

x(7/10) = 1

7x = 10

x = 10/7

it takes them together 10/7 days to mow the whole lawn.

solve pls Brainliest

Answers

Answer:

25

Step-by-step explanation:

155-180=25 degrees

Answer:

x = 25°

Step-by-step explanation:

Multiply.
[−2 3/11⋅(−4)]⋅(1 13/20)⋅(−10)
What is the product?

Answers

The answer - 5198/11

Answer:

[tex]{ \rm{ \{ - 2 \frac{3}{11} \times ( - 4) \}. \{1 \frac{13}{20} \times ( - 10) \} }} \\ \\ = { \rm{9 \frac{1}{11} \times - 16 \frac{1}{2} }} \\ \\ { \boxed{ \rm{ \: = - 150 \: \: }}}[/tex]

I have more question then this

Answers

reflection over y axis...........

Please help

Ignore the first 2 questions please

Answers

Answer:

12

Step-by-step explanation:

Waterfalls to Canoes = 6 units

-4 to +2 = 6

Canoes to Fishing Area = 6 units

-2.5 to +3.5 = 6

Total = 6+6 = 12

crows are migrating and travel 35 km on a bearing of 047°. Then then fly 15 km of a bearing of 105°. How far , and on wha…

Answers

Answer:

American Crows can be considered partially migratory. That is, some populations migrate, others are resident, and in others only some of the crows migrate. Crows in the southern parts of their range appear to be resident and not migrate. They may make some changes in their use of space at this time, spending more time off the territory to forage and roost. Crows migrate out of the northern most parts of their range. It has been stated that crows migrate out of those areas where the minimum January temperature averages 0 ° F. Certainly crows leave the northern Great Plains in the fall, leaving Saskatchewan and Alberta to winter in the lower Plains states of Nebraska, Kansas, and Oklahoma (Kalmbach, E. R., and S. E. Aldous. 1940. Winter banding of Oklahoma crows. Wilson Bull. 52: 198-206). Crows can be seen crossing the Great Lakes in spring and fall, and these birds undoubtedly are migrating to and from parts of Canada.

Step-by-step explanation:

because  They may make some changes in their use of space at this time, spending more time off the territory to forage and roost. Crows migrate out of the northern most parts of their range. It has been stated that crows migrate out of those areas where the minimum January temperature averages 0 ° F.

1. How much of a difference is there, in interest, between an investment of $899 with simple interest of 5% and an investment of $499 with a simple interest of 9%, both for a six year term?

2. What balance will you have in your account, in 8 years, if you invest $4000 at 3.5% compounded quarterly?

3. Gina deposited $1500 in an account that pays 11% interest compounded monthly. What will the balance be in 5 years?

4. You invested $4,400 for 2 years at 7.3% compounded semianually. What is your total balance after 12 years?

5. You want to buy a new motorcycle so you borrow $14,200 for 5 years at an interest rate of 13% and it’s compounded daily. How much interest will you have paid after the 5 year term has ended?

Answers

The answer to the question is 06

1. A senator is thinking about running for president. But she will only do so if more than 60% of the voters view her favorably. She gathers some data to see if she has this level of support. Which statistical method would be best for her to use?

Answers

The senator is faced with the making a decision to run for President, based

on the conclusion she can make from the data she gathers.

The statistical method that would be best for her to use is inferential

statistic method such as finding the percentage of supporters she has to a

given confidence level.

Reason:

The two main types of statistical methods are;

Inferential statistics methods; Theses are methods used to reach a

conclusion that extends past the given or available data.

Descriptive statistics methods; Theses are statistical method used as a

summary of a data set.

Given that the senator is trying to draw conclusion based on the data she

gathers, she should use inferential statistic method.

The type inferential statistic method that can be used is the confidence

interval.

From the data collected, the proportion of voters that view her favorably is

used at a given confidence level to determine the true proportion of voters

that view her favorably.

Therefore;

The statistical method that would be best for her to use is the

finding of the confidence interval which is a inferential statistic method.

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You deposit $400 in an account earning 8% interest compounded annually. How much will you have in the account in 15 years?

Answers

Answer:

you will gain 280,462.92 in peso.but you convert in in dollar you will gain $5,520.00

I NEED A 100% ACCURATE ANSWER FOR THIS QUESTION ASAP NO LINKS !!!

Answers

Answer:

y = 5

Step-by-step explanation:

Group all y terms on the left side of the equation

Subtract 3y from both sides: 3-y-3y=3y+10-3y

Group like terms: -y-3y+30=3y+10-3y

Simplify the arithmetic: -4y+30=3y+10-3y

Group like terms: -4y+30=3y-3y+10

Simplify the arithmetic: -4y+30 = 10

Group all constants on the right side of the equation

Subtract 30 from both sides: -4y+30-30=10-30

Simplify the arithmetic: -4y=10-30

Simplify the arithmetic: -4y=-20

Isolate the y

Divide both sides by-4: -4y/-4 = -20/-4

Cancel out the negatives: 4y/4 = -20/-4

Find the greatest common factor of the numerator and denominator: y = 5·4/1·4

Factor out and cancel the greatest common factor:

y=5

Heyyyyyyyyyyyy can you help

Answers

Answer:

1.45 x 10   {2}

Step-by-step explanation:

Graph the line that represents the equation 3y = 2x + 9.

Please show a photo!! I need answer ASAP

Answers

These are the coordinates and a picture of the graph is below (0,3) (3,5)

Helpppp plzzzzzzzzzzzzz

Answers

Answer:

x=90 possibly

Step-by-step explanation:

3x all at 30 degrees. but not posative so please check elsewhere.

Please help me out. Thanks

Answers

Answer:

y=-2x+5

Step-by-step explanation:

2,1 and 3,-1

gradient

=(3-1)/-1-1

gradient = -2

y=5

y=-2x+5

PLEASE HELP ITS MATH THANK YOUUUU

Answers

Answer:

81 cm

Step-by-step explanation:

I'm pretty sure it's 81 cm cause you just times it by 27

Answer:

108 devided by 4 = 27 so the answer is 27 centimeters in the drawing

Step-by-step explanation:

What is the slope of the line represented by the equation y = -2/3- 5

Answers

-2/3

slope can also be classified as m in y=mx+b

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]-\frac{2}{3}[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

I am assuming that the equation is: [tex]y = -\frac{2}{3}x-5[/tex].

⸻⸻⸻⸻

[tex]\boxed{\text{General Slope-Intercept Form:}}\\\\y = mx+ b\\\rule{150}{0.5}\\\text{m - Slope}\\\text{b - Y-Intercept}\\\rule{150}{0.5}[/tex]

Since [tex]-\frac{2}{3}[/tex] take's m's spot, it is the slope of the equation.

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

What are the coordinates of the point?
(3,6)
(6, – 3)
(-3, -6)
(-3,6)

Answers

Answer:

The answer is D ( the last option in your list of possible answers. -3,6)

Answer:

(-3,6)

Step-by-step explanation:

It goes backwards 3 units to the left meaning the x value is negative 3. It goes up 6 meaning the y value is 6. Plug the values into (x,y) and you get (-3,6)

Help!!!! Jack walked 3 1/3 miles in 4/3 hours. If he walked at a constant rate, how far did he walk in 15 minutes?

Answers

Answer: I think the answer is 0.625 miles.

Step-by-step explanation:in the picture

At a movie theater, the price of 2 adult tickets and 4 child tickets is $48. The price of 5 adult tickets and 2 child tickets is $64. What is the ticket price for one adult and for one child?

Adult: Child:

Answers

Answer:

adult=10

Child=7

One adult and one child=10+7=17

Step-by-step explanation:

Let a be the price of an adult ticket

c = price of the child ticket

2a+4c = 48

5a+2c = 64

Multiply the second equation by -2 and add to the first equation

2a+4c = 48

-10a-4c = -128

---------------------

-8a +0c = -80

Divide by -8

-8a/-8 = -80/-8

a = 10

Now find c

2a+4c=48

2(10)+4c=48

20+4c=48

4c=48-20

4c=28

4c/4=28/4

c=7

Answer:

look at the photo..........

The cost for one ticket to a jazz concert is $7.50. Two tickets cost $15. Write an equation in point-slope form to represent the total cost y for x tickets.

Answers

An equation in the point-slope form to represent the total cost y for x tickets is [tex]y-15 = 2(x-2)\\[/tex]

Let the cost of ticket be C

Let the number of tickets be x

The coordinate for the cost of a ticket will be written as: (x, C)

If the cost for one ticket to a jazz concert is $7.50, this is represented in coordinate form as (1, 7.50)

If two tickets cost $15, his is represented in coordinate form as (2, 15)

Get the slope of the equation

[tex]m =\frac{15-7.5}{2-1}\\m=\frac{7.5}{1}\\m = 7.5\\[/tex]

Get the equation in point-slope form

[tex]y-y_1 = m(x-x_1)\\[/tex]

Substitute the slope and one of the point into the formula:

[tex]y-15 = 2(x-2)\\[/tex]

Hence an equation in the point-slope form to represent the total cost y for x tickets is [tex]y-15 = 2(x-2)\\[/tex]

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