how do I determine whether each linear relationship is a direct variation and if so how do I state the constant of proportionality.
Pictures, x 3
Profit, y 24

Expression -4/-9 equals fraction numerator 9 minus 4 in math.

Fraction definition:

It has two negative numbers, hence the result will be the same because of the rule, which is why it is equivalent (minus times minus is equal to zero)

4/9= -4/-9

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The range of the function is {-11, -9, -7, -5}.

The given function is g(x)=x−13.

We need to find the range of g(x).

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Now, put x=2,4,6,8 in the given function and find the range of function.

So, g(2)=2−13=-11

g(4)=4−13=-9

g(6)=6−13=-7

g(8)=8−13=-5

Therefore, the range of the function is {-11, -9, -7, -5}.

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The quadratic function is defined as follows:

- 2 / 3 x² + 7 / 3 x + 8

The quadratic function has the following sets of values below:

(0,8) (2,10) (3,1).

The quadratic function is represented as follows:

f(x) = ax² + bx + c

using  (0,8)

8 = a(0)² + b(0) + c

8 = c

Therefore, using (2, 10)(3 , 1).

f(x) = ax² + bx + c

10 = a(2)² + b(2) + 8

10 - 8 = 4a + 2b

2 = 4a + 2b

1 = 2a + b

1 = a(3)² + b(3) + 8

1 = 9a + 3b

Hence, combine the equations,

2a + b = 1

9a + 3b = 1

multiply equation(i) by 3

6a + 3b = 3

9a + 3b = 1

3a = - 2

a = - 2 / 3

Therefore,

9a + 3b = 1

9(- 2  / 3) + 3b = 1

-6 + 3b = 1

3b = 7

b = 7 / 3

Therefore, the quadratic function is defined as follows:

- 2 / 3 x² + 7 / 3 x + 8

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Answer:

y=

Step-by-step explanation:

1. The value of x is 14°

2. The value of x is 23°

3. The value of x is 22.5°

From the question, we are to determine the value of x in the given diagrams.

1.

∠ CBA = 180° - 6x (Linear pair theorem)

and

m ∠BAC + m ∠CBA = m ∠FCB (Exterior angle theorem)

Thus,

2x + 180° - 6x = 124°

180° - 4x = 124°

180° - 124° = 4x

56° = 4x

x = 56/4

x = 14°

Hence, the value of x is 14°

2.

m ∠ABE = 4x (Alternate angles theorem)

m ∠ABD + m ∠ABE + m ∠EBF = 180° (Sum of angles on a straight line)

x + 4x + 65° = 180°

x + 4x = 180° - 65°

5x = 115°

x = 115°/5

x = 23°

Hence, the value of x is 23°

3.

m ∠EAB = 2x (Vertical angles theorem)

m ∠AEB = 180° - 4x (Linear pair theorem)

m ∠ABE = 180° - 6x (Linear pair theorem)

m ∠EAB + m ∠AEB + m ∠ABE = 180° (Sum of angles in a triangle)

Thus,

2x + 180° - 4x + 180° - 6x = 180°

180° + 180° - 180° = 6x + 4x -2x

180° = 8x

x = 180°/8

x = 22.5°

Hence, the value of x is 22.5°

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The equation which describe the relationship between the profit, y, and the number of candles sold, x is x - y = 3.

Given that:-

When 10 candles are sold, the store makes a profit of $7.

When 15 candles are sold, the store makes a profit of $12.

When 20 candles are sold, the store makes a profit of $17.

We have to write an equation which describe the relationship between the profit, y, and the number of candles sold, x.

As we can observe from the given data,

number of candles sold - 3 = profit (in $)

Hence, we can write,

x - 3 = y

x - y = 3.

Where,

x represents the number of candles sold and,

y represents the profit

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The technique researchers use to reduce the impact of confounding variables is randomization.

Confounding variables are variables that affects or influences both the dependent and independent variable.

Some techniques used to reduce this influence are;

The most effective way of reducing the impact of confounding variables is the conduction of random trials.

Thus, the technique researchers use to reduce the impact of confounding variables is randomization.

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The number 78.263 using ones, tenths, and thousandths means

This is the value of each digits based on its position in a number.

It is divided into whole number part and fractional part.

Whole number part:

Fractional part:

78.263

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The formula for calculating Alex's earnings from his employment at the theme park is 8(40 x 9 + 100) = 8(360 + 100) = 8(460) = $3,680.

Given: that the plane ticket costs $2,200 and that y = 11.5x gives the function that represents the potential earnings Alex may make from the tech internship, the inequality that reflects the maximum number of hours Alex can work at the internship follows.

He puts in 20 hours every week at the internship, which translates to 160 hours of work over the course of 8 weeks.

Given that the internship pays $11.5 an hour for 160 hours, her earnings of 11.5 x 160 = $1,840 will not be sufficient to cover the cost of the plane ticket.

A few of the theme park employment that are available in this sector include costume character work, ride technician, admissions attendant, lifeguard, and gaming attendant. Workers at concession stands must be swift to prevent long queues and receive cash for food and drinks.

Hence, Alex's employment at the internship will not generate enough income to pay for the ticket.

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To spray on 2 lawns is required [tex]3\frac{1}{9}[/tex]  gallons.

Mixed fraction A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given ;

  A container with [tex]3\frac{1}{2}[/tex] gallons of weed killer can spray =  [tex]2\frac{1}{4}[/tex] lawans

∵ in [tex]\frac{9}{4}[/tex] lawn the week killer can spray =  [tex]\frac{7}{2}[/tex]gallons

∴ in 1 lawn the weed killer is  used = [tex]\frac{7}{2}[/tex] × [tex]\frac{4}{9}[/tex] gallon

∴ in 2 lawns the weed killer can spray =[tex]\frac{7}{2}[/tex]  ×  [tex]\frac{4}{9}[/tex]× 2 =[tex]\frac{28}{9}[/tex]  gallon =[tex]3\frac{1}{9}[/tex]gallons

  [tex]3\frac{1}{9}[/tex] gallons require to spray 2 lawns.

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Answer: 1/2

Step-by-step explanation: 2/4 = 0.5

1/2 = 0.5

Answer:

1) [tex]\frac{51}{2}[/tex]    2) [tex]\frac{55}{12}[/tex]

Step-by-step explanation:

Answer:  I simplify the answer for u my friened 25.5

Solutions of given exponents are :

1.  [tex]9^{18}[/tex]   2. [tex]16x^4[/tex]   3.  [tex]\frac{6561}{y^2}[/tex]

In, mathematics a exponent or exponential equation or exponential function is inverse of a logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The shows the behavior of something to the power of something. The basic form of the exponential can be written as [tex]a^x[/tex]

where, a = the base of function

            x = exponential

Important properties of exponential :

According to the question,

1. given, [tex](9^{3})^6[/tex]

  use the property, [tex](a^n)^m = a^{nm}[/tex]

   [tex](9^{3})^6[/tex] = [tex]9^{3.6} = 9^{18}[/tex]

2. Given, [tex](2x)^4[/tex]

   use the property, [tex](ab)^n = a^n.b^n[/tex]

    [tex](2x)^4[/tex] = [tex]2^4.x^4 = 16x^4[/tex]

3. Given , [tex](\frac{3^4}{y}) ^{2}[/tex]

    use the property, [tex](\frac{a}{b})^n = \frac{a^n}{b^n}[/tex]

     [tex](\frac{3^4}{y}) ^{2}[/tex] = [tex]\frac{(3^4)^2}{y^2}[/tex]

    now use ,  [tex](a^n)^m = a^{nm}[/tex]

     = [tex]\frac{3^8}{y^2} = \frac{6561}{y^2}[/tex]

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Answer:

Median

Step-by-step explanation:

Median: (16+17)/2= 16.5

Mean: 11+13+15+15+16+17+18+19+19+20= 163

163/10= 16.3

Median is greater.

The equation which correctly models the decreasing supply of helium as described in the task content is; y = 35 - 0.21x.

It follows from the task content that the equation which correctly models the decreasing supply of helium according to the description is to be determined.

Let, y = amount of helium remaining.

Let x = no of years since 2018.

First, one must convert 210 million to billion cubic feets as follows;

210 million = (210/1000) billion.

= 0.21 billion cubic meters per year.

The number above represents the rate of change of the linear model, otherwise termed the slope.

On this note, since the starting deposit of helium in 2018 was; 35 billion.

This insinuates that the y-coordinate of the y-intercept of the required model is; 35.

Hence, the required decreasing Linear model for the supply of helium is;

y = 35 - 0.21x.

The equation above follows from the slope-intercept form of a linear equation.

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Answer: 6 hours

Step-by-step explanation: 6 apartments divided by 2 is 3 apartments and 4 hours divided by 2 is 2 hours. 3 apartments per 2 hours. So, 3/2 x 3/3 is 9/6 which is 9 apartments for 6 hours.

hi

A = 6x^(2)+4x+3*y + 6y + y^(2)

A= 6x²+y²+4x+9y

The factors of the equation is  (x - 5)  (x + 2).

Given the equation is x²-3x-10

we are asked to factorize the equation.

Factorization is the process of identifying two or more expressions whose product is an algebraic expression. It is often referred to as finding the factors of an expression. Finding two or more expressions whose product is the given expression—known as factorization—is the process of breaking down algebraic expressions. A factor is any number that divides the given number by itself without leaving any remainder. It simply implies representing a number as the product of two other integers.

x²-3x-10

x² - 5x + 2x - 10

x(x - 5) + 2(x - 5)

(x - 5)  (x + 2)

Thus, the factorization of the given expression  x²-3x-10

= (x - 5)  (x + 2)

Hence we get the factors as (x - 5)  (x + 2)

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Answer:

To factor the quadratic expression a2 - 3x - 10, we need to find two numbers that multiply to give -10 and add to give -3. These numbers are -5 and 2. Therefore, we can write:

a2 - 3x - 10 = (a - 5)(a + 2)

So the factors of the quadratic expression a2 - 3x - 10 are (a - 5) and (a + 2).

Answer:

f(x) = 12x+35

f(5) = 95 pages written at 5 months

Step-by-step explanation:

Step 1: write the slope intercept equation

f(x) = mx+b

f(x) = the value of the equation at month x

m = slope of the linear equation (pages written PER month)

x = the month

b = intercept of the equation (pages already written)

Step 2: relate given information to the variables

m = 12 pages per month

b = 35 pages already written

Step 3: update equation

f(x) = 12x+35

Step 4: solve for x = 5 months

f(5) = 12(5) + 35 = 60 + 35 = 95

There are total 35 such ways in which a person can adopt rules.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

According to the question, we are Given,

Total rules = 7

No of rules a person can adopt = 5

using combinations,

= ⁷C₅

= 7! / 5! (7 - 5)!

= 7! / 5! 2!

= 35

So a person can choose it in 35 possible ways.

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Answer:

51/8

Step-by-step explanation:

each bracelet length as a fraction will be 51/8 inches if the artist uses the 51 inches of the string to make 8 bracelets

Answer:  

10/100= 0.1

100/10= 10

Step-by-step explanation:

The scale of the drawing is 6 feet = 17 inches

Scaling is the process of increasing or reducing the size of a figure by a factor k.

In the given statement is:

Shane made a scale drawing of a hotel. a room in the hotel, which is 18 feet wide in real life, is 51 inches wide in the drawing.

A figure which is 18 feet wide in real life, is 51 inches wide in the drawing, hence the scale is:

Now, According to the question is

18 feet = 51 inches

Divide both sides by 3:

6 feet = 17 inches

Therefore, the scale of the drawing is 6 feet = 17 inches

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The statement that is true about the segment connecting points B and C is D. The segment has a finite length that can be measured.

It should be noted that ieometry, a line segment is the part of a straight line bounded by two distinct end points, and contains every point on the line that is between its endpoints.

It should be noted that the length of a line segment is given by the Euclidean distance between its endpoints.

Therefore, in this case, the statement that is true about the segment connecting points B and C is that the segment has a finite length that can be measured.

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Answer:

3x - 8y = -12

Step-by-step explanation:

Standard form is:

[tex]Ax + By = C[/tex]

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

[tex]8y - 12 = 3x\\\rule{150}{0.5}\\8y - 8y -12 =3x - 8y\\\\-12 = 3x-8y\\\\\boxed{3x - 8y = -12}[/tex]

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

A graph is attached. Hope this helps!

Hence she got 90 correct answer.

Ratio of the number of problems she got incorrect to the number of problems she got correct = 2:9

Number of incorrect answers = 8

Let the number of incorrect answers be 2x

Let the number of correct answers be 9x.

So, According to question, we get that

[tex]2x = 20\\ x =\frac{20}{2} \\ x = 10[/tex]

So, the number of correct answers would be

  [tex]9x = 9\times 10\\\\ =90[/tex]

Hence she got 90 correct answer.

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1 - there will be increase of  233.33 %  ,  2 - there will be increase of 122.22 % , 3 - there will be decrease of 15 % , 4 - there will be decrease of 55.56 % , 5 - there will be increase of 100%

% is a relative number that is used to represent hundredths of any quantity. Since one percent (1%) equals one tenth of something, 100 percent denotes the entire amount, and 200 percent denotes twice the amount mentioned percentage.

1 - Start : 3 end : 10

  formula for finding percentage increase is = [tex]\frac{end - start }{start } * 100[/tex]

so substituting value in the formula ;

       that is equal to = [tex]\frac{10-3}{3} * 100[/tex]

                                 = [tex]\frac{7}{3} * 100[/tex]

                                 = 233.33% increase

2 - Start : 9  End : 20

      directly substituting the values in the above mentioned formula

                                            = [tex]\frac{20-9}{9} * 100[/tex]

                                            = [tex]\frac{11}{9} * 100[/tex]

                                            = 122.22% increase

3 - Start : 100 end : 85

             plugging in the values = [tex]\frac{85-100}{100}*100[/tex]

                                                   = [tex]\frac{-15}{100} * 100[/tex]

                                                   = -15% i.e. decrease of 15%

4 -  Start : 45 end : 20

             putting in the values = [tex]\frac{20-45}{45} * 100[/tex]

                                                = [tex]\frac{-25}{45}*100[/tex]

                                                = -55.56% i.e. decrease of 55.56 %

5 - Start : 30 end : 60

                  putting in the values = [tex]\frac{60-30}{30}* 100[/tex]

                                                       = [tex]\frac{30}{30} * 100[/tex]

                                                       = 100%  increase

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