determine weather y varies directly with x. if so find the constant of variation and write the equation

Answer:

The golden ratio is a proper term in the field of mathematics, but it finally covers more than the research in the field of mathematics. According to the current literature discussion, we can say that the discovery of the Golden ratio and how it evolved is still a mystery. But studies have shown that the Pythagorean school of ancient Greece in the 6th century BC studied the formation of regular 5-sided and regular 10-sided plots, leading modern mathematicians to conclude that the Pythagorean school had touched on and even mastered some of the rules of the golden ratio and also discovered irrational numbers. It focuses on the relationship from mathematics, to explore the principle of beauty and that beauty is harmony and proportion, according to the proportional relationship can form beautiful patterns, this is actually a digital proportional relations, the line is divided into two parts, a long and a short period of the ratio of the equal to the ratio of length to a long, their proportion is around 1.618:1, This mathematical principle is also embodied in the famous Frederikian sequence, in which everything in this proportion shows the harmony and balance of its internal relations.

In the 4th century BC, the Greek mathematician Eudoxus was the first to systematically study this problem and establish the theory of proportion. Around 300 BC, Euclid absorbed the research results of Eudoxus in writing The Elements of Geometry and further systematically discussed the Golden Section, which became the earliest treatise on the golden Section (i.e. the middle and the end ratio) [5].

After the Middle Ages, the golden ratio was shrouded in mystery. Italian mathematician Luca Pacioli called the middle and the end of the ratio sacred and wrote a book about it. The German astronomer Johannes Kepler called the divine ratio the Golden Ratio. Golden in the 19th century the name only gradually, and the evidence is that German mathematician Martin Ohm (English: Martin Ohm) wrote the second edition of the basic pure mathematics annotation wrote about the interpretation of the golden ratio: "people used to put any straight line along the way will be divided into two parts, the method of known as the golden mean". And in the ninth edition of the Encyclopaedia Britannica, published in 1875, Sully notes: "The interesting, experimental and strong idea put forward by Frederick... proclaimed the supposed superiority of the 'golden Section' in visual proportion." So the Golden Section was already popular. In the 20th century, American mathematician Mark Barr gave it the name Phi. The Golden Section has many interesting properties and has been widely used by humans to make it famous today. The most famous example is the golden ratio or 0.618 method in optimization, which is first proposed in 1953 by Jack Kiefer (English: Jack Kiefer), an American mathematician, and is promoted in China in 1970s.

Answer:

x= 0, y= -1

Step-by-step explanation:

To obtain the values of x and y from a system of equations, start by labelling the given equations.

8x +5y= -5 -----(1)

7x -3y= 3 -----(2)

Let's solve by elimination.

Here, I will be working to eliminate the y term. This is done by ensuring both equations have the same numerical value in the coefficient of y.

(1) ×3:

24x +15y= -15 -----(3)

(2) ×5:

35x -15y= 15 -----(4)

Add the two equations together since the coefficient of y has opposite signs.

(3) +(4):

24x +15y +35x -15y= -15 +15

59x= 0

Divide both sides by 59:

x= 0

Now, substitute the value of x into any equations to find the value of y.

Substitute x= 0 into (1):

8(0) +5y= -5

5y= -5

Divide both sides by 5:

y= -5 ÷5

y= -1

Additional:

For similar questions on system of equations, do check out the following!

Perpendicular lines have slopes that are negative reciprocals of each other, so since the slope of the given line is 1, the slope of the line we want to find is -1.

Substituting into point-slope form,

[tex]y+4=-1(x-5)\\\\y+4=-x+5\\\\\boxed{y=-x+1}[/tex]

Answer: 20

Step-by-step explanation:

f(-4) = -4² - (-4)

f(-4) = 16 + 4

f(-4) = 20

Step-by-step explanation:

first function, f(x) = 5x-3 goes with option B

2nd function, 4- 4x goes with option A

3rd function goes with option D

4th goes with option C

The balance in Yolanda's saving plan after 14 years is; $9,455.36

We want to find the balance in Yolanda's saving plan after 14 years.

For Yolanda;

PV = 0

PMT = 250

i% = 4%/12 = 0.33%

N = 14 yrs * 12 = 168

FV = ?

For Zach:

PV = 0

PMT = $3300

i% = 4%

N = 14 yrs

FV = ?

From online future value calculator, we have;

Yolanda FV = $9,455.36

Zach FV = $47,204.19

Read more about Future Value at; https://brainly.com/question/24703884

#SPJ1

Answer:

80

Step-by-step explanation:

when you do the math you get two answers, -90 and 80

we dont use -90 because -90 units cannot be manufactured

Answer:

Wht is the total matches they played?

Answer:

13, 19, 25.

Step-by-step explanation:

y=3x+10

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

x=1, y=3(1)+10=3+10=13

x=3, y=3(3)+10=9+10=19

x=5, y=3(5)+10=15+10=25

Answer:

Even though only 6% of students scored higher than Karl, we cannot know his personal score based on his percentile. He could have gotten a 62, as long as everyone else [94% of the class] got an even lower score.

So, we cannot know Karl's mark, we are only able to understand Karl's score in relation to the rest of the students in his law course.

Answer:

log12=log(2.2.3)

=log2+log2+log3

=0.30103+0.30103+0.47712

=0.60206+0.47712

=1.07918

In scientific Notation , After 10 years he will have in total 2 x 10 ³ pounds.

Scientific Notation is a way of writing very large or small quantities.

It is written in the form of  x 10ˣ

It is given that

The colony of bees has a single queen, hundreds of male drones and roughly 60,000 female worker bees.

The quantity of honey produced is 200 pounds.

After 10 years he will have in total

200 * 10 = 2000 pounds

In scientific Notation it will be written as

2 x 10 ³ pounds.

To know more about Scientific Notation

https://brainly.com/question/18073768

#SPJ1

The complete question is

"What is the value of this expression when c= -4 and d= 10?

1/4 (c^3+d²)

A.2

B.9

C.21

D.41"

The value of this expression when c = -4 and d = 10 will be option B 9.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

The given expression is

[tex]1/4 (c^3+d^2)\\\\1/4 ((-4)^3+(10)^2)\\\\1/4 ( -64 + 100)\\\\1/4 (36)\\\\9[/tex]

Hence, the value of this expression when c = -4 and d = 10 will be option B 9.

Learn more about an expression here:

https://brainly.com/question/1249625

#SPJ1

Answer:6

Step-by-step explanation:at first calculate (-3)^2=9

then 9+2=11

finally the answer is 11-5=6

Answer:

6

Step-by-step explanation:

Given Problem:

[tex]-5+(-3)^2+2[/tex]

Using the PEMDAS order of operation:

P - Parentheses

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

Thus, Solving in parentheses first.

[tex]-5+(-3)^2+2[/tex]

[tex](-3)^2=9[/tex]

[tex]-5+9+2=[/tex]

[tex]-5+11=[/tex]

[tex]6[/tex]

Hence, the answer to [tex]-5+(-3)^2+2=6[/tex]

RevyBreeze

using elimination method

2x + 3y = 6 -----(1)

-

x + 3y = 12-------(2)

———————

x = 12

substitute x as 12 into equation (1) or (2), let's choose equation (1)

2(12) + 3y = 6

24 + 3y = 6

collect like terms

3y = 6 - 24

3y = 18

divide both sides by 3 ( to make y the subject of formula )

3y = 18

— —

3 3

y = 6

therefore X = 12 and y = 6

Hope this helps eh

Good luck ✅.

Answer:

1050 max profit

Step-by-step explanation:

cow 5brr 30br 600 × 6 cows 570

sheep 2brr 20br 500 ×10 sheeps 480

sheep&cows = 1050 max profit

Answer:

It's 3

Step-by-step explanation:

if you go to desmos graphing calculator it'll help you get the solutions for these if you type it in every number and letter and for exponents type ^ its shift then type 6.

The coordinates of point F are 4 and negative 2.5. Option C is correct.

A Cartesian coordinate plane is a two-dimensional plane with infinite dimensions. On an endless 2d plane, any two-dimensional figure may be drawn. A location is assigned to each point on a Cartesian plane.

It is the perpendicular distance between that point and the horizontal and vertical axes, which are commonly referred to as the x-axis and y-axis.

The location is then written as (a,b), where 'a' is the point's shortest distance from the y-axis, 'b' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x-axis.

'c' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x.

The coordinates of point F are 4 and negative 2.5.

Hence, the Option C is correct.

To learn more about the Cartesian plane refer;

https://brainly.com/question/27538987

#SPJ1

The value of the height of the prism is 8.68 inches

The surface area is the sum of the area of the faces.

The formula for calculating the surface area of the pyramid is;

TSA  = [tex]a^2+2a\sqrt{\frac{a^2}{4} + h^2}[/tex]

where

a is the side length. = 7in

h is the height

Substitute

[tex]189=7^2+2(7)\sqrt{\frac{7^2}{2} + h^2} \\189=49+14\sqrt{\frac{49}{2} + h^2}\\140=14\sqrt{\frac{49}{2} + h^2}\\10=\sqrt{\frac{49}{2} + h^2}\\[/tex]

Square both sides to have

100 = 49/2 + h²

h² = 100 - 49/2

h² = 151/2

h² = 75.5

h = 8.68in

Hence the value of the height of the prism is 8.68 inches

Learn more on surface area here; https://brainly.com/question/1297098

#SPJ1

Answer:

the second option listed

(A = 53 degrees)

(a = 13.3)

(c = 16.6)

Step-by-step explanation:

SOH CAH TOA

(sin = opposite / hypotenuse)

(cos = adjacent / hypotenuse)

(tan = opposite / adjacent)

For this question, you are provided an angle (37), and its opposite (10)

so, we can solve for either sin or tan first.

tan = opposite / adjacent

tan 37 = 0.7535540501

0.7535540501 = 10/a  [multiply by a]

0.7535540501a = 10 [divide by [0.7535540501]

a = 13.2704482163

rounded to the nearest tenth, a = 13.3

we know that the three angles shown here must add up to 180

so,

90 + 37 + A = 180

127 + A = 180

- 127           - 127

A = 53

--this is enough information to answer, but I will also solve side c to prove my answer

c = hypotenuse

a²+ b²=c²

[13.3]² + [10]² = c²

176.89 + 100 = c²

276.89 = c²

√276.89 = √c²

16.6400120192 = c

c = 16.6 (rounded to the nearest tenth)

**I am assuming this is a right triangle, otherwise there wouldn't be a matching answer

[tex] \sqrt{72} + \sqrt{162} \\ \\ \sqrt{2 \times 2 \times 2 \times 3 \times 3} + \sqrt{2 \times 3 \times 3 \times 3 \times 3} \\ \\ 2 \times 3 \sqrt{2} + 3 \times 3 \sqrt{2} \\ \\ 6 \sqrt{2} + 9 \sqrt{2} \\ \\ (6 + 9) \sqrt{2} \\ \\ 15\times1.4 \\ \\ 21[/tex]

[tex] \sqrt{50} - \sqrt{8} \\ \\ \sqrt{2 \times 5 \times 5} - \sqrt{2 \times 2 \times 2} \\ \\ 5 \sqrt{2} - 2\sqrt{2} \\ \\ (5 - 2) \sqrt{2} \\ \\ 3 \sqrt{2} \\ \\ 1.7 \times 2 \\ \\ 3.4[/tex]

[tex]2 \sqrt{28} + \sqrt{28} \\ \\ 2 \sqrt{2 \times 7 \times 7} + \sqrt{2 \times 7 \times 7} \\ \\ 2 \times 7 \sqrt{2} + 7 \sqrt{2} \\ \\ 14 \sqrt{2} + 7 \sqrt{2} \\ \\ (14 + 7) \sqrt{2} \\ \\ 21 \times 1.4 \\ \\ 29.4[/tex]

Answer: 13/69

Step-by-step explanation:

13 students are female and got a B out of a total of 69 students, so the probability is 13/69

Answer:

f(x) = x(x - 4)(x + 3)

Step-by-step explanation:

given f(x) with zeros x = a and x = b then the corresponding factors are

(x - a) and (x - b)

f(x) is then the product of these factors

Given zeros are x = 4, x = 0, x = - 3 then the factors are

(x - 4) , (x - 0), (x - (- 3)) , that is

(x - 4) , x , (x + 3)

f(x) = x(x - 4)(x + 3)

The sum of the function will be (r – s)(x) = –2x² + x – 3, The difference of the function will be (r – s)(x) = –2x² + x – 3, and The product of the function will be (r × s)(x) = 2x³ – 6x².

The complete question is attached below.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The functions are given below.

r(x) = x – 3

s(x) = 2x²

The sum of the function will be

(r + s)(x) = x – 3 + 2x²

(r + s)(x) = 2x² + x – 3

The difference of the function will be

(r – s)(x) = (x – 3) – 2x²

(r – s)(x) = –2x² + x – 3

The product of the function will be

(r × s)(x) = (x – 3) (2x²)

(r × s)(x) = 2x³ – 6x²

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

Answer: 98.5

Step-by-step explanation:

There were 942 people in total, 928 of which recognized Exxon.

So, the probability is 928/942, which is about 98.5%

The probability of random consumers knowing of exon will be 98.5%.

Probability helps us to know the chances of an event occurring.

[tex]P =\dfrac{Desired \ Outcomes}{Possible outcomes}[/tex]

Given that:-

The probability will be calculated as:-

Total consumers are 942 out of which 928 knew exon and 14 did not.

P = 928 / 942

P = 0.985

P = 98.5%

Therefore the probability of random consumers knowing of exon will be 98.5%.

Learn more about Probability:

brainly.com/question/795909

#SPJ1

The value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

We have (−5, 3) be a point on the terminal side of θ.

Perpendicular = -5

Base = 3

From Pythagoras' theorem:

Hypotenuse² =  (3)² + (-5)²

Hypotenuse = √34

cosθ = 3/√34

cscθ = -√34/5

tanθ = -5/3

Thus, the value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.

Learn more about Pythagoras' theorem here:

https://brainly.com/question/21511305

#SPJ1

The blue graph shows a upward translation by 4 units and horizontal translation by 3 units to have the equation h(x) = -1/2(x -3)² + 4

The given graph is a quadratic graph. Given the function of the blue parabola expressed as:

f(x) = -1/2x²

The blue graph shows a upward translation by 4 units and horizontal translation by 3 units to have the equation

h(x) = -1/2(x -3)² + 4

Note that the upward translation will be positive while the horizontal shift to the right will be negative

Learn more on translation here: https://brainly.com/question/12861087

#SPJ1

Parent function

Now look the transformations

x is changed and shifted 6 units right

Then

Horizontally Streched with a factor of 5

Answer:

B)  The graph of k(x) is vertically stretched by a factor of 5 and shifted 6 units right.

Step-by-step explanation:

Translations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

Given functions:

[tex]f(x) = x^2[/tex]

[tex]k(x) = 5(x - 6)^2[/tex]

Parent function:  [tex]f(x) = x^2[/tex]

Translated 6 units right:  [tex]f(x-6)=(x-6)^2[/tex]

Then stretched vertically by a factor of 5:   [tex]5f(x-6)=5(x-6)^2[/tex]

[tex]\implies 5f(x-6)=5(x-6)^2=k(x)[/tex]

Therefore, the graph of k(x) is vertically stretched by a factor of 5 and shifted 6 units right.

Learn more about translations here:

https://brainly.com/question/27845947