A 1x1 square and an n-tiling is a group of n tiles placed so that every tile is contiguous along at least one side to another tile. (The tiles cannot be offset. That is, they must be placed into a grid like Scrabble tiles.) The edge length of a tiling is the total length of edges that are not touching other tiles. For instance, a 20-tiling, the edge length is 36.
Required:
Prove that for all n-tilings where n >= 1, the edge length is even.
Answers
Answer:
Step-by-step explanation:
The first picture below shows the missing image in the question.
There are 4 edges of each tile;
This clearly explains to us that the total number of edges present in the n tiles is 4n.
Now, if a tile "X" touches and comes in contact with another tile "Y", then edges touching each other are one edge of a tile X and one edge of a tile Y.
From the second diagram below, the edge, X_2, and Y_4 are touching each other.
Now, the total number of edges that touch some edges is always even.
We can now say that:
The edge length of filling = No. of edges that do not touch another file
= Total no. of edges - No. of edges that touch another edge.
However, the total number of edges is even.
The number of edges that touch another edge is also even.
Thus, the difference is also even and the number of edges that do not touch another is even.
So, the edge length of filling is always even.
Related Questions
A triangle has a base of (x+9) feet and a height of (4x+4). The expression below represents the area of the triangle.
12(x+9)(4x+4)
Which of the following choices represents the simplified form of the expression above?
Select one:
A. 4x2+36x+36
B. 2x2+80x+18
C. 2x2+18x−18
D. 2x2+20x+18
Answers
Answer:
I think the answer would be B
Step-by-step explanation:
Because we multiply, distribute and combine like terms
Help me out thanks u !!!
Answers
Answer:
116
Step-by-step explanation:
All angles will add up to 360°
So just do 360 -55 -79 -110 = 116
Answer:
The answer is 116 because the sum of angles in a quadrilateral is 360 degrees.
What’s the answer to 7x when x=8 I need help please
Answers
Answer:
56
Step-by-step explanation:
7x8=56
Step-by-step explanation:
7(8)
= 56
use tye substitution property
12. What is the perimeter of triangle ABC to
the nearest whole number?
A
19.5
49°
B
40°
C
Answers
Step-by-step explanation:
61.945
62the perimeter of triangle ABC to
the nearest whole number
-3/4 ( 8y - 12 ) + 1/5 ( 15y - 30 )
Answers
-3(y-1)
Find the area of the figure.
= m
(simplify your answer)
Answers
2. Which of the following statements shows the distributive property?
5 + (4 – 2) = 20 – 10
5(4 – 2) = 20 – 10
5 + (4 – 2) = 9 + 3
5(4 – 2) = 9 – 7
PLEASE HELP ME!!! ITS A MONTH PAST DEW! I NEED HELP ASAP!
Answers
13) A certain radioactive isotope decays at a rate of 0.1% annually. Determine the half-life of this isotope, to the
nearest year.
C) 301 yr
D) 500 yr
A) 7 yr
B) 693 yr
Answers
Answer:
se__xxxx cha_t
Step-by-step explanation:
aaah aaaah
solve the equation for the value of x; 8x + 12 = 52.
a) x = 12
b) x = -5
c) x = 5
d) x = 52
Answers
Answer:
5
Step-by-step explanation:
8x + 12 = 52
move constant to right
8x=52-12
subtract numbers
8x=40
divide both sides
x=5
WO-Step Equations Pra
Solve each equation.
1) 3+ 5r=-47
Answers
Answer:
r=-10 Hope this helps! If I could have brainliest I'm trying to level to level up.
Step-by-step explanation:
Let's solve your equation step-by-step.
3+5r=−47
Step 1: Simplify both sides of the equation.
5r+3=−47
Step 2: Subtract 3 from both sides.
5r+3−3=−47−3
5r=−50
Step 3: Divide both sides by 5.
5r/5=-50/5
r=−10
Answer:
r=−10
Please help, will give brainliest! Which is NOT equivalent to this expression? 4(3x^2+6x)
Answers
During a competition, numismatist Aditi has been given Rs. 200 in Rs.1 denominations. The judge asks Aditi to allocate the Rs. 1 denominations into a number of pouches such that any amount required between Rs.1 & Rs. 200 can be given by giving out a certain number of pouches without opening them. Aditi thinks and asks the judge to give her 'x' number of pouches to keep the money, where 'x' is the minimum number of bags required to keep the total money. Can you guess the value of 'x'?
Answers
9514 1404 393
Answer:
8
Step-by-step explanation:
If the bags can either be given or not, each bag can assume one of two states. In order for there to be 200 possible combinations of items in one of two states, there must be at least log2(200) = 7.64 items. The minimum number of bags is x = 8.
_____
The contents of the 8 bags will be Rs. 1, 2, 4, 8, 16, 32, 64, 73.
a triangle has angles that measure 50 degrees and 50 degrees what is the measure lf the third angle?
Answers
Answer:
80
Step-by-step explanation:
the combined angles of any triangle equal 180 degrees. take the known angles ( 50 and 50) and subtract their sum from 180. 180-100=80
Twelve friends met for for dinner. They learned that three-twelfths of them
were born in Texas, two-twelfths in New York and the rest in Idaho.
How many friends were born in Idaho?
Answers
the answer is seven twelfth
The weekly amount of money spent on maintenance and repairs by a company was observed, over a long period of time, to be approximately normally distributed with mean $480 and standard deviation $20. How much should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.05
Answers
Answer:
$512.90 should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.05
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Normally distributed with mean $480 and standard deviation $20.
This means that [tex]\mu = 480, \sigma = 20[/tex]
How much should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.05?
This is the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 480}{20}[/tex]
[tex]X - 480 = 1.645*20[/tex]
[tex]X = 512.9[/tex]
$512.90 should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.05
HELPP!! I report wrong answers!!
Answers
Please help me with the question
Answers
Answer:
4(7+y) and 4·7+4·y
Step-by-step explanation:
4(7+y)= 28+4y
4·7+4·y= 28+4y
Pls help I’m failing I need a good grade
Answers
The answer is B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
HELPP ASAP PLSS I’ll mark brainliest!!!
Answers
Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of the cable by arranging the cable in a Y-shaped configuation. Centerville is located at ( 10 , 0 ) in the x y -plane, Springfield is at ( 0 , 5 ) , and Shelbyville is at ( 0 , − 5 ) . The cable runs from Centerville to some point ( x , 0 ) on the x -axis where it splits into two branches going to Springfield and Shelbyville. Find the location ( x , 0 ) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer.
To solve this problem we need to minimize the following function of x : f ( x ) =
We find that f ( x ) has a critical number at x =
To verify that f ( x ) has a minimum at this critical number we compute the second derivative f ' ' ( x ) and find that its value at the critical number is ,
a positive number. Thus the minimum length of cable needed is
Answers
Answer:
hi i dont understand this
Step-by-step explanation:
sorry
The function will be
[tex]f(x) = 9 - x + \sqrt[2]{ {x}^{2} + 9} [/tex]
and minimum value required will be
[tex]9 + \sqrt[3]{3} [/tex]
How to solve this problem?The steps are as follow:
[tex]f(x) = (9 - x) + \sqrt[2]{ (x^2 + 3^2) } \\ =(9 - x) + \sqrt[2]{ (x^2 +9)} \\ f(x) = \frac{2x}{ \sqrt{ {x}^{2} + 9} } - 1 \\ f(x) = 0 \\ \frac{2x}{ \sqrt{ {x}^{2} + 9} } - 1 = 0 \\ \frac{2x}{ \sqrt{ {x}^{2} + 9}} = 1 \\ 2x = \sqrt{ {x}^{2} + 9} \\ 4{x}^{2} = { x}^{2} + 9 \\ 3 {x}^{2} = 9 \\ {x} = \sqrt{3} [/tex]
so putting value of in f(x) we will get
[tex]f( \sqrt{3} ) = 9 - \sqrt{3} + \sqrt[2]{ { (\sqrt{3} )}^{2} + 9} \\ = 9 + 2 \sqrt{3} [/tex]
So The function will be
[tex]f(x) = 9 + \sqrt[2]{ {x}^{2} + 9}[/tex]
and minimum value required will be
[tex]9 + \sqrt[3]{3} [/tex]
Learn more about functions here:
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Periodic grab some phase shifts
Answers
Answer:
The sine function is:
[tex]y(x)=\frac{2}{3}sin[3\pi (x-\frac{2\pi}{3})]-2[/tex]
Step-by-step explanation:
We need to recall that a sine function can write as:
[tex]y(x)=Asin[B(x+C)]+D[/tex]
Where:
A is the amplitude of the functionB is the periodC is the phase shift leftD is the vertical shiftSo we just need to use the listed attributes
Therefore, the sine function is:
[tex]y(x)=\frac{2}{3}sin[3\pi (x-\frac{2\pi}{3})]-2[/tex]
I hope it helps you!
sketch a graph of the relation y=cos^-1x
Answers
the point (2, -3 ) is reflected in the line x = 0 find the image
Answers
Answer:
The image of [tex]P(x,y) = (2,-3)[/tex] is [tex]P'(x,y) = (-2, -3)[/tex].
Step-by-step explanation:
According to this statement, we need to find the image of a given point by reflection with respect to the y-axis. The reflection can be done by following operation:
[tex]P(x,y) = (x, y) \to P'(x,y) = (-x, y)[/tex] (1)
Where:
[tex]P(x,y)[/tex] - Original point.
[tex]P'(x,y)[/tex] - Reflected point.
If we know that [tex]x = 2[/tex] and [tex]y = -3[/tex], then the reflecting point is:
[tex]P'(x,y) = (-2, -3)[/tex]
The image of [tex]P(x,y) = (2,-3)[/tex] is [tex]P'(x,y) = (-2, -3)[/tex].
I need help please anyone help me???????
Answers
If you are given the diameter, how can you calculate the radius
Answers
Answer:
divide the diameter by 2
Compute the discriminant D(x,y)D(x,y) of the function. f(x,y)=x3+y4−6x−2y2+3 f(x,y)=x3+y4−6x−2y2+3 (Express numbers in exact form. Use symbolic notation and fractions where needed.) D(x,y)=D(x,y)= Which of these points are saddle points? (2⎯⎯√,0)(2,0) (2⎯⎯√,1)(2,1) (−2⎯⎯√,1)(−2,1) (2⎯⎯√,−1)(2,−1) (−2⎯⎯√,−1)(−2,−1) (−2⎯⎯√,0)(−2,0) Which of these points are local minima?
Answers
The discriminant of function [tex]f(x,y)=x^3 + y^4 - 6x-2y^2+3[/tex] is 72xy³ – 24x and points (√2,0), (-√2, 1) and (-√2, -1) are saddle point, and points (√2, 1) and (√2, -1) are local minima.
A function is an expression in terms of one or more variable.
If f(x, y) is a two-dimensional function that has a local extremum at a point ([tex]x_o, y_o[/tex]) and has continuous partial derivatives at this point, then [tex]f_x (x_o, y_o)=0[/tex] and [tex]f_y (x_o, y_o)=0[/tex]. The second partial derivatives test classifies the point as a local maximum or local minimum.
Then
1. If D > 0 and [tex]f_{xx}(x_o, y_o) > 0[/tex] , the point is a local minimum.
2. If D > 0 and [tex]f_x_x (x_o, y_o) < 0[/tex], the point is a local maximum.
3. If D < 0, the point is a saddle point.
4. If D = 0, higher order tests must be used.
Given that
[tex]f(x,y)=x^3 + y^4 - 6x-2y^2+3[/tex]
[tex]f_x = 3x^2-6[/tex]
[tex]f_x = 0[/tex] implies that [tex]x = \pm\sqrt2[/tex]
[tex]f_y= 4y^3-4y[/tex]
[tex]f_y= 0[/tex] implies that y = 0; y = [tex]\pm[/tex]1.
Thus, the critical points are (√2,0), (√2,1), (√2, -1);(-√2,0), (-√2,1); (√2, -1).
[tex]f_{xx} = 6x[/tex]; [tex]f_y_y = 12y^3 - 4[/tex], [tex]f_{xy}= 0[/tex]
D(x, y) = [tex]f_{xx}f_{yy} - f_{xy}^2[/tex]
= 6x × (12y³ – 4)
D(√2, 0) = -24√2 < 0 implies (√2,0) is a saddle point.
D(√2, 1) = 48√2 > 0 ; [tex]f_{xx}(2, 1) = 6\sqrt2 > 0[/tex] implies (√2, 1) is local minimum.
D(√2, -1) = 48√2 > 0; [tex]f_{xx}(2, -1) = 6\sqrt2 > 0[/tex] implies (√2, -1) is local minimum.
D(-√2, 0) = 24√2 > 0; [tex]f_{xx}(-2,0) = -6\sqrt2 < 0[/tex] implies (-√2, 0) is local maximum.
D(-√2, 1) = -48√2 < 0 implies (-√2, 1) is a saddle point.
D(-√2, -1) = -48√2 < 0 implies (-√2, -1) is a saddle point.
Thus, (√2,0), (-√2, 1) and (-√2, -1) are saddle point, and (√2, 1) and (√2, -1) are local minima.
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The owner of a restaurant is concerned about customers who ask for a water cup when placing an order but fill the cup with a drink from the beverage fountain instead of filling the cup with water. The owner randomly selected 90 people who order a water cup and found that 21 of those customers filled the cup with a soft drink.a. Construct and interpret a 95 percent confidence interval for the proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with a soft drink from the beverage fountain. b. The owner estimates that each customer who asks for a water cup but fills it with a soft drink costs the restaurant $0.35. Suppose that in the month of June 2,500 customers ask for a water cup when placing an order. Use the confidence interval constructed in part (a) to give an interval estimate for the cost to the restaurant for the month of June from the customers who ask for a water cup but fill the cup with a soft drink.
Answers
Answer:
This is very confusing.
Can you try and make this a shorter question for me to answer?
Step-by-step explanation:
A number increased by 20% of the number result is 11. What is the number?
Answers
Answer:
9.167
Step-by-step explanation:
120% is 11
100% is x
[tex]\frac{11*100}{120} \\\\= \frac{110}{12}\\[/tex]
≅ 9.167
19.214÷13
pls someone help me
Answers
Answer:
1.478
Step-by-step explanation:
Complete the comparison : 17>?
Answers
Answer:
17>16
Step-by-step explanation:
Answer:
17 is greater than or (>) than any number lower than 17 :)
Step-by-step explanation:
For example, 17>16.. 17> 15, or 17> 14...ect.
Hope this helps! :)
Have a nice day <3