My square patio is tiled with square tiles, all the same size. All the tiles are gray, except the tiles along the two diagonals, which are all yellow. (The corners are yellow, the center is yellow, and all the tiles along the diagonal in between are yellow.) If there are $89$ yellow tiles, how many gray tiles are there

Answers

Answer 1

Answer:

1936

Step-by-step explanation:

We can start by removing the center tile, because all four diagonals over lap on that tile. We'll add it back later. 88/4=22. which means there are 22 tiles per half, 44+1(the center tile) total tiles per side, which means there are a total of 1936 tiles.

Answer 2

AOPS ANSWER:

Suppose that we have a square with dimensions [tex]$e \times e$[/tex]. The diagonals each have [tex]$e$\\[/tex] tiles. If [tex]$e$\\[/tex] is even, the number of yellow tiles is [tex]$2e$[/tex], because the [tex]2[/tex] diagonals don't intersect. If [tex]$e$[/tex] is odd, then the number of yellow tiles is [tex]$e+e-1=2e-1$[/tex]. (We have to subtract [tex]1[/tex] because the center tile is counted [tex]2[/tex] times). We know that there are [tex]89[/tex] yellow tiles, which is an odd number, so [tex]$89=2e-1$[/tex]. This implies that [tex]$e = 45$[/tex]. So the dimensions of the floor are [tex]$45 \times 45$[/tex], or [tex]2025\\[/tex] square units. Since all of the other tiles are gray, there are [tex]$2025-89=\boxed{1936}$[/tex] gray tiles.


Related Questions

Wilma is 5 times as old as yvonne. in ten years, yvonne's age will be a third of wilma's age. how old are they now?

Answers

Using a system of equations, it is found that Wilma is 50 years old and Yvonne is 10 years old.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

Variable x: Wilma's age.Variable y: Yvonne's age.

Wilma is 5 times as old as yvonne, hence:

x = 5y.

In ten years, yvonne's age will be a third of wilma's age, hence:

[tex]y + 10 = \frac{1}{3}(x + 10)[/tex]

Since x = 5y:

[tex]y + 10 = \frac{1}{3}(x + 10)[/tex]

[tex]y + 10 = \frac{1}{3}(5y + 10)[/tex]

3y + 30 = 5y + 10

2y = 20.

y = 10.

Then:

x = 5y = 5 x 10 = 50.

Wilma is 50 years old and Yvonne is 10 years old.

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What is the line that has a slope of -2/3 and passes through point -3,-1?

Answers

Answer:

y = (- 2/3)x - 3

Step-by-step explanation:

y = mx + c

y = (- 2/3)x + c

Now let's substitute the values (-3,-1)

- 1 = (- 2/3)(-3) + c

-1 = 2 + c

c = - 3

Therefore,

y = (-2/3)x - 3

Answer:

y = -2/3x - 3

Step-by-step explanation:

y = mx + b

y = y coordinate              → given: - 1

m = slope                        → given: - 2/3

x = x coordinate              → given: - 3

b = y intercept                 → need to find

y = -2/3x + b → -1 = -2/3(-3) + b

-1 = 2 + b

subtract 2 from both sides

-1 - 2 = 2 - 2 + b

-3 = b

y = -2/3x - 3

Es para hoy ayúdenme por favor

Answers

Answer:

Con qué necesitas ayuda?

Step-by-step explanation:

The table shows the probability of how a certain score will
compare to a listed score on a popular video game. Use the
probability distribution to find the variance, o².

Answers

The variance of the probability distribution is 400

The Variables of X and their Probability Distribution.

To find Variance, first we should find out Mean and then Variance

The expected value of a discrete random variable X, symbolized as E(X), is often referred to as the long-term average or mean (symbolized as μ)

The variance of a probability distribution is symbolized as σ2. To find the variance σ2 of a discrete probability distribution, find each deviation from its expected value, square it, multiply it by its probability, and add the products.

Step – 1: Calculation of Mean                               Step – 2: Calculation of Standard Deviation= σ2=∑(x−μ)²P(x)

Mean = X * P(X)     Variance = Sum of (X – Mean)²*P(X)

X P(X) X*P(X)

-50 0.029 -1.45

-30 0.121 -3.63

-10 0.210 -2.1

10 0.485 4.85

30 0.145 4.35

50 0.010 0.5

Mean  2.52

X  P(X) X - Mean  (X – Mean)² (X – Mean)²*P(X)

-50 0.029 -52.52 2758.35                 79.99216

-30 0.121 -32.52 1057.55                 127.9636

-10 0.210 -12.52 156.7504         32.91758

10 0.485 7.48          55.950                  27.13594

30 0.145 27.48 755.1504         109.4968

50 0.019 47.48 2254.35                 22.5435

Variance=400.00

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simplify 6e × 2f please help​

Answers

So first multiply the numbers
6 x 2 which gives you 12
then just add the letters which gives you
The answer (12ef) and that’s your answer

please help i just started summer school online Part F
Several minutes later, Raul decides to measure the water temperature again. He finds that the temperature changed by -0.6°F. What is the temperature of the water now? Show your work.

Answers

Answer:

Step-by-step explanation:

basically all you do is

Which model best represents the situation

Answers

Answer:

A

Step-by-step explanation:

she worked a total of 34 hours , then

x + y = 34

earnings are $10 per hour babysitting , that is 10x for x hours

$15 per hour for yardwork, that is 15y for y hours

she made a total of $410 , then

10x + 15y = 410

system of equations is

x + y = 34

10x + 15y = 410

Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of function g if g(x) = f(x) − 11?

Answers

Using translation concepts, it is found that the graph of function g if g(x) = f(x) − 11 is a shift down of 11 units of function f(x).

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have that g(x) = f(x) − 11 represents a shift down of 11 units of function f(x).

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which expressions are equivalent ??

Answers

Answer:

[tex]\huge\boxed{E.\ 5^{4+x}}[/tex]

Step-by-step explanation:

Use:

[tex]a^n\cdot a^m=a^{n+m}[/tex]

[tex]5^4\cdot5^x=5^{4+x}[/tex]

The base of the Hawaiian mountain Mauna Kea is about 5,853 meters below sea level. Its summit is 4,205 meters above sea level. What is the total height of Mauna Kea? The base of the Hawaiian mountain Mauna Kea is about 5,853 meters below sea level . Its summit is 4,205 meters above sea level . What is the total height of Mauna Kea ?​

Answers

Answer:

100,58 meters

Step-by-step explanation:

You add 5,853 plus 4,205 to get 100,58 Meters. You add the number below and above sea water tog et the total height of the mountain.

Answer:

Mouna Kea is 10,058 meters high

Step-by-step explanation:

in order to calculate the whole height of the Mouna Kea you will need to add the base to the summit.

5,853 +4,205 = 10,058

Select the correct answer.
A graph plots two points at (negative 7, 8) and (negative 2, negative 9) on the x y coordinate plane. A diagonal curve connects both points.


What is the range of the function shown on the graph above?
A.


B.


C.


D.

Answers

The range of the function shown on the graph below is equal to 0 ≤ y ≤ 7.

What is a range?

A range refers to the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range is the solution set on the y-axis.

How to determine the range?

Based on the graph of the two points, we can logically deduce the following information:

The least value on the y-axis is 0.The greatest value on the y-axis is 7.The endpoints on the y-axis are 0 and 7.

Therefore, the range of the function shown on the graph below is equal to 0 ≤ y ≤ 7.

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Absolute value of (-1, -3/7)

Answers

The absolute value of -1 is 1 and -3/7 is 3/7.

We have given that,

(-1, -3/7)

We have to determine the absolute value of (-1, -3/7)

What is the absolute value?

The absolute value or modulus of a real number x denoted |x|, is the non-negative value of x without regard to its sign. Namely, [tex]{\displaystyle |x|=x}[/tex]if x is a positive number, and [tex]{\displaystyle |x|=-x}[/tex] if x is negative, and[tex]{\displaystyle |0|=0}[/tex].

Therefore the absolute value of -1 is 1 and -3/7 is 3/7.

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work out the size of angle x

Answers

Answer:

x =83

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

x+43 = 126

Subtract 43 from each side

x = 126 -43

x =83

Let's take this problem step by step:

For the angle adjacent to the exterior angle of 126°:

  ⇒ exterior angle plus the that angle is equal to 180 degrees

      ⇒ since it is on a straight line

                 [tex]126 + that_.angle=180\\\rm \hookrightarrow that.angle=180-126\\\rm \hookrightarrow that.angle=54[/tex]

The sum of all the angles in a triangle is: 180°

                [tex]that.angle+43+x=180\\\rm \hookrightarrow 54+43+x=180\\\rm \hookrightarrow 97+x=180\\\rm \hookrightarrowx=83[/tex]

The size of angle x is 83°

Answer: 83°

Hope that helps!

#LearnwithBrainly

     

Please hurry

How could you solve this problem?
2 × 3 × 4
Check all that are true.

Multiply 3 × 4 to get 12 and then multiply 12 × 6.

Multiply 2 × 3 to get 6 and then multiply 6 × 12.

Multiply 3 × 4 to get 12 and then multiply 12 × 2.

Multiply 2 × 3 to get 6 and then multiply 6 × 4.

Multiply 2 × 3 to get 6, multiply 3 × 4 to get 12, and then multiply 6 × 12.

Answers

Answer:

multiply 2×3 to get 6and then multiply 6×4 to get 24

Answer:

Multiply 3 × 4 to get 12 and then multiply 12 × 2.

Multiply 2 × 3 to get 6 and then multiply 6 × 4.

Explanation:

Original Answer : 2 × 3 × 4 = 24

1) 12 × 6 = 72

2) 6 × 12 = 72

3) 12 × 2 = 24

4) 6 × 4 = 24

5) 6 × 12 = 72

Hence, only option 3 and 4 is correct.

What is the value of k?

Answers

Answer:

The value of K in free space is 9 × 109

Step-by-step explanation:

131 = 2k + 11
131-11 = 2k
120 = 2k
120/2 = 2k/2
k = 60

Which graph shows the solution to the system of linear inequalities? Edge.

x + 3y > 6

y ≥ 2x + 4

Answers

A system of inequalities can be solved graphically.

See attachment for the required graph

The inequalities are given as

[tex]x + 3y > 6\\y \geq 2x + 4[/tex]

The options are not given.

So, I have attached the graph that illustrates the solution to the system of inequalities.

What is the inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

From the graph, we have the solutions as

[tex]x > -0.857[/tex]

[tex]y\geq 2.276[/tex]

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Two circles are concentric if they have the same center.

On a coordinate plane, a circle has center (4, 6) and has a radius of 2 units.

Which equation represents a circle that is concentric with the circle shown but has a radius that is twice as large?

(x – 4)2 + (y – 6)2 = 4
(x – 4)2 + (y – 6)2 = 16
(x – 6)2 + (y – 4)2 = 16
(x – 6)2 + (y – 4)2 = 4

Answers

The equation of the circle is (x - 4)² + (y - 6)² = 16. The correct option is the second option (x - 4)² + (y - 6)² = 16

Equation of a circle

From the question, we are to determine the equation of the circle

The equation of circle is given by

(x - h)² + (y - k)² = r²

Where (h, k) is the center

and r is the radius

From the given information,

The two circles are concentric

∴ (h , k) = (4, 6)

But the other circle has a radius that is twice as large

∴ r = 2 × 2

r = 4

Thus,

The equation of the circle becomes

(x - 4)² + (y - 6)² = 4²

(x - 4)² + (y - 6)² = 16

Hence, the equation which represents a circle that is concentric with the circle shown but has a radius that is twice as large is (x - 4)² + (y - 6)² = 16. The correct option is the second option (x - 4)² + (y - 6)² = 16

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f (x) = √x + 9 what is the domain?

Answers

Answer:

Step-by-step explanation:

Hopes this helps:

Answer: x ≥ 0

Anything inside a square root must not be negative. The domain has to be x ≥ 0.

And if you have to graph it it has to start at 0 and go up to 9 and curve over.

When water flow in two Hoses. The first is four times the second's speed, what is the ratio of the radius of the first to the second?​

Answers

Answer:

4:1

Step-by-step explanation

this should be the answer from how  u gave the question, also can i get brainliest ;)

An oatmeal container has a volume of 269 cubic inches. If the radius of the container is 3 cm, which statement below describes how to calculate the height?

Answers

The height of the volume of the container is 93.898cm.

We have given that,

An oatmeal container has a volume of 269 cubic inches.

Volume=269 cubic inches.

Radius=3cm

What is the formula for volume?

[tex]V=\pi r^2h[/tex]

[tex]269=\pi (3)^2h\\\269=9\pi h\\\h=\frac{269\pi }{9}\h=93.89871[/tex]

The height of the volume of the container is 93.898cm.

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Which of the following are solutions to the equation below?
Check all that apply.
(3x - 5)^2 = 19

Answers

Answer:

To solve the answer, you can do it in 2 ways:

1) you could take the square root on both sides and solve for x

OR

2)you could multiply 3x-5 times itself and subtract 19 on both sides and use the grouping or quadratic formula method to find x.

Hope it helps.

Take the square root of each side of the equation to set up the solution for

Remove the perfect root factor

under the radical to solve

The complete solution is the result of both the positive and negative portions of the solution.

The result can be shown in multiple forms.

What is the asymptote of the following function: Y = e^x-x

Answers

Answer:

y = -x

Step-by-step explanation:

Breaking down the equation

[tex]y=e^x-x[/tex] can be written as [tex]y=e^x + (-x)[/tex], making it more clear that this function is composed of two functions:

An exponential function, and a linear function

asymptotes of the parts

The regular exponential function normally has an asymptote at y=0, a horizontal line because as "x" gets more and more negative, e^(x) gets closer and closer to zero (see blue graph).  This asymptotic behavior perhaps can be more easily understood by recognizing that [tex]e^{-x}[/tex] is equivalent to [tex]\dfrac{1}{e^x}[/tex], so that as the x values get more and more negative, it is effectively dividing 1 by a larger and larger number, thus getting closer and closer to zero.

In this situation, that exponential function is added to "-x", which is a linear function with a slope of negative 1.

As the left end of the exponential function gets closer and closer to zero, the exponential part contributes almost nothing to the sum, whereas as the "x" gets more and more negative, the linear function "-x" gets more and more positive (linearly).  Since the exponential piece adds almost nothing to it (when moving to the left), the combined function is essentially "-x" (although it is ever so slightly greater than it, just as it was ever so slightly greater than zero) (see pink graph, with dashed asymptote).

Clarifications

To be clear, on the right side of the graph, the exponential part of the function completely overwhelms the linear piece, and the function behaves much more like an exponential function, nearly completely masking the behavior of the linear piece.  Since an exponential function is unbounded, and the domain of both the exponential and linear functions are all real numbers, on the right side of the graph, there is no asymptotic behavior.

c) How long does he travel at 30 km/h, if he travels 1.2 h at 20 km/h?​

Answers

Answer:

1.8 hrs

Step-by-step explanation:

1.2 hr = 20 km/hr

A hr = 30 km/hr

(cross multiply)

30 x 1.2 = 20 x A

(30 x 1.2) / 20 = A

on simplifying...

1.8 = A

Therefore, it takes 1.8 hrs to travel 30 km/hr

[this is totally my method]

F(x)=-x^2+3 find(-2)

Answers

Answer:

F(-2) = 7

Step-by-step explanation:

 Finding a specific point on a function given the x position can be done by substituting x in the function for the given number, then solving said function. The value on the right side of the function is the y position.

For this specific function [F(x) = x² + 3], substitute x for -2.

F(-2) = (2)² + 3

Next, solve the equation.

F(-2) = 4 + 3

F(-2) = 7

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

Required answer: f(2) = -1

Detailed explanation:

To find f(-2), we will substitute -2 for x in the function:

[tex]\bf{f(x)=-x^2+3}[/tex]

[tex]\bf{f(-2)=-(-2)^2+3}[/tex]

[tex]\bf{f(-2)=-4+3}[/tex]

[tex]\bf{f(-2)=-1}[/tex]

[tex]\hrulefill[/tex]

Have a wonderful day!

In a spelling bee $50\%$ of the students were eliminated after the first round. Only $\frac{1}{3}$ of the remaining students were still in the contest after the second round. If 24 students were still in the contest after the second round, how many students began the contest

Answers

There were 144 students when the contest began

What is Equation ?

Equation is formed when an algebraic expression is equated by a constant or another algebraic expression.

On the basis of given data :

Let the total number of students are x

50% of the students are eliminated after the first round

the remaining students are 0.5x

After the second round = (1/3) * 0.5 x were remaining

and

(1/3) * 0.5 x = 24

then solving this equation will give the total number of students

0.5x = 24 * 3

x = 24*3 /0.5 = 144

Therefore there were 144 students when the contest began

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Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3


Help me please

Answers

Answer:

y-2=1/3(x-3)

Step-by-step explanation:

please mark me as brainlest

Answer: y-2=1/3(x-3), which is Choice [B]

Step-by-step explanation:

Hii, do you need to know the answer to your question? No problem! (:

First, do you remember what the "point-slope" formula is? It's

y-y1=m(x-x1)

Now it's just a matter of sticking in the known values.

y-2=1/3(x-3)

Voila! There's our solution, cheers! (:

--

Hope that this helped! Best wishes.

[tex]\bigstar\underbrace[/tex]

I'm just confused. I know we've learnt this before but I just forget. I'm doing one of the review sheets before our exam tomorrow. If you could help me out that would be great

Answers

Answer:

b. y= 4x-34.

Step-by-step explanation:

We can use the information in the problem to make an equation in slope-intercept form (y=mx+b).

Steepness typically means the slope of the graph, thus m=4.
This means we can automatically cross out "a" and "c", which leaves us with "b" and "d" as possible answers.

Next, I will plug in the given point (8, -2) into "b" and "d".
b. y=4x-34
-2=4(8)-34
-2=32-34

d. y=4x+34
-2=4(8)+34
-2 does not equal 66

Thus, the answer is b. y= 4x-34.

Ria left home at 13:00
She drove for 30 minutes at a constant speed of 40 mph.
She then stopped for a break.
Ria then drove to the hospital at a constant speed.
She was at the hospital for 30 minutes.
She then drove home at a constant speed of 32 mph.
Show that she does not arrive home before 16:30

Answers

Ria will not arrive before half past four because in total the activities that she did will take her at leat three hours and forty-five minutes.

How to know the time Rita spent in each activity/movement?

The time can be determined by using the graph. In the graph, the time is represented by small squares. Each of this squares will be equivalent to 15 minutes.

You can infer this because Rita first drove for 30 minutes and in the graph the line goes from 0 in the x axis to two squares to the right (30/2 = 15 minutes.)

How much time did Rita spent?First movement: 30 minutesBreak: 30 minutes (2 more squares)Drive to the hospital:  60 minutesTime at the hospital: 30 minutes Drive back home: 75 minutes(Total distance 40 miles/ 32 miles per hour = 1.25 hours)Total: 225 minutes or  3 hours and 45 minutes

If she started this activities at 13:00 so she will go back home at 4:45.

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Find the length of x. Assume the triangles are similar.

Answers

Triangles are similar and only differ in size meaning they are dilated

So first we have to find the scale factor of dilation (by how much the smaller triangle got bigger)

Find scale factor:

2.4a=4.8

z=2

Find x:

we multiply the original side of the small side with the scale factor of 2

2.8(2)=x

5.6=x

So, x=5.6

Please find x! These are probably simple! ASAP pls! 2 problems!
1) 3 + x + (-7) ; x = 6
2) x + (-5) + 5; x = -3
17 points:)

Answers

The numeric values of the given expressions are given as follows:

1) 2.

2) -3.

How to find the numeric value of an expression?

We find the numeric value of an expression replacing all instances of x by the number.

The expression 1 is:

3 + x + (-7) = 3 + x - 7 = x - 4.

When x = 6, the value is:

x - 4 = 6 - 4 = 2.

The expression 2 is:

x + (-5) + 5 = x - 5 + 5 = x.

Hence, when x = -3, the value is:

x = -3.

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Luckily, the framers of the Constitution had the foresight to build into it a means to rectify unjust situations by allowing for the addition of amendments, or additions, to the Constitution. Through amendments, women and free people of color were eventually guaranteed the right to vote.If voting is such a powerful tool, why is there such appalling voter turnout in many elections? People think their vote doesnt count or doesnt matter. Long lines of voters at the polls before sunrise are typical only of big elections, such as the election of a senator or representative to serve in the federal government or the election of a president for the country. But it is the off-year elections, those smaller elections for local and state offices, that should matter most. For the vast majority of the population, the local elections are the ones that touch their everyday lives. It is in these elections that people decide who runs the local school boards, who makes the rules and regulations governing behavior and activities in their locality, and who will judge the population in the local courts. There also may be issues on the ballot that will affect their daily lives that have nothing to do with who the candidate is, but actions will be taken (or not) that will affect them. When a candidate is elected, he or she feels a mandate has been given by the electorate to fulfill promises made to get into office.Who is voting? In some studies and polls, the most active voters are usually more educated and more involved with their communities. This electorate knows the issues and problems, and knows who can and cannot help make the communities better. They read more, listen to others opinions more, and make a decision based on the track record of the person running. They understand that voting is a learned activity, and they want to help those in their communities who do not understand the importance of voting to better understand the process. They get involved with the populace, teaching them the requirements for voting, such as finding the polling place, numbers to call for help, learning their voting optionssuch as early or electronic votingand teaching them the impact voting will have on the issues that they are concerned about.What are other benefits of voting? Some studies have shown that voting can have a psychological effect on the voter. Voters feel empowered because they embraced the electoral process. It gives the participant a sense of satisfaction, almost like saying, I made my voice heard today. I voted. Voting also benefits future generations when children see their parents and other responsible adults exercising their constitutional right to vote and be heard. Voting addresses the future needs of coming generations because the policies put into place by the elected officials will affect lives now and in the future. Low voter turnout in a country that guarantees every eligible citizen over the age of eighteen the right to vote is unacceptable. Every election you are eligible to vote in commands your participation. Make your voice heard. Dont hesitate. Vote! An imaginary element, Y, has two different isotopes.y has a percentage abundance of 25% and 29y has a percentage abundance of75%.Which of the following is the relative atomic mass of Y?26252728 You are a Junior IT Technician in your organisation. One of the duties is to demonstrate and explain how the computer works to new intern stuff. Discuss how you would demonstrate and explain? Why did the Aboriginals stop coming to North America? Which of the following is a slow rise of plastic deformation under the action of shear stresses when it is below the yield strength of the material.a.Brittle Structureb.Ductile fracturec.Creepd.Fatigue Most enlightened despots:A) were tried and executed.B) censored the ideas of the philosophers.C) showed interest in the ideas of the philosophers.D) successfully implemented most of the ideas of the philosophers. if n 18 = find n Need help simple explanation if possible What can be inferred about the Cyclops in this excerpt from Homers Odyssey? "The land of Cyclops first, a savage kind, Nor tamed by manners, nor by laws confined: Untaught to plant, to turn the glebe, and sow, They all their products to free nature owe: The soil, untill'd, a ready harvest yields, With wheat and barley wave the golden fields; Spontaneous wines from weighty clusters pour, And Jove descends in each prolific shower, By these no statues and no rights are known, No council held, no monarch fills the throne; But high on hills, or airy cliffs, they dwell, Or deep in caves whose entrance leads to hell. Each rules his race, his neighbour not his care, Heedless of others, to his own severe." A.The Cyclops is warm and hospitable toward his guests. B.The Cyclops cares for his neighbors well-being and advice. C.The Cyclops does not follow typical rules of the civilized human world. D.The Cyclops can survive only in the deep, dark caves on the island. If you vacillate, do you make immediate and decisive choices?Yes or No Mrs. Andrews asked how a Private Fee - for - Service ( PFFS ) plan might affect her access to services since she receives some assistance for her health care costs from the State . What should you tell her ?