if a borrowed car averges 38 miles per gallon how many miles can u travel with 12 gallons of gas

Table (x, y) equals (0, 0), (6, 3), and (12, 6) represents a linear relationship that is also proportional.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

The first option is linear but not proportional as 3 ×2 = 6 and 6×2 = 12.

By observing the given options we conclude that the third option is linear and proportional as,

6 ÷ 2 = 3 and 12 ÷ 2 = 6.

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All the table show the linear relationship, but none of the table show the proportional relationship.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

A). x → y

0 → 3

3 → 6

6 → 9

To show the linear relationship:

We have to find the constant first difference.

That means,

6-3 = 3

And 9 - 6 = 3

The values of this table show the linear relationship.

To show the proportional relationship:

Let x/y = k (k is constant)

We have to find the k:

0/3 = 0,

3/6 = 1/2,

6/9 = 2/3.

The values of this table do not show the proportional relationship.

B). x → y

0 → 4

2 → 6

4 → 8

To show the linear relationship:

We have to find the constant first difference.

That means,

6-4 = 2

And 8 - 6 = 2

The values of this table show the linear relationship.

To show the proportional relationship:

Let x/y = k (k is constant)

We have to find the k:

0/4 = 4,

2/6 = 1/3,

4/8 = 1/2.

The values of this table do not show the proportional relationship.

C). x → y

0 → 0

6 → 3

12 → 6

To show the linear relationship:

We have to find the constant first difference.

That means,

3-0 = 3

And 6 - 3 = 3

The values of this table show the linear relationship.

To show the proportional relationship:

Let x/y = k (k is constant)

We have to find the k:

0/0 = undefined,

6/3 = 2,

12/6 = 2.

The values of this table do not show the proportional relationship.

D). x → y

0 → 3

5 → 5

10 → 7

To show the linear relationship:

We have to find the constant first difference.

That means,

5 - 3 = 2

And 7 - 5= 2

The values of this table show the linear relationship.

To show the proportional relationship:

Let x/y = k (k is constant)

We have to find the k:

0/3 = 0,

5/5 = 1,

10/7 = 10/7.

The values of this table do not show the proportional relationship.

Therefore, none of the table show the proportional relationship.

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On solving the provided question, we can say that - the equation, 21 = xy; 40 = [tex]x^2-y^2[/tex] x= 2 and y = 2

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

21 = xy;

40 = [tex]x^2-y^2[/tex]

x= 2

and

y = 2

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Answer:

To find the coordinates of the point on the x-axis that is reflected over the x-axis from the point P, you can use the formula (x, -y). In this case, the x-coordinate of point P is 4, so the x-coordinate of the reflected point will also be 4. The y-coordinate of point P is 7, so the y-coordinate of the reflected point will be -7. Therefore, the coordinates of the reflected point are (4, -7).

Answer: 889.909090909

Step-by-step explanation:

divide

They will walk 6 laps and run 10 laps for a total of 16 miles considering each lap is of 1 mile.

The mile is a customary unit of measurement in both the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is also referred to as the international mile or statute mile to distinguish it from other miles.

In 1959, the statute mile was formally redefined with respect to SI units as exactly 1,609.344 metres, establishing a standard between the British Commonwealth and the United States.

With qualifications, mile is also used to describe or translate a wide range of units derived from or approximately comparable to the Roman mile, such as the nautical mile (now exactly 1.852 km), the Italian mile (roughly 1.852 km), and the Chinese mile (now 500 m exactly).

6 laps + 10 laps = 16 laps

1 mile each laps = 16 miles

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The solution to the equation is

x = b/a ± √(b^2/a^2) / a.

Generally, To solve the equation using the completing the square method, we first move all the terms to one side of the equation by subtracting abx and 2b² from both sides, giving us:

a²x² = abx + 2b²

Which is

a²x² - abx - 2b² = 0

Next, we need to add and subtract a term so that the left side of the equation can be written as a perfect square.

We need to find the square of half of the coefficient of the x term, which is -ab/2a.

So we add and subtract (ab/2a)^2 = (b^2/a^2) on the left side of the equation:

a²x² - abx - 2b² + (b²/a²) - (b²/a²) = 0

This gives us the left side of the equation as

(ax - b/a)² = b²/a².

We can then take the square root of both sides:

ax - b/a = ±√(b²/a²)

Finally, we can add b/a to both sides to get the solution:

x = b/a ± √(b²/a²) / a

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Answer: 6

Step-by-step explanation:

The angle at the center of the circle will be;

⇒ θ = 0.5 radian

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

Given that;

A sector of a circle of radius 10 cm and has an area of 25 cm².

Now,

Since, We know that;

⇒ A = 1/2 r²θ

Where, A is area of circle , r is radius of circle and θ is the angle at the center of the circle.

Here, A sector of a circle of radius 10 cm and has an area of 25 cm².

Substitute all the given values, we get;

⇒ A = 1/2 r²θ

⇒ 25 = 1/2 × 10² × θ

⇒ 25 = 50 × θ

⇒ θ = 25 / 50

⇒ θ = 0.5 radian

Thus, The angle at the center of the circle = 0.5 radian

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The percent markup of the supplied statement is equal to 50% after the problem is solved.

There isn't a predetermined "optimal" markup percentage, however most companies set their markup at 50%. A 50% markup, also referred to as "keystone," denotes a price that is 50% greater than the cost of the commodity or service.

The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage. The markup percentage is computed as (12 - 8) / 8 and equals 50% if an item is priced at $12 but costs the manufacturer $8 to produce.

Cost price of game=$25

Selling price of game=$37.50

Profit =  selling price - cost price

Profit =  37.50 - 25

Profit / markup percentage = (profit /cost price ) * 100

= (12.50/25) * 100

= 50%

The percent markup of the supplied statement is equal to 50% after the problem is solved.

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Using the Double Number Line above, note that the unit that helps to find the missing numbers is given as:

Note that a unit rate is like a secret code to help you compare things. It helps you find missing numbers on a number line. For example, if 4 cookies cost $2, you can use the unit rate of $0.50/cookie to find out how much 8 cookies cost."

In the above case, we have several clues about the rate. The first relationship on the line is between 1 and 3.

But it only makes when we compare it to other iterations on the line such as 2 and 6.

Note that we can establish a relationship here which is that the greater number must be divided by three to get the lower number. That is:

3/3 = 1

6/3 = 2

Note well that the relationship between 0, 3, and 6 on the number line tell us that the upper units graduate in progressions of 3. that is:

0, 3, 6, 9, etc.

Thus, the missing numbers are:

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Answer:

59.5765%

Step-by-step explanation:

$35.74/$59.99

Answer:

2000 workers

Step-by-step explanation:
All the workers: 100%
Women: 60%
Others: 40% = 800 workers
=> 1% of the workers: 800/40 = 20 workers
=> 100% = 20 x 100 = 2000 workers
(I can't think of another one)

Answer: it depends on the number you took

Step-by-step explanation:

LJ and LI are the figure's two congruent portions. Congruency means that the segments' sizes and shapes will be comparable.

Two triangles are said to be congruent to one another according to the Side-Angle-Side Congruence Theorem (SAS) if the included angle and corresponding two sides of one triangle match those of the other. Two sides that are being considered are determined to have an included angle. Therefore, using the SAS Congruence Theorem to prove that two triangles are congruent based on the fact that they have two pairs of corresponding sides and one pair of corresponding angles is insufficient.

given

The two segments LI and LJ that are marked in the illustration are congruent to one another.

Congruency means that the segments will have the same size and shape.

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Sevati has 18 magazines in her collection. Sevati's collection of periodicals is represented by the phrase x - 7 = 25.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.  Let's examine the writing of expressions. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.

given

If x is the alita collection,

then sevati is equal to x - 14 + x = 50.

Sevati's collection of magazines is represented by the formula 2x - 14 = 50, hence the alita collection is equal to 2x = 36

x = 18

Sevati has 18 magazines in her collection. Sevati's collection of periodicals is represented by the phrase x - 7 = 25.

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Both Kylie and Bennet are correct.

Opposite of the opposite of a number is negative if the number is a positive number.

Opposite of the opposite of a number is positive if the number is a negative number.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = x

The Opposite of x is -x.

Opposite of -x.

= -(-)

= x

Number = -x

The opposite of -x.

= -(-x)

= x

The opposite of x.

= -x

Thus,

Both the person is correct.

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Answer:

18 × 3 = 54

18 + 54 = 72

Therefore, the answer is 72.

for an inequality graph, if the line is dashed, that means that the border line is not part of the shaded region, so any points on it are not a solution of it, any points inside the shaded region or "true" region are solutions to it, only if the border line is solid then the border is part of the "true" region, Check the picture below.

laucs ori nisiquiera estoy en universidad estoy en eseyo pe

Answer: B strange and harrowing story.

Step-by-step explanation: Based on the description of the stranger's face in the novel, it is likely that the captain would expect the stranger to tell a strange and harrowing story. The stranger's face is described as "wild" and "ghastly," which suggests that the story he is about to tell may be disturbing or unsettling in some way. The captain may also expect the story to be emotionally intense, given the stranger's appearance and demeanor.

Answer:

Step-by-step explanation:
Step 1: Subtract 8cx from both sides of the equation to get

10ax + 9b - 8cx = d

Step 2: Subtract 9b from both sides of the equation to get

10ax - 8cx = d - 9b

Step 3: Multiply both sides of the equation by (-1/10) to get

-8cx/10 = -(d - 9b)/10

Step 4: Add (d - 9b)/10 to both sides of the equation to get

-8cx/10 + (d - 9b)/10 = 0

Step 5: Simplify the left side of the equation to get

x = (9b - d)/80

Therefore, x = (9b - d)/80 is the solution to the equation 10ax + 9b = 8cx + d.

The value of the exponential graph y = ( 1/2 )ˣ is graphed

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

y =  ( 1/2 )ˣ   be equation (1)

On simplifying the equation , we get

y = 1 / (2ˣ)

Now , the graph of the function y =  ( 1/2 )ˣ  will be a slanting line which will not touch the x axis and passes through the point y = 1

The graph of the function y =  ( 1/2 )ˣ is given below

Hence , the function is solved and the graph is plotted

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Answer:

  (b)  y < x-1; y ≤ -2x+2

Step-by-step explanation:

You want to know the inequalities represented on the graph showing a solid line with negative slope and a y-intercept of 2, and a dashed line with positive slope and a y-intercept of -1, where the shading is below both lines.

If the line is included in the solution set (≤ or ≥ is used), the boundary line is graphed as a solid line. If the line is not included in the solution set (< or > is used), the boundary line is graphed as a dashed line.

Here, the line with positive slope is dashed, and the line with negative slope is solid.

  y = x -1 . . . . is a line with positive slope

  y = -2x +2 . . . . a line with negative slope

The shading is below the line for y-values less than those on the line:

  y < x -1 . . . . shading below a dashed line with positive slope

  y ≤ -2x +2 . . . . shading below a solid line with negative slope

These are the inequalities of interest.

It will it take 56 years for the account value to reach $20,900.

This amount is calculated based on the principal amount of a loan or the first deposit in a savings account. Simple interest does not compound, thus, a creditor will only pay interest on the principal amount and a borrower would never have to pay more interest on the previously accumulated interest.

formula for calculating Simple Interest, S.I:

S.I = P * R * T

            100

Where,

S.I =  Simple Interest

P =Pricipal

R = rate ( in percentage)

T= Time

To how long will it take for the account value to reach $20,900

S.I = $20,900

R = 6.5%

P =$ 5,700

T =?

S.I = P * R * T

            100

$20,900 = $ 5,700 * 6.5 * T

                            100

Cross multiplying and Making Time, T  subject of the formula we have:

$20,900 * 100 = $ 5,700 * 6.5 * T

T=   $20,900 * 100

         $ 5,700 * 6.5

T=  56.41

T ≈  56 years

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Answer:

x=0

Step-by-step explanation:

[tex]16^{x^2}=8^0\\\\16^{x^2}=1\\\\x^2\ln(16)=0\\\\x^2=0\\\\x=0[/tex]

Answer:

Percent change = 15 - 25/25 × 100% = -10/25 × 100 = -40%

Step-by-step explanation:

Answer:

5 percent

Step-by-step explanation:

divide 25 by5 which gives you percent

The statement five less than four times a number is greater than or equal

to 3 indeed has a solution results to 2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A statement five less than four times a number is greater than or equal to 3.

Let, The unknown number be 'n'.

Therefore, The numerical form of the statement is,

4n - 5 ≥ 3.

4n ≥ 8.

n ≥ 2.

So, Yes 2 is a solution.

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