a car averages 35 miles per gallon of gasoline. how many liters of gasoline will be needed for a trip of 450 km? some conversion factors which may be helpful are the following:

The standard form of the equation is (x' - 8x) + (y - 3)^2 = 48

To write the equation in standard form and identify the related conic, let's rearrange the given equation:

x' + y^2 - 8x - 6y - 39 = 0

Rearranging the terms, we have:

x' - 8x + y^2 - 6y - 39 = 0

Now, let's complete the square for both the x and y terms:

(x' - 8x) + (y^2 - 6y) = 39

To complete the square for the x terms, we need to add half the coefficient of x (-8) squared, which is (-8/2)^2 = 16, inside the parentheses. Similarly, for the y terms, we need to add half the coefficient of y (-6) squared, which is (-6/2)^2 = 9, inside the parentheses:

(x' - 8x + 16) + (y^2 - 6y + 9) = 39 + 16 + 9

(x' - 8x + 16) + (y^2 - 6y + 9) = 64

Now, let's simplify further:

(x' - 8x + 16) + (y^2 - 6y + 9) = 8^2

(x' - 8x + 16) + (y - 3)^2 = 8^2

(x' - 8x + 16) + (y - 3)^2 = 64

Now, we can rewrite this equation in standard form by rearranging the terms:

(x' - 8x) + (y - 3)^2 = 64 - 16

(x' - 8x) + (y - 3)^2 = 48

The equation is now in standard form. From this form, we can identify the related conic. Since we have a squared term for y and a constant term for x (x' is just another variable name for x), this equation represents a parabola opening horizontally.

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Step-by-step explanation:

a. 960÷15=64

check:64×15 = 960

Answer:

The correct proportion that can be used to find the amount of orange juice, j, that is needed to add to 27 L of pineapple juice is:

3/5 = j/27

So, the answer is: 3 over 5 equals j over 27.

In inferential statistics, we calculate statistics of sample data to estimate the characteristics of the entire population from which the sample was taken. The process involves drawing inferences about a population from a random sample of data taken from that population.

The sample statistics are used to estimate the parameters of the population. To make an inference, we use a hypothesis test or confidence interval based on the sample statistics. The key to inferential statistics is random sampling, which allows us to make generalizations about the population based on the characteristics of the sample.

In order to ensure that the sample is representative of the population, we use a variety of sampling techniques, including simple random sampling, stratified sampling, cluster sampling, and systematic sampling.

Each of these techniques has its own advantages and disadvantages, and the choice of technique depends on the characteristics of the population being studied and the research questions being asked.

Once we have a representative sample, we use statistical methods to draw conclusions about the population. This allows us to make predictions and to test hypotheses about the population with a high degree of confidence.

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Answer:

Hi! In order to determine how much money Aiden will have in his account after 8 months, let's figure out how much he deposits each month.

He started with $250. After one month, he had $586; after two months, he had $922; after three months, he had $1,258. Each month, there is a gain of $336.

Therefore, after four months, Aiden will have $1,594. After five months, he will have $1,930. After six months, he will have $2,266. After seven months, he will have $2,602. Finally, after eight months, he will have $2,938.

Hope this helps!

The percentage of the games that Natasha scores between 93 and 142 is given as follows:

96.9%.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation are given as follows:

\(\mu = 115, \sigma = 11\)

The proportion of games with scores between 93 and 142 is the p-value of Z when X = 142 subtracted by the p-value of Z when X = 93, hence:

Z = (142 - 115)/11

Z = 2.45

Z = 2.45 has a p-value of 0.992.

Z = (93 - 115)/11

Z = -2

Z = -2 has a p-value of 0.023.

0.992 - 0.023 = 0.969, hence the percentage is of 96.9%.

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The value of the Land Rover LX will be approximately $16,624.41 in 9 years, considering a depreciation rate of 11% each year.

To find the value of the Land Rover LX after 9 years, we need to calculate the depreciation for each year. The car depreciates at a rate of 11% each year.

We can calculate the value in each year by multiplying the previous year's value by (1 - 0.11) or 0.89 (100% - 11%).

Starting with the initial value of $47,450, we can calculate the value in each subsequent year as follows:

Year 1: $47,450 * 0.89 = $42,190.50

Year 2: $42,190.50 * 0.89 = $37,548.45

Year 9: $16,624.41 * 0.89 = $14,793.02

Therefore, the value of the Land Rover LX in 9 years will be approximately $16,624.41. Option C, $16,624.41, matches this calculated value and is the correct answer.

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\(x_{axis} = 1 \: unit = 0.5 \: sec\)

\(y_{axis} = 1 \: unit = 4 \: meters\)

\(h(x) = - 16x {}^{2} + 32x + 48 \\ h'(x) = - 32x + 32 \\ h'(x) = 0 \\ x = \frac{ - 32}{ - 32} = 1 \\ \\ h(1) = - 16 + 32 + 48 = 64\)

\(h(x) = 0 \\ - 16x {}^{2} + 32x + 48 = 0 \\ - x {}^{2} + 2x + 3 = 0 \\ x {}^{2} - 2x - 3 = 0 \\ (x -3)(x + 1) = 0 \\ x - 3 = 0 \: \: \: \: \: \: x + 1 = 0 \\ x = 3 \: \: \: \: \: \: \: \: \: \: \: \: x = - 1 \\ \)

\( \alpha = - 16 \\ (x - r)(x - t) = (x - 3)(x + 1)\\h(x) = \alpha (x - r)(x - t) \\ h(x) = - 16(x - 3)(x + 1)\)

Answer:

B. rotation of 90° counter-clockwise about the origin

Step-by-step explanation:

Pla Brainlest me thank you :)

Answer:

The answer is 15 ft.

Step-by-step explanation:

I hope this helps

Using the concept of similar triangles, the depth of water, d from the shore is 15 feets

From the figure attached ; the following relationship can be established :

Using cross multiplication :

\( d \times 5 = 50 \times 1.5 \)

\( 5d = 75 \)

Divide both sides by 5

\(\frac{5d}{5} = \frac{75}{5} \)

\( d = 15 \)

Hence, the depth of water from the shore ls 15 feets.

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Answer:

(-5x - 2)(8x - 5)

I hope this helps!

Answer:

It means adding the inverse so -3-(-6)=-3+6=3

Answer:

C

Step-by-step explanation:

The situation can be modeled by an exponential decay function with a percent change of -10%, option A is correct.

percentage, a relative value indicating hundredth parts of any quantity.

The ratio between the value after 1 year and the value after 0 years is 18,000/20,000 = 0.9.

The ratio between the value after 2 years and the value after 1 year is 16,200/18,000 = 0.9.

The ratio between the value after 3 years and the value after 2 years is 14,580/16,200 = 0.9.

Since the ratio between consecutive values is constant and less than 1, we can conclude that the situation can be modeled by an exponential decay function.

r = (18,000/20,000) - 1 = -0.1

So the percent change per year is -10%, which means that statement A is true.

Hence, the situation can be modeled by an exponential decay function with a percent change of -10%, option A is correct.

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As we can see, the equality is equal for only one value of xx, which was the same as the one we found in part (a).
(a) \(x = \frac{L\pi }{4+\pi }\)
(b) True
(c) Yes

What is maximum and minimum?

The smallest value in the data set is the minimum. The largest value in the data set is the maximum.

(a) The circumference of the circle is xx, which means that

\(P_ 1= 2\pi r\\x = 2\pi r\\r = \frac{x}{2\pi }\)

The area of the circle is,

\(A_c = \pi r^2\\A_c = \frac{x^2}{4\pi }\)

The circumference of the square is L - x, which means

\(P_2 = 4a \\L-x=4a\\a = \frac{L-x}{4}\)

The area of the square is,

\(A_s = a^2\\A_s=\frac{(L-x)^2}{16}\)

The sum of the areas of the circle and the square is

\(A = A_c + A_s\\A = \frac{x^2}{4\pi } +\frac{(L-x)^2}{16} \\A = \frac{4x^2+(L-x)^2\pi \pi }{16\pi } \\A = \frac{4x^2+(L^2 -2Lx+x^2)\pi }{16\pi } \\A = \frac{(4+\pi )x^2-2Lx\pi +L^2\pi }{16\pi }\)

The derivative of the function of the total area is

\(A = \frac{4+\pi }{8\pi }x-\frac{L}{8}\)

We solve the equation A'(x) = 0

\(\frac{4+\pi }{8\pi }x-\frac{L}{8}=0\\ \frac{4+\pi }{\pi }x=L\\ x = \frac{L\pi }{4+\pi }\)

So, \(x = \frac{L\pi }{4+\pi }\) is a critical point A, and it is a global minimum of A since

\(A"(x) = \frac{4+\pi }{8\pi } > 0\) for all x.

(b) The area of the circle for \(x = \frac{L\pi }{4+\pi }\) is

\(A_c = \frac{(\frac{L\pi }{4+\pi } )^2}{4\pi } \\A_c = \frac{(\frac{L^2\pi ^2}{(4+\pi )^2} )}{4\pi } \\A_c= \frac{L^2\pi }{4(4+\pi )^2}\)

The area of the square for \(x = \frac{L\pi }{4+\pi }\)  is

\(A_s = \frac{(L-\frac{L\pi }{4+\pi } )^2}{16}\)

The ratio of the area is,

\(\frac{A_s}{A_c} = \frac{(\frac{(L-\frac{L\pi }{4+\pi })^2 }{16} )}{(\frac{L^2\pi }{4(4+\pi )^2} )}\)

\(= \frac{(L - \frac{L\pi }{4+\pi })^2 }{16}*\frac{4(4+\pi )^2}{L^2\pi } \\ = \frac{L^2-\frac{2L^2\pi }{4+\pi }+(\frac{L\pi }{4+\pi } )^2 }{4} *\frac{(4+\pi )^2}{L^2\pi } \\= \frac{(4+\pi)^2 }{4\pi }-\frac{4+\pi }{2}+\frac{\pi }{4}\\ = \frac{4}{\pi }\)

The ratio of the length of wire in the square to the length of wire in the circle for \(x = \frac{L\pi }{4+\pi }\)  is

\(\frac{L-x}{x} =\frac{L-\frac{L\pi }{4+\pi } }{\frac{L\pi }{4+\pi } } \\= \frac{\frac{4L}{4+\pi } }{\frac{L\pi }{4+\pi } } \\= \frac{4}{\pi }\)

As we can see (1) = (2)

(c) To prove this, we solve the equation

\(\frac{A_s}{A_c} = \frac{L-x}{x} \\ \frac{\frac{(L-x)^2}{16} }{\frac{x^2}{4\pi } } = \frac{L-x}{x}\\ \frac{(L-x)^2}{4}*\frac{\pi }{x^2} = \frac{L-x}{x} \\ \frac{L-x}{4} *\frac{\pi }{x} =1\\L\pi -\pi x=4x\\L\pi = (4 + \pi )x\\x = \frac{L\pi }{4+x}\)

As we can see, the equality is equal for only one value of xx, which was the same as the one we found in part (a).

Hence,

(a) \(x = \frac{L\pi }{4+\pi }\)

(b) True

(c) Yes

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To find the value of x, we need to use the fact that when two lines intersect, the sum of the adjacent angles formed is equal to 180 degrees.

In this case, the angle formed between lines s and t is 23 degrees, and the angle formed between lines r and s is 106 degrees. Let's denote the angle between lines t and r as x.

Using the information given, we can set up the equation:

(106 degrees) + (23 degrees) + x = 180 degrees

Combine the known values:

129 degrees + x = 180 degrees

To isolate x, subtract 129 degrees from both sides of the equation:

x = 180 degrees - 129 degrees

x = 51 degrees

Therefore, the value of x is 51 degrees.

In conclusion, the value of x, the adjacent angles formed between intersecting lines t and r, is 51 degrees.

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The correct option stating number of roses and carnation to be bought are 4 roses and 7 carnations.

The equation to be formed here is -

Cost of each Rose × number of roses + cost of each carnation × number of carnations = total amount.

We will keep each option in the formula to find the correct choice.

Option 1

5×4 + 1.75×7

20 + 12.25

32.25 which is less than $35

Option 2

5×8 + 1.75×4

40 + 7

47 which is greater than total amount

Option 3

5×6 + 1.75×6

30 + 10.5

40.5 which is greater than total amount

Option 4

5×7 + 1.75×4

35 + 7

42 which is greater than total amount

Since only option 1 is less than total amount, it is the feasible and correct option.

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The complete question is -

Myra wants to buy flowers for her mom. Roses cost $5 each and carnations cost $1.75 each. If Myra has $35, how many roses and how many carnations can she buy?

4 roses and 7 carnations

8 roses and 4 carnations

6 roses and 6 carnations

7 roses and 4 carnations

The perimeter of square ABCD is 28 units.

The perimeter of a square is the sum of all its sides. In this case, we need to find the perimeter of square ABCD.

The question provides two possible answers: 28 units and 37 units. However, we can only choose one correct answer. To determine the correct answer, let's think step by step.

A square has all four sides equal in length. Therefore, if we know the length of one side, we can find the perimeter.

If the perimeter of the square is 28 units, that would mean each side is 28/4 = 7 units long. However, if the perimeter is 37 units, that would mean each side is 37/4 = 9.25 units long.

Since a side length of 9.25 units is not a whole number, it is unlikely to be the correct answer. Hence, the perimeter of square ABCD is most likely 28 units.

In conclusion, the perimeter of square ABCD is 28 units.

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Answer:

2/16

5/40

Step-by-step explanation:

Answer:

1.82142857143 or 1 23/28

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

51/28 or 1 23/28

Step-by-step explanation:

The LCD here is 9.  Rewrite 5 2/3 first as 17/3, and then multiply numerator and denominator both by 3, obtaining the equivalent 51/9.

Then divide 51/9 by 28/9:  Equivalently, invert the divisor (28/9) and multiply:

(51/9)(9/28) = 51/28 or 1 23/28

5 2/3 divided by 3 1/9 is 1 23/28.

The distance from home plate to second base is 180 feet, which is double the distance from home plate to first base.

A baseball diamond is a square with four bases, with home plate in the middle. 90 feet separate first base from home plate, and 90 more feet separate first base from second base. Therefore, the total distance from home plate to second base is twice that distance, or 180 feet. The same applies to all of the bases; the distance between them is always 90 feet, so the total distance from home plate to any base is twice that of the distance from home plate to first base. This means that the distance from home plate to second base, third base, and home plate is all 180 feet.

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\(\sf\fbox\red{Answer:-}\)

(2+3)²

=(5)²

=25

\(\small\fbox{\blue{\underline{mαrk \; mє \; вrαínlíєѕt \; plєαѕє ♥}}}\)

Hi there!

\(\large\boxed{\text{x = 12, x = 5}}\)

Problem 1:

The angles pictured are vertical angles, so each will be equivalent. Therefore:

(5x + 5)° = 65°

Subtract 5 from both sides:

5x = 60

Divide both sides by 5:

x = 12°.

Problem 2:

The two angles are supplementary, so they add up to 180°. Therefore:

180° = (9x)° + (12x + 75)°

180 = 9x + 12x + 75

Combine like terms:

180 = 21x + 75

Subtract 75 from both sides:

105 = 21x

Divide both sides by 21:

x = 5°.

Simply plug in x to the formula to y.

y = -2 + 3

y = 1

and

x = -2

I hope this is what you were looking for.

Answer:

y=1

Step-by-step explanation:

Plug x=-2 into the equation y=x+3:

y=(-2)+3

y=1

Answer:

answer is 792

Step-by-step explanation:

........................ .

The length of the rectangle are:

7. MP = 10 units

8. MQ ≈ 9.2 units.

Recall that the diagonals of a rectangle have the same length and they intersect at the center of the rectangle, dividing it into two congruent sections.

7. MP and NQ are the diagonals of rectangle MNPQ. Therefore:

MP = NQ

NQ = 2(5) = 10 units

Length of MP = 10 units.

8. Applying the Pythagorean theorem:

MQ = √(MP² - PQ²)

MQ = √(10² - 4²)

MQ = √84

MQ ≈ 9.2 units

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Answer:

(-4,4) (3,-4) is the answer

Step-by-step explanation:

The correct answer is: " \(- \frac{7}{15}\) " ;  or, write as:  " \(\frac{-7}{15}\) " .

________________________________________

Step-by-step explanation:

   →   -1/6 * 7 * 2/5 ; \(\frac{-7}{15}\)

         =  "  \(\frac{-1}{6} *\frac{7}{1} *\frac{2}{5} = \frac{(-1*7*2)}{(6*1*5)} = \frac{-14}{30}\) " ;

Now, simplify the value:  " \(\frac{-14}{30}\) " ;

_______

→  "    \(\frac{-14}{30} = \frac{(-14/2)}{(30/2)} = - \frac{7}{15}\) " ;

_______

The correct answer is:  " \(- \frac{7}{15}\) " ; or, write as: " \(\frac{-7}{15}\) " .

_______

Hope this is helpful to you!

  Wishing you well !

_______