what is the approximate side length of a square game board with an area of 162 in^2?

Using proportions, the solution for the golden section is given as follows:

|AC|/|AB| = 1.6181.

A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.

Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.

For this problem, the segment lengths are given as follows:

The following proportion is true for the segment:

|AC|/|AB| = |AB|/|BC|

Hence:

1/x = x/1 - x.

x² = 1 - x

x² + x - 1 = 0.

Which is a quadratic equation with solution x = 0.618.

Then the solution for the golden section is given as follows:

|AC|/|AB| = 1/x = 1/0.618 = 1.6181.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

  (1 +√5)/2 ≈ 1.618034

Step-by-step explanation:

Given point B on segment AC, you want the "golden proportion" ratio AC/AB, such that AC/AB = AB/BC. A diagram is shown with A=0, B=x, C=1.

We can solve for the golden proportion directly by redefining points on the line segment as ...

Then we have AB = 1, AC = r, BC = r-1 and the proportion of interest is ...

  AC/AB = AB/BC

  r/1 = 1/(r -1)

Cross-multiplying gives ...

  r² -r = 1

Completing the square, we have ...

  r² -r + 1/4 = 5/4

  (r -1/2)² = 5/4

Taking the square root gives ...

  r - 1/2 = 1/2√5

  r = 1/2 + 1/2√5 = (1 +√5)/2 ≈ 1.618034

The golden ratio is (1+√5)/2 ≈ 1.618034.

__

Additional comment

This ratio appears many places in math, science, and nature. It is commonly given the name Φ or φ (phi). For example, it is the limiting value of the ratio of successive terms of the Fibonacci sequence, and is deeply embedded in the quantum description of the universe.

Diffusion is the principle that the statistical analysis of plaintext and ciphertext results in a form of dispersion rendering one structurally independent of the other.

In a simple language, whenever there is a change in one character of the plaintext there is a multiple changes in the ciphertext. The changes do not reveal the information as the structure of plaintext.

What is ciphertext?

Whenever the encrypted text changes from plaintext to encrypted algorithm then it is known as the ciphertext. It cannot be read until it is decrypted with the help of the key. And the decryption cipher algorithm changes ciphertext to plaintext text to make it readable.

To learn more about the ciphertext from the given link:

https://brainly.com/question/9380417

#SPJ4

Answer:

this is geometric, you are multiplying by 1/5.

Step-by-step explanation:

The attached below is the graph and the three points to solve the equation is (0,1) , (1,5/2) and (-1,-1/2)

According to the question the equation that we have been given is

              -3x + 2y = 2

We need to graph the linear equation. For this we will first put different values of x in the above equation and then find the values of y which will be the coordinates of the graph.

First put x = 0

                  -3(0) + 2y = 2

                         2y = 2

                          y = 1

hence the first coordinate is (0,1)

Similarly put,     x = 1

                       -3(1) + 2y = 2

                           2y = 5

                             y = 5/2

            when x= -1 then y = -1/2

Thus the three point or coordinates are (0,1) , (1,5/2) and (-1,-1/2) and below is the graph.

Learn more about graph here : https://brainly.com/question/25020119

#SPJ9

The rate of change of the area of circle with respect to radius is: 8π.

The rate at which one quantity changes in relation to another quantity is known as the rate of change of a function.

Now,

Area of a circle having radius (=r) is given by: A = πr²

The rate of change of area of the circle will then be given by:

[tex]\frac{dA}{dr}=\pi \frac{d}{dr}(r^{2})=2\pi(r)[/tex]​

For r = 4, [tex]\frac{dA}{dr}=2\pi(4)=8\pi[/tex]

Hence, the rate of change of area of the circle when the radius is 8π.

To learn more about the rate of change of a function, refer to the link: https://brainly.com/question/25184007

#SPJ4

The distance between the two points in the simplest radical form is √61

From the question, we are to determine the distance between the two marked points

The marked points are (-8, 6) and (-3, 0)

The distance, d, between two points can be calculated by using the formula,

d = √((x₂ - x₁)² + (y₂ - y₁)²)

x₁ = -8

x₂ = -3

y₁ = 6

y₂ = 0

Thus,

The distance, d, between the points is

d = √((-3 - -8)² + (0 - 6)²)

d = √((-3 + 8)² + ( -6)²)

d = √((5)² + 36)

d = √(25 + 36)

d = √61

Hence, the distance between the two points in the simplest radical form is √61

Learn more on Distance between two points here: https://brainly.com/question/17273444

#SPJ1

By using athematic operations, we get the cost of the company A's 3000 copies is greater than that of the other two.

What are arithmetic operations?

The arithmetic operator is used to carry out mathematical operations on the specified operands, including addition, subtraction, multiplication, division, and modulus. A few examples of arithmetic operators are as follows: 5 + 3 = 8, 5 - 3 = 2, 2 * 4 = 8, etc.

Given that:

Copier rentals from company A cost $90 per month + 6 cents every copy and

Copier rentals from company A cost $180 per month + 3 cents every copy

Let the number of copies be x

Total rents for a month of Company A [tex]= 90+0.06x[/tex]

Total copiers rents for a month of  Company B [tex]= 180+0.03x[/tex]

Total rents for a month of Company A = Total copiers rents for a month of  Company B

⇒[tex]90+0.06x= 180+0.03x[/tex]

Taking unknown value left side

[tex]0.06x-0.03x=180-90\\0.03x=90\\x=\frac{90}{0.03} \\x=3000[/tex]

Therefore, by using athematic operations , we get the cost of the company A's 3000 copies is greater than that of the other two.

To learn more about arithmetic operation from given link

https://brainly.com/question/4721701

#SPJ9

Answer:

B, C, A

Step-by-step explanation:

B, C, A

Answer:

¼ per month or 2 books in 2½ months

Mariam read 4 books in 5 months, resulting in a rate of reading of 4/5 books per month.

Use the concept of fraction defined as:

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.

Given that,

Mariam read 4 books

She read the books in 5 months

We need to find her rate of reading, in books per month

To find the rate of reading,

Divide the number of books read by the number of months it took to read them.

In this case, Mariam read 4 books in 5 months.

So, the rate of reading would be 4 books divided by 5 months.

Simplifying this fraction, we have 4/5,

Hence, Mariam's rate of reading is 4/5 books per month.

To learn more about fractions visit:

https://brainly.com/question/5454147

#SPJ3

Answer:

(8,4)

Step-by-step explanation:

The rule is (x,y) becomes (-y,x)

Answer:

Step-by-step explanation:

A direct object is the object in which the verb is acting on. For example, in the sentence “He sold his car,” “car” is a direct object. An indirect object is the recipient of the direct object, as in “The man gave his wife a necklace.” “Necklace” is the direct object, and “wife” is the indirect object

When we rotate a  Parallelogram PQRS of 90 degrees clockwise about the origin, each point of the given figure has to be changed from (x, y) to (y, -x) and graph the rotated figure.

P(x₁, y₁) ⇒ P'(y₁ , -x₁ )

Q(x₂, y₂) ⇒ Q'(y₂ , -x₂ )

R(x₃, y₃) ⇒ R'(y₃ , -x₃ )

S(x₄, y₄) ⇒ S'(y₄ , -x₄ )

The Greek word "parallelogrammon," which means "bounded by parallel lines," is the source of the English word "parallelogram." Thus, a quadrilateral with parallel lines as its borders is referred to as a parallelogram. The opposing sides of this form are parallel and equal. Each of the three primary varieties of parallelograms—square, rectangle, and rhombus—has distinct characteristics.

A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but it must have opposing sides that are parallel for it to be a parallelogram. If the opposing sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both sets of opposite sides are parallel and equal is referred to as a parallelogram.

To learn more about this visit parallelogram , https://brainly.com/question/1563728

#SPJ9

Answer:

-14

Step-by-step explanation:

If u put x+5y into -2(-x+5y)

Add all that up

-2(x+5y) =(-2) (7) = -14

465 is the cost of the cash price will she pay overall for the car.

What is cost ?

25 % of cash price 4500 ×  25%  = 1125

12 monthly    320 ×  12  = 3840

All 1125 + 3840  =  4965

more than  4965  -  4500  = 465

Learn more about cost

brainly.com/question/15135554

#SPJ9

The magnitude of his displacement is 77.221952836296 m

In this question,

A baseball player hits a triple and ends up on third base.

A baseball "diamond" is a square, each side of length 25.740650945432 m, with home plate and the three bases on the four corners.

We need find the the magnitude of his displacement.

The magnitude of his displacement is the distance from home plate to the third base.

the distance from home plate to the third base is

= 3 × 25.740650945432

= 77.221952836296 m

Therefore, the magnitude of his displacement is 77.221952836296 m

Learn more about the displacement here:

https://brainly.com/question/4801377

#SPJ4

Answer:

correct

3x4=12

Step-by-step explanation:

Answer:

(see attached file)

vertex: (-4, 23)

axis of symmetry: x = -4

Step-by-step explanation:

The axis of symmetry always passes through the vertex of the parabola. The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

(i'm not the best at explaining things, but khan academy has some amazing math resources if you want to check it out)

Answer:

Step-b 4.55 g/cmy-step explanation:

Answer:

the answer is 8/21

Step-by-step explanation:

to be sure that it's right 21 can't be divided by 8 and the two numbers don't have an LCD ( Least Common Denominator )

Answer:

Draw the figure that illustrates what is to be proved. ...

List the given statements, and then list the conclusion to be proved. ...

Mark the figure according to what you can deduce about it from the information given. ...

Write the steps down carefully, without skipping even the simplest one.

Step-by-step explanation:

Step-by-step explanation:

2)4(5x+6)

3)a)its 4x not 16x because 2x+ 6x is 8x and 8x-4x=4x

b)2x+6x-4x=15+12-3

4x=24

x=24/4=6

that's all I can answer

==============================================

Work Shown:

JK + KL = JL

(3x-4) + (5x+6) = 9x-8

(3x+5x) + (-4+6) = 9x-8

8x+2 = 9x-8

8x-9x = -8-2

-x = -10

x = 10

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

Check:

JK + KL = 26 + 56 = 82 = JL

Therefore, the answer is confirmed.

I’m not sure but I think it’s 8 in.; 50.27 in.

The magnitude of the resultant velocity of the soccer ball is 10 m/s .

Let the horizontal component of velocity be [tex]V_{x}[/tex] and the vertical component  of velocity be [tex]V_{y}[/tex].

The magnitude of the resultant velocity will be represented by V.

So, we can write

The horizontal component of velocity = [tex]V_{x}[/tex] = 8 m/s

The vertical component  of velocity = [tex]V_{y}[/tex] = 6 m/s

The relation between horizontal component, vertical component and resultant velocity is,

[tex]V^{2} = V_{x} ^{2} + V_{y} ^{2}[/tex]

On substituting value of horizontal component and vertical component, we get

[tex]V^{2}[/tex] = [tex](8)^{2} + (6)^{2}[/tex]

[tex]V^{2}[/tex] = 64 + 36

[tex]V^{2}[/tex] = 100

V = [tex]\sqrt{100}[/tex]

V = 10 m/s

The magnitude of the resultant velocity of the soccer ball is 10 m/s .

To know more about Velocity refer to the link:

https://brainly.com/question/28552266

#SPJ4

Answer:

it reflects over the y axis

Step-by-step explanation:

why does it keep talking it down if its right

Answer:

many solutions

Step-by-step explanation:

15=15

Answer:

10. 4x

11. r - 7

Step-by-step explanation:

10.

"a number" refers to any number. Since we don't know the specific number, we use x, a variable, to represent "a number." Then we multiply x by 4.

Answer: 4x

11.

When you decrease a number by 7, you are subtracting 7 from that number.

Answer: r - 7

Answer:

n=4

Step-by-step explanation:

12n/12 = 48/12 the n=4

n = 60

n=36

n=4

n=1/4

Different starting lineups can be created - 120+60+120=300. A certain college team has on its roster 4 centers, 5 guards, 5 forwards, and one individual (x) who can play either guard or forward.

1. A lineup without x is an example. You must decide.

It can be made as -

2C5 × 2C3× 1C4 = 10× 3×4 = 120 ways

2. Consider starting lineups with guard x. You must decide.

1C5×2C3×1C4 = 5×3×4 = 60 ways

3. Think about lineups where x is the forward. You must decide.

2C5×1C3×1C4 = 10×3×4 = 120 ways.

Therefore, total number different lineups is - 120+60+120=300.

To learn more about combinations from given link

https://brainly.com/question/8781187

#SPJ4

The correct option is option A , such that inequality is x - 3y < 5.

What are the inequalities ?

Inequalities are the expressions in which both sides are not equal and the equal sign in between is replaced by less than , greater than, etc.

We know that the slope intercept form of equation is given by y = mx + c , where m is the slope and c is the y - intercept.

In the graph , the upward sloping line has x and y intercepts of 5 and -3.

So its equation in slope intercept form is given by ,

- 3y = - x + 5

And the inequality with that boundary line is given by ,

- 3y < - x + 5

or

x - 3y < 5

Therefore , the inequality represented by graph is x - 3y < 5 or option A is correct.

Learn more about inequalities here :

https://brainly.com/question/8921818

#SPJ1