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

Determine Weather Y Varies Directly With X. If So Find The Constant Of Variation And Write The Equation

Answers

Answer 1

This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality. The correct option is B.

What is the directly proportional and inversely proportional relationship?

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.


Since the graph of the equation is a line, therefore, it can be concluded that the relationship is linear as a result y varies directly with x.

Therefore we can write the relationship as,

y ∝ x

y = k x

The line goes through the point (-2,3), thus, substitute the points in the equation formed above,

3 = k × (-2)

k = -3/2

Now, substitute the value of k in the equation,

y = -(3/2)x

Hence, the correct option is B.

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Related Questions

Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible region. Click to set the corner points. 2 x + 4 y ≤ 36 7 x + 5 y ≤ 63 x ≥ 0 y ≥ 0 { 2x+4y ≤ 36 7x+5y ≤ 63 x ≥ 0 y ≥ 0

Answers

Feasible region for the given inequalities is shaded via black color in graph.

What is Inequalities?

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Here, given Inequalities are;

      2 x + 4 y ≤ 36

      7 x + 5 y ≤ 63

      x ≥ 0 y ≥ 0

The graph of given inequalities are given below and the feasible region is shaded with the black color.

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Urgent my safari wont work! 20 pts!!

What’s the square root of 32006???

Answers

178.902208 this is it

Find the equation of a line that is perpendicular to Y= 4X +5 that passes through (2,-5)

Answers

Answer:

4y +x =18

Step-by-step explanation:

y - (-5) -1

----------- = ------

x - 2 4

4y +20 = -x+2

4y +x =18

The price of 11 pizzas and 5 hamburgers is 40$. The price of 1
hamburger is 2.50$. What is the price of a hamburger?

Answers

Step-by-step explanation:

you mean, what is the price of a pizza, right ? and I guess it is pizza slices ...

1 hamburger = $2.50

5 hamburgers = 5×1 hamburger = 5×2.5 = $12.50

that leaves for the 11 pizzas (slices)

40 - 12.5 = $27.50

so, 1 pizza (slice) is

27.5 / 11 = $2.50

Answer:

One hamburger costs $2.50

One pizza also costs $2.50

Step-by-step explanation:

Let's say Nigel is the one purchasing lots of food for no reason.

Nigel bought 11 pizzas and 5 hamburgers for $40 (DAMMMM WHAT COUPON IS THAT??)

We can write this algebraically:

11p + 5b = 40

We know that the price of 1 Hamburger is $2.50.

Now we can plug that into out equation and find the price of one pizza:

11p + 5(2.50) = 40

11p + 12.5 = 40

11p = 27.5

p = 2.5

Now, we have the price of one pizza, $2.50

3.14(a2 + ab) when a = 4 and b = 3​

Answers

Step-by-step explanation:

how does the picture fit into this question ?

I guess you mean

(a² + ab)

when a = 4 and b = 3. then we simply replace the variable names by the actual values and calculate :

4² + 4×3 = 16 + 12 = 28

.

now to the picture :

i am not sure what the requested result of procedure is.

so, I am just going to simplify the expression :

(log(25) - log(4)) / (log(55) - 1/2 × log(2)

remember the rules of the logarithm :

log(a) - log(b) = log(a/b)

k × log(a) = log(a^k)

a^(1/2) = sqrt(a) (the square root of a)

I assume we are using the logarithm to the base of 10.

so, we have here

log(25/4) / log(55/sqrt(2)) =

= 0.795880017... / 1.589847692... = 0.500601423...

Select the correct answer. Consider functions h and k. Every x value has a relationship in k of x. What is the value of (h o k)(1)? A. 28 B. 4 C. 1 D. 0

Answers

Answer: 0

Step-by-step explanation:

[tex](h \circ k)(1)=h(k(1))=h(4)=\boxed{0}[/tex]


[15 PTS] PLS HELP!!!

What is the end behavior of the function?

Answers

The correct answer is the fourth option.

Lief starts saving for his future and deposits $425 each month at 5.7% annual interest, compounded monthly, for 25 years. At the end of 25 years, he has an account balance of $281,292.21. How much of this did Lief contribute and how much of this is interest?

Answers

Using proportions, it is found that the amounts are given as follows:

Amount deposited: $127,500.Amount of interest: $153,792.21.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The amount deposited is of $425 each month for 25 years, that is, $425 in 25 x 12 times, that is:

D = 425 x 25 x 12 = $127,500.

The amount of interest is the total amount subtracted by the amount deposited, hence:

I = 281,292.21 - 127,500 = $153,792.21.

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According to the graph, what is the factorization of x² - 5x+6?
OA. (x-3)(x+2)
OB. (x+3)(x-2)
OC. (x+3)(x+2)
OD. (x-3)(x-2)
y xẻ 5Xtộ

Answers

Answer:

OD.(x-3)(x-2)

Step-by-step explanation:

we need two numbers (negative ir positive) that multiply to get 6 abd add to get -5.

so its OD

as -3×-2=6

and -3+-2=-5

The temperature of a chemical reaction ranges between -10 degrees Celcius and 50 degrees Celcius. The temperature is at its lowest point when t=0, and the reaction completes 1 cycle during a 6 hour period. What is a cosine function that models this reaction?

Answers

Answer:

The cosine function is f(t) = -30sin(π÷3)t + 20

Step-by-step explanation:

Given : The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period.

To find : What is a cosine function that models this reaction?

General form of cosine function is f(x) = A cos(Bx)+C

Where A is the amplitude

B=2π÷Period

C is the midline    

Now, We have given

The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius.

A is the average of temperature,

i.e,

A=(-10-50)÷2 = -30

Period of 1 cycle is 6 hour

So,

B = 2π÷6 = π÷3

The temperature is at its lowest point when t = 0 and we know lowest point is -10

So,

f(t) = A cos t + C

-10 = -30 cos 0 + C

Therefore, C = 20

Substituting the values, we get

The cosine function is f(t) = -30sin(π÷3)t + 20

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PLEASE HELP!!!!

Which operation should you perform last in the expression 3^2 + 2?

Answers

Answer: the +2

Step-by-step explanation: PEMDAS. Exponents are before addition in the sequence. I hope this helps!

(The E standing for exponents and the A standing for addition)

The circle below is centered at the point (-1, 2) and has a radius of length 3.
What is its equation?
O A. (*+ 1)2 + (y- 2)2 = 9
O B. (x- 2)2 + (y + 1)? =
32
O c. (x- 1)2 + (y + 2)2 = 9
l
O D. (x+ 2)2 + (y- 1)2 =
32

Answers

Answer:

it should be option A

and in option there should be "x" instead of "*"

Equation of circle is,

⇒ (x + 1)² + (y - 2)² = 9

What is mean by Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The circle below is centered at the point (-1, 2) and has a radius of length 3.

Now, We get;

The equation of circle is,

⇒ (x - (- 1))² + (y- 2)² = 3²

⇒ (x + 1)² + (y - 2)² = 9

Thus, Equation of circle is,

⇒ (x + 1)² + (y - 2)² = 9

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Josh made $35,000 in taxable income last year.
Suppose the income tax rate is 15% for the first $8500 plus 17% for the amount over $8500.
How much must Josh pay in income tax for last year?

Answers

First you take 8500 and mutiply it by .15 to get 1275 take 8500-1275 to get 7225
Then take 26500 which you get from taking 8500 from 35000. Then you 26500 times .17 to get 4505 then 26500-4505 to get 21995 then for the total do 21995+7225=29220

Please hurry!!!! What is the domain of the function on the graph?
all real numbers
all real numbers greater than or equal to –2
all real numbers greater than or equal to –5
all real numbers greater than or equal to 0

Answers

A. all real numbers

the doman are the x values and in this equation they are infinite making the domain all real numbers

John is buying a new car. The value of one car he is considering is $20,000. The value of the car as it ages can be modeled by the function V = 20 , 000 ( 0 . 84 ) t , where t is the number of years from the time of purchase. One of the factors John is using to make his decision is the value of the car over time until it reaches half its original value. What values of domain are reasonable for the given function in this context?
A. all real numbers greater than or equal to 0 and less than 2.8
B. all real numbers greater than or equal to 10,000 and less than or equal to 20,000
C. all real numbers greater than or equal to 0
D. all real numbers greater than or equal to 0 and less than 4

Answers

Option D is the correct answer.

All real numbers greater than or equal to 0 and less than 4.

What is Domain?

The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined.

Here, The function of the car value is given as:

V(x) = 20000 X (0.84)ˣ

When the car reaches half its value, we have:

V(x) = 10000

Substitute V(x) = 10000 in V(x) = 20000 * (0.84)ˣ

10000 = 20000 X (0.84)ˣ

Divide both sides by 20000

0.84ˣ = 0.5

Take the logarithm of both sides

x log(0.84) = log(0.5)

Divide both sides by log(0.84)

           x = 4

This means that the maximum value of x is 4.

Thus, all real numbers greater than or equal to 0 and less than 4.

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Can you do this because it is confusing to me

Answers

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The volume of the cylinder is 1330.4644 cm³.

What is a cylinder?

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.

Given the height of the cylinder is 14 cm, while the diameter of the cylinder is 11 cm. Therefore, the volume of the cylinder can be written as,

The volume of the cylinder = (π/4)×(D²) × H

                                               = (π/4)×(11)² × 14

                                               = 1330.5 cm³

Hence, the volume of the cylinder is 1330.5cm³.

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In the equation y/6 = 156, what is the next step in the equation solving sequence

Answers

Answer:

Linear Equations In One Variable =

Next step :

in the equation y/6 = 156, it would be equivalent to y = 156 × 6.

so that :

y = 156 × 6

y = 936

this equation solved. (Answer : 936)

The Taieri Plain in New Zealand is 6 feet below sea level (or –6 feet). If you are standing 3 feet above sea level, is your elevation the opposite of the elevation of the plain? Describe the steps you would follow with a vertical number line to find the answer.

Answers

Answer :Opposite numbers are the same distance from 0 on the number line, but in opposite directions. Steps I would follow:

first, check the directions to make sure they are opposite,

then read the digits, or count the tick marks or compare lengths with dividers or ruler or marks on a piece of paper to see if the distances are the same.

3 is not the opposite of -6

__

6 is the opposite of -6

? Question
Select the graph of the transformation.
The graph f(x)=√√ is transformed to form
shows g(x).

Answers

Answer: The vertex of the graph of [tex]y=x^2[/tex] is shifted to the right 4 units and up 3 units.

Graph the feasible region subject to the following constraints:
7x+11y≤ 1540
x+3y ≤ 360
x+y≤ 200
x≥0
y≥0

Answers

The attached graph represents the graph of the constraints

How to graph the feasible region?

The constraints are given as:

7x+11y≤ 1540

x+3y ≤ 360

x+y≤ 200

x ≥ 0, y ≥ 0

Next, we plot the graph of the constraints using a graphing calculator

From the graph (see attachment), we have the coordinates of the feasible region to be (66, 98), (120,80) and (165,35)

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given the formula p=k*2 w, find the value of p if k= 5 and w= - 3

Answers

P=-75 step-by-step solved it

find the distance between the pair of points (7,6) and (4,10)​

Answers

Answer:

5 units

Step-by-step explanation:

to find out the answer for this you must first find the distance between 7 and 4 and then 6 and 10

then you would square them and then add them

lastly you would take the square root of that and youd have your answer

so

7 - 4 = 3

6 - 10 = -4 (just use 4)

3^2 + 4^2 = 9  + 16 = 25

then you take the square root of this

sqrt(25) = 5

that is your answer

To solve this problem, you will use the Distance Formula to find the distance between two coordinate points.

Set Up the Distance Formula

The Distance Formula is defined as follows:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

We must title our points by the standard coordinate naming system:

[tex](x_1, y_1) \ \text{and} \ (x_2, y_2)[/tex]

Therefore, our points can be labeled:

[tex]x_1 = 7[/tex][tex]y_1 = 6[/tex][tex]x_2 = 4[/tex][tex]y_2 = 10[/tex]

Substitute Known Values for Variables

Now, substitute the known values as the variables in the Distance Formula:

[tex]d=\sqrt{(4 - 7)^2 + (10 - 6)^2}[/tex]

You must know the BPEMDAS acronym, which stands for:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Simplify the expression using BPEMDAS:

[tex]d=\sqrt{(-3)^2 + (4)^2}[/tex]

Remember that when a number is raised to the 2nd power, it is the same thing as multiplying the number by itself:

[tex]-3\times-3 = 9[/tex]

[tex]4\times4=16[/tex]

Simplify further by removing the parentheses:

[tex]d=\sqrt{9+16}[/tex]

Compute the additive operation:

[tex]d=\sqrt{25}[/tex]

Simplify the Radicand

The number that is placed inside of a square root symbol (or a radical symbol) is referred to as the radicand.

In this situation, the radicand is 25.

To simplify the radicand, you may either use a calculator to compute the result, or you can determine which number raised to the 2nd power will result in a final answer of 25.

In this case, we can determine that 5² will result in a final answer of 25.

[tex]5^{2} = 25[/tex]

The final answer is 5 units.

What is 60 percent of 92?

1.53

5.52

15.3
O 55.2
49:03 mins pls help me with this

Answers

60 percent of 92 is 55.2

How to determine the percentage?

The statement is given as:

60 percent of 92

This means:

60% of 92

Express of as *

60% * 92

Evaluate the product

55.2

Hence, 60 percent of 92 is 55.2

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4. During a camping trip, a group went one-third of the total distance by boat, 10km by foot and One-sixth of it by riding horses. Find the total distance of the trip. Plss answer thiissss ​

Answers

Answer:

20 km

Step-by-step explanation:

So 1/3 = 2/6
2/6 = distance traveled by boat + 1/6 traveled by riding horses = 3/6 = 1/2

Meaning the 10 km by foot left is the other half

If BC is 1

CD is 2

DA is 3

AB is 4,

what is EF?

Answers

The length of the side EF will be 1 unit, approximately.

The complete figure is attached below.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The figure is given below.

The length of EF will be

EF = CF – CE

Then the value of CF will be

CF = BC × cos 30

CF = 2 × 0.866

CF = 1.732

Then the value of CE will be

CE = BC × cos 42

CE = 1 × 0.743

CE = 0.743

Then we have

EF = 1.732 – 0.743

EF = 0.989 ≈ 1

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Find the area of a 150° sector of a circle whose radius is 3.

Answers

Answer: [tex]\frac{15\pi}{4}[/tex]

Step-by-step explanation:

[tex]A=\pi(3^{2})\left(\frac{150}{360} \right)=\boxed{\frac{15\pi}{4}}[/tex]

Someone answer this, thank you!

Answers

Step-by-step explanation:

1) the equation of the line represented is

y=0.5x+3 (slope-interception form), the slope is 0.5, the intercept is 3.

x-2y+6=0 (common form);

2) x-intersection is at -6, y-intersection is at 3.

2. Ahmed has ¢15.25 and spent $7.50 at the
Total Shop. How much money does he have
left?

Answers

Answer:

D)¢ 8.75

Step-by-step explanation:

that is my answer please

A building has a height of 40 feet and a length of 20 feet. On a scale drawing of the building, the height is 20 centimeters. What is the length of the building on the scale drawing in centimeters?

Answers

Answer:

10 centimeters

Step-by-step explanation:

For the height:

40 ft / 20 cm = 2 ft / cm

With this ratio, we find the length as follows:

2 ft / cm = 20 ft / x cm

[tex]2 = \frac{20}{x} [/tex]

[tex]2x = 20[/tex]

[tex]x = 10[/tex]

Answer:

10 cm

Step-by-step explanation:

Look at the answer

graph the equation y+3=2(x+3)?

Answers

Answer:

  see attached

Step-by-step explanation:

You recognize the equation of the line as being given in point-slope form:

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

  y +3 = 2(x +3) . . . . . . given equation

This tells you the point is (h, k) = (-3, -3), and the slope is m = 2.

__

You can graph the equation by plotting the point (-3, -3) and drawing a line with a slope of 2. It will rise 2 units for each unit to the right.

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