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.
Answers
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.
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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]
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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.
Related Questions
Use the monthly payment formula to find the monthly payment for a $1,000, one year
loan at an APR of 7.5%
Answers
Step-by-step explanation:
The formula :
[tex]\displaystyle \rm S=A\cdot \left (1+\frac{N}{100} \right )^{\big r}[/tex]
where r is years ; N is the percentage by which we increase the price ; A is the original price
In our case :
[tex]\rm r=1 \ \ ; \ \ A=100 \ \ ; \ \ N=7,5\% \\\\ S=1000\cdot \bigg( 1+\dfrac{7,5}{100} \bigg)^1=1000\cdot 1,075=\boxed{1075\$}[/tex]
Then the monthly salary is equal to:
[tex]\dfrac{1075}{12} \approx 89,58 \$[/tex]
5(x + y)2 + (x + y) − 4
Answers
Answer:
11x+11y-4
Step-by-step explanation:
True or false
Quotient x Remainder + Dividend - Divisor
Answers
EXPLANATION: s not true that Dividend over Divisor is equal to Quotient plus Remainder. For example if 37 is divided by 8 , then quotient is 4 and remainder is 5 .
Create a proportion from each set of numbers. Only use 4 numbers from each set.
Answers
Step-by-step explanation:
Approach: If four numbers a, b, c and d are in proportion then a:b = c:d. The solution is to sort the four numbers and pair up the first 2 together and the last 2 together and check their ratios this is because, in order for them to be in proportion, the product of means has to be equal to the product of extremes.
P g In the figure, lines m and nare parallel to each other. Lines p and q are also parallel to each other. 689 х The value of x is. degrees, and the value of y is degrees.
Answers
Answer:
220 i think
Step-by-step explanation:
17. Bailey rode Coaster B four times. How
many feet did she ride? What is your
answer rounded to the nearest thousand?
DATA
18. Janna rode each of the four roller
coasters listed in the table twice. How
many feet of roller coaster did she ride?
Answers
Answer:
Step-by-step explanation:
if carl runs 4 laps in 18 minutes, how many laps can he run in 1 1/2 hours
Answers
Answer:
20 laps
Step-by-step explanation:
18 divide by 4 = 4.5
so 1 lap equals 4.5 minutes
and 1 and half hours is 90 minutes so 90 divide by 4.5 = 20 laps
90 minutes is 1 1/2 hours
We setup the equation to solve:
4/18=x/90
Solve for x by isolating and then cross multiply.
2/9=x/90
Cross multiply,
180=9x
Swap sides,
9x=180
Divide both sides by 9
X=20 :)
Can someone help me please
Answers
Answer:
a.(x)=7
b.(x)=14
Step-by-step explanation:
plz mark me as brainliest
Answer:
For A x equals 7
For B x equals 14
Explanation:
Simply cross multiply
A. 21×2=42÷6=7
Or find the relationship
B. 150÷6=25
84÷6=14
Hope this helps, mark BRAINLIEST please...
Can someone help me please
Answers
Answer:
15) 104 lbs
16) 263 miles
Step-by-step explanation:
15)
4/7 of their weight (182) = the water weight
4/7 × 182 = 104 lbs
16)
3.5 months = 920 miles
1 month = 920 ÷ 3.5
= 262.8571429 ≈ 263 miles
Answer:
15) 104 lb
16) 262 6/7 miles/month
Step-by-step explanation:
15)
4/7 * 182 lb = 4/7 * 182/1 lb = (4 * 182)/(7 * 1) lb = (4 * 7 * 26)/7 lb = 104 lb
Answer: 104 lb
16)
(920 miles)/(3 1/2 months) = (920 miles)/(7/2 months) =
= 920/1 miles * 2/(7 months) = (920 * 2 miles)/(7 months) =
= 1840/7 miles/month = 262 6/7 miles/month
• A man observes the angle subtended by a pole to be 30'. He walks 10 metres towards its base and finds that it subtends an angle of 45'. Find the height of the pole.
(A) 12.65 m (B) 13.66 m (C) 15 m (D) 14 m
Answers
Answer:
13.66m
Step-by-step explanation:
In a state's Pick 3 lottery game, you pay $1.35 to select a sequence of three digits (from 0 to 9), such as 966. If you select the same sequence of three digits that are drawn, you win and collect $394.46
Answers
Answer:
-96 cents
Step-by-step explanation:
(Conjectured Problem) In a state's Pick 3 lottery game, you pay $1.35 to select a sequence of three digits (from 0 to 9), such as 966. If you select the same sequence of three digits that are drawn, you win and collect $394.46. That is your expected win?
Expected Win =
(Probability you match the drawn sequence)(Amount won if there is a match) - (Amount you pay) =
(1/10)(1/10)(1/10)(394.46) - 1.35 =
0.39446 - 1.35 =
-0.95554 =
-96 cents, rounded to the nearest cent
A line has a slope of 1 and passes through the point (-8, -7). What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer: y = x + 1
Step-by-step explanation:
y = 1x + c
-7 = 1(-8) + c
-7 = -8 + c
-7 + 8 = c
1 = c
y = 1x + 1 or
y = x + 1
Answer:
y+8=m(x+7)
hope this helps:
I used this formula y-y1=m(x-x1)
The lines represented by the equations y=-\frac{5}{2}x+7y=− 2 5 x+7 and y-\frac{2}{5}x=-4y− 5 2 x=−4 are
Answers
Answer:
bxjfjxucjkkdndjkjhkjjnn
What is the value of the expression (2.75) (5.2)?
Answers
Answer:
14.3
Step-by-step explanation:
2.75 * 5.2=14.3
y < -2x + 1
x + 2y > -4
Answers
Answer:
99
Step-by-step explanation:
A rectangular solid measures 150cm by 100cm by 200cm calculate the volume
Answers
Answer:
3000000cm³
Step-by-step explanation:
150cm x 100cm x 200cm = 3000000cm³
PLS HELP ME WILL GIVE BRAINLIEST NO LINKS PLZ!!!
Answers
Answer:
130
Step-by-step explanation:
sorry if wrong
have a great day
A person's heart beats 200 times in 3 minutes. How many times will it beat in an hour (remember...60 minutes in an hour) ?
Answers
200 times / 3 minutes = x times / 60 minutes
3x = 12000
x = 4000 times in an hour
A person's heart will beat 4000 times in an hour.
Hope this helps!! :)
Answer: 4000 beats per hour
Step-by-step explanation:
200 beats X 60 minutes
3 minutes 1 hour
The term 'minutes' cancel out therefore you are left with beats per hour
200 x 60 = 12000 = 4000 beats per hour
3 3
Clear Plumbing charges a flat fee of $28.50 for a repair trip and $38. 50 per hour for labor. What is the total cost of a repair job that takes 3.5 hours?
Answers
Answer:
163.25
Step-by-step explanation:
38.50x3.5= 134.75
134.75+28.50= 163.25
38.5 per hour which explains 38.5x3.5= 134.75
28.50 is a one time fee so you add that to the total of hours 134.75+ 28.50= 163.25 in total.
What does the initial amount represent on the linear equations word problems?
Answers
Answer:
0
Step-by-step explanation:
The initial value or y-intercept is the output value when the input of a linear function is zero.
On a coordinate plane, how are the locations of the points (-4 , 8) and (-4 , -8) related?
A.
reflection across the y-axis
B.
reflection across the x-axis
C.
reflection across both axes
D.
locations unrelated
Answers
Answer:
A. reflection across the y-axiss
Step-by-step explanation:
Given:
The locations of the two points are (-4 , 8) and (-4 , -8).
To find:
The relation between two points.
From the given points (-4, 8) and (-4 , -8), it is clear that the y-coordinates are same but the sign of x-coordinates are opposite.
If a figure is reflected across the y-axis, then we change the sign of x-coordinate and the y-coordinates remain same, i.e.,
[tex](x,y)[/tex]→[tex](-x,y)[/tex]
For (-4,8)
[tex](-4,8)[/tex]→ [tex](-4,-8)[/tex]
So, it is reflection across the y-axis.
Therefore, the correct option is A.
PLEASE HELP!! WILL GIVE BRAINLIEST!!!
Answers
Answer: it b
Step-by-step explanation:
IT B
1/4 + 23/28 - 1
please help
Answers
Answer:
[tex]\frac{1}{14}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4} + \frac{23}{28} - 1 = ?[/tex]
First off, let's change everything to a common denominator. This will allow us to add the fractions!
To find a common denominator, we find a number that both 4, 28, and 1 can go into. 28 is the best choice, as 4 goes into it 7 times, 28 goes into it once, and 1 goes into it 28 times.
Let's change the first fraction into a number with a denominator of 28!
[tex]\frac{1}{4} * \frac{7}{7} = \frac{7}{28}[/tex]
[tex]\frac{7}{7}[/tex] = 1. Multiplying a number by one doesn't change its value.
The second fraction, [tex]\frac{23}{28}[/tex], already has a denominator of 28, so we don't have to do anything with it.
Now to the third number, -1:
[tex]-1 = -\frac{1}{1} * \frac{28}{28} = -\frac{28}{28}[/tex]
Now, let's add them all up!
[tex]\frac{7}{28} + \frac{23}{28} - \frac{28}{28} = \frac{7 + 23 - 28}{28} = \frac{2}{28}[/tex]
One last step, to simplify:
[tex]\frac{2}{28} = \frac{1}{14}[/tex]
Your answer is 1/14!-12 1/2 + 4 1/2
I need the work
Answers
Answer:
-4
Step-by-step explanation:
1/2 of -12 is -6. 1/2 of 4 is 2.
-6 + 2 is -4.
Pls help ASAP I’ll brainlest
Answers
EXPERIMENT
PROBLEM
CONCLUSION
INFERENCE
Help ASAP! i will give brainliest!
Answers
9514 1404 393
Answer:
-3/4a^3b^23.2·10^-1-0.1a^(n+1)Step-by-step explanation:
To find the cube root, divide all of the exponents by 3. For a cube root, the sign is unchanged.
A) ∛(-27/64a^9b^6) = -∛(3^3/4^3·a^9·b^6) = -3/4a^3b^2
__
B) 9.6×10^-8 ÷ (3×10^-7) = (9.6/3)×10^(-8-(-7)) = 3.2×10^-1
__
C) ∛(-0.001a^(3n+3)) = -∛(0.1^3·a^(3n+3)) = -0.1a^(n+1)
Question 25
Multiply two or more consecutive integers to obtain a six-digit palindrome whose first two digits are “47”. What is the sum of these consecutive integers?
(A palindrome is a number that reads the same backwards as forwards)
Answers
Answer:
234Step-by-step explanation:
The number is in the form of:
47AA74This is divisible by 2, can be divisible by 3 but not divisible by 4 as 74 is not divisible by 4.
So possible number of integers is 2 or 3.
Two consecutive integersThere is no possible product ending with 4 (test it yourself)Three consecutive integersThe numbers are x - 1, x and x + 1
The product is between 470074 and 479974
Their product is between:
(x - 1)³ < x³ < (x + 1)³470074 ≤ x³ ≤ 479974∛470074 ≤ x ≤ ∛47997477.75 ≤ x ≤ 78.29x = 78 is the only integer within this intervalLets test:
77*78*79 = 474474Sum of these:
77 + 78 + 79 = 234Can someone help me please
Answers
Answer:
The financial aid covers $ 1,875
Student needs to pay out-of-pocket $635
Step-by-step explanation:
(2,500) * (3/4) = 7500/4 = 1,875
2,500 - 1,875 = 635
Find a point-slope form for the line with slope 1/5 and passing through the point (-3, -8).
Answers
i think it would be y+8=1/5(x+3)
Step-by-step explanation:
point slope formula is y-y1=m(x-x1)
slope=m
m=1/5
PLEASE DO!! will give brainliest
Which statement correctly describes the end behavior of the function f(x) = x2 – 2x + 8?
Answers
Answer:
3
Step-by-step explanation:
in both f approaches +infinity