if a car gets 13 kilometers per liter of gasoline, how many miles per gallon of gasoline would it get?

Answer:

y=3x+5

Step-by-step explanation:

gradient =(y2-y1)÷(x2-x1)

(-4--3)÷(3-2)

=-3/1

y=mx+c

y+1/x-2=_3/1

y+1=-3x+6

y=3x+5

\(\huge\underline\mathtt\colorbox{orange}{ y = -3 x + 5}\)

Find the equation of the line in slope-intercept form with the properties:

point: p_1 = (2, -1)

point: p_2 = (3, -4)

The slope of the line through points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1):

m = (-4 - (-1))/(3 - 2) = -3

Substitute the slope m = -3 and point (x_1, y_1) = (2, -1) into the point-slope equation y - y_1 = m (x - x_1):

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

Subtract 1 from both sides:

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

Distribute: -3 (x - 2) = 6 - 3 x:

Answer:

y = -3 x + 5

The exercise highlights that converting the dual problem into standard form and applying the primal simplex method does not yield the same algorithm as the dual simplex method. By considering a specific standard form problem and its dual, it is shown that the primal simplex method applied to the dual problem may require one or more changes of basis, unlike the dual simplex method where termination occurs immediately due to the specific structure of the problem.

In the given exercise, we have a standard form problem and its dual:

Primal Problem:

minimize 21x1 + 22x2

subject to x1 = 1

x1, x2 ≥ 0

Dual Problem:

maximize P1 + P2

subject to P1 < 1

P2 < 1

P1, P2 ≥ 0

Since there is only one possible basis in this case, the dual simplex method terminates immediately because of the specific structure of the problem.

However, if we convert the dual problem into standard form and apply the primal simplex method to it, one or more changes of basis may be required. This is because the primal simplex method operates differently from the dual simplex method and may encounter different pivot elements and entering/leaving variables during the iterations. These differences in the algorithm can lead to changes in the basis during the primal simplex method's execution.

Therefore, it is evident that converting the dual problem into standard form and applying the primal simplex method does not result in the same algorithm as the dual simplex method. The primal simplex method may require one or more changes of basis during its execution, unlike the dual simplex method, which terminates immediately in this specific problem due to the singular structure of the basis.

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The quotient for the given exponential expression (-8a⁸b⁻²)/(10a⁻⁴b⁻¹⁰) is (-4/5)(a¹²b⁸).

Exponents are of the form aˣ, read as "a to the power of x", and signify the product of a multiplied by itself x number of times.

In the question, we are given an exponential expression (-8a⁸b⁻²)/(10a⁻⁴b⁻¹⁰) and are asked to find the quotient of it.

To find the quotient, we will try to simplify the equation using the laws of exponents in the following way:-

(-8a⁸b⁻²)/(10a⁻⁴b⁻¹⁰),

= (-4/5)(a⁽⁸ ⁻ ⁽⁻⁴⁾⁾b⁽⁻² ⁻ ⁽⁻¹⁰⁾⁾) {Using the law of exponent: \(\frac{x^{a} }{x^{b} } =x^{(a-b)}\) }

= (-4/5)(a¹²b⁸).

Therefore, the quotient for the given exponential expression (-8a⁸b⁻²)/(10a⁻⁴b⁻¹⁰) is (-4/5)(a¹²b⁸).

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The required complete table regarding the distance traveled has been shown.

From the given condition, let y be the distance left and x be the time,
According to the question an equation model is given as,

Distance traveled = 5x
Distance remaining to travel = y = 5000 - 250x

Now,
Put x = 5
Distance traveled = 250x
                           = 250(5) = 1250

Distance remaining to travel = y
y = 5000 - 1250
y = 3750 ft

Similarly,
At
x = 20
Distance traveled = 5000

X = 10
Distance remaining = 2500

Thus, the required complete table has been shown.

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Using a proportional relationship, it is found that Sam buys milk at a lower rate, of $3.4 per gallon.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

Researching the problem on the internet, Edwin's graph goes through (2,7), hence the price is:

p = (7/2)g = 3.5g.

3.5 > 3.4, hence Sam buys milk at a lower rate, of $3.4 per gallon.

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The distance between the tip of the ladder to the ground or the value of 'x' is 13.27 ft.

We know that the ladder is leaning on the wall and thus it makes a right-angle triangle, where:

the hypotenuse(h) is the length of the ladder,

the base(b) is the distance between the foot of the ladder and the bottom of the wall,

and the height(x) is the distance between the tip of the ladder to the bottom of the wall which we need to find.

As the question is on right angled triangle we can use the Pythagoras theorem to find the value of 'x':

\(Height^2 + Base^2 = Hypotenuse^2\\x^2 + b^2 = h^2\)

Now we know that h= 15ft, and b=7ft.

Substituting the values in the above equation we get :

\(x^2 + 7^2 = 15^2\\x^2 = 225 - 49\\x = \sqrt{176}\\x= 13.27 ft.\)

Therefore the distance between the tip of the ladder to the ground or the value of 'x' is 13.27 ft.

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Answer:

C ≈ 25.13 ft

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr ( r is the radius ) , then

C = 2π × 4 = 8π ≈ 25.13 ft ( to 2 decimal places )

SOLUTION

We want to find the interquartile range of the box and whisker plot in the picture.

Interquartile range is calculated as

In the box and whisker plot

Hence the answer is 6

Answer:

233

Step-by-step explanation:

Look at the tenths place. It is above 5 so you round to 233,

Answer:

233

Step-by-step explanation:

Simple, 7 is closer to 10 than 0, round up to 233.

Answer:

you have to create a poster some photos of property society limited

Answer:

c. 29.3 cubic mi.

Step-by-step explanation:

Volume of cone: \(\pi\) × r² × \(\frac{h}{3}\)

Volume of cone = \(\pi\) × 2² × \(\frac{7}{3}\)

                           = 9\(\frac{1}{3}\)\(\pi\)

                           = 29.3 cubic mi. (rounded to 3 s.f.)

Answer:

Please read below

Step-by-step explanation:

We are told that 1/2 of the orange juice is concentrate

So 50% is concentrate

100 - 50 = 50

This leaves another 50% to be water
50:50 is the same as 1:1

In linear equation, 90 ft  is  the distance between the two players .

What in mathematics is a linear equation?

Let player 1 distance  from home plate = x ft

 so, dx/dt = 20 ft/sec

let player 2 distance from 2nd base  = y ft

       dy/dt = 15 ft/sec

we know that baseball around is of square type with length 90 ft .

 we have to find change in s.

   x = 40 ft ,     y = 50 ft

applying Pythagoras .

                     S² = (90)²  +  ( 90 - ( x + y ) )²

                     S² = ( 90)² + ( 90 - ( 50 + 40 ))²

                     S² = 90²

                     S = 90

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Answer:

Step-by-step explanation:

Givens

m = 1/4

y2 = 4

y1 = 1

x2 = 2

x1 = x

m = (y2 - y1) / (x2 - x1)

Solution

1/4 = (4 - 1) / (2- x)                Simplify

1/4 = 3 / (2 - x)                      Cross multiply

2- x =12                               Subtract 1 from both sides

-x = 12 - 2

-x = 10                                 Multiply by -1

x = -10

Check

1/4 = (4 - 1) / (2 - - 10)

1/4 = 3/(2 + 10)

1/4 = 3 / 12

1/4 = 1/4

Odd as the answer is, it does check.

Answer:

4x and 5.9

Step-by-step explanation:

Answer:

x1=.13 x2=-.13

Step-by-step explanation:

Do the square root of .0169 and you get .13 and -.13

False. It is not best to determine a few key metrics and stick to them rigidly.

The choice of metrics should be driven by the specific objectives and context of the situation. Different goals may require different metrics to effectively measure progress and success. Relying solely on a fixed set of metrics may overlook important aspects or fail to capture the full picture.

Businesses and organizations operate in dynamic environments that evolve over time. Factors such as market conditions, customer needs, and industry trends can change, necessitating a reassessment of metrics. By being open to adjusting and refining metrics, organizations can ensure that they align with current priorities and provide valuable insights.

Moreover, a narrow focus on a limited set of metrics can lead to a skewed perspective and miss out on valuable information. Taking a broader view and considering a range of relevant metrics can provide a more comprehensive understanding of performance and help identify areas for improvement.

Therefore, it is important to regularly evaluate and adjust metrics to ensure they remain meaningful and aligned with the evolving goals and context of the situation. This flexibility allows organizations to adapt and optimize their measurement approaches for better decision-making and success.

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Answer:

\(4x - 4 \\ = 4( - 8) - 4 \\ = - 32 - 4 \\ = - 36\)

Answer:

-1.1

Step-by-step explanation:

3.1 - 1.3 = t + 2.9

t = 3.1 - 1.3 - 2.9

t = -1.1

Answer:

t = -1.1

Step-by-step explanation:

\(3.1 - 1.3 = t + 2.9 \\ 1.8 = t + 2.9 \\ 1.8 - 2.9 = t \\ - 1.1 = t \)

Step-by-step explanation:

55hugggyfhyg u yjrb u tjkthj

Answer:

the awnser to the question is: 40°

Answer:

g= 8/21

Step-by-step explanation:

\(g=\frac{5}{7} -\frac{1}{3} \\g=\frac{15}{21} -\frac{7}{21} \\g=\frac{8}{21}\)

Answer:

y axis is the top and bottom line like the straight line abd Example on the coordinate plane ut had two lines one jn the middle and one going across well the one going across is the x axis abs the one going straight is y axis so final answer Y axis us that

Answer:

8 ÷ 15 = 0.5333333333333333 or 0.53

Step-by-step explanation:

Answer:

0.5333  as a decimal

5333/10000

53.33%

Step-by-step explanation:

Answer:

0.583

Step-by-step explanation:

Use a caluclator

Answer:

more the letter x is often used in algebra to mean a value that is not yet known is is calld a variable or sometimes an unknown. in x+2=7,x is a variable but we can work out its value if we try

Sampling is the use of a subset of the population to represent the whole population or to inform about processes that are meaningful beyond the particular cases, individuals or sites studied.

In non-probability sampling, the sample is selected based on non-random criteria, and not every member of the population has a chance of being included. Common non-probability sampling methods include convenience sampling, voluntary response sampling, purposive sampling, snowball sampling, and quota sampling.

x ≤ 2.6 would look like this on the number line, the 2.6 part would be shaded in as well and not left open since x is less than OR EQUAL to 2.6

The equation or system of equations that can be used to determine the number of cats and dogs Bea has in her pet shop is d = 2c - 5 d + 3 = c + 3. We can solve the system of equations using substitution and plug it back into either equation to find the value of d, which is 8 cats and 10 dogs.

The equation or system of equations that can be used to find the number of cats and dogs Bea has in her pet shop is:

d = 2c - 5

d + 3 = c + 3

No, Bea's Pet Shop could not initially have 15 cats and 20 dogs. This is because the equation or system of equations states that the number of dogs is five less than twice the number of cats, which would mean that 15 cats would result in 25 dogs, which is not equal to 20.

To determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop, we can use the equation or system of equations that we previously created.

d = 2c - 5

d + 3 = c + 3

We can solve the system of equations using substitution:

d = 2c - 5

d + 3 = c + 3

d + 3 = c + 3

d = c + 3

2c - 5 = c + 3

2c = c + 8

c = 8

Once we determine the value of c, we can plug it back into either equation to find the value of d:

d = 2(8) - 5

d = 15 - 5

d = 10

Therefore, Bea initially had 8 cats and 10 dogs in her pet shop.

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The complete question is: At Bea's Pet Shop, the number of dogs, d, is initially five less than twice the number of cats, c. If she decides to add three more of each, the ratio of cats to dogs will be – Write an equation or system of equations that can be used to find the number of cats and dogs Bea has in her pet shop. Could Bea's Pet Shop initially have 15 cats and 20 dogs? Explain your reasoning. Determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop.​

Answer:

3.3 = \(3^{2}\) = 9

Step-by-step explanation: