3,072 c= _______ gal

Answer:

vertex (  [tex]\frac{1}{7}[/tex], [tex]\frac{131}{7}[/tex]).

Step-by-step explanation:

Given : The equation of a parabola is given.

       y=−14x²+4x−19

To find  : What are the coordinates of the vertex of the parabola.

Solution : We have given that

y = −14x²+4x−19

we will be "completing the square" .

Factor out -14 to make leading coefficient 1

y = -14 ([tex]x^{2} -\frac{2x}{7} +\frac{19}{14}[/tex])

Add and subtract [tex](\frac{-1}{7}) ^{2}[/tex]

y = -14 ([tex]x^{2} -\frac{2x}{7} +\frac{19}{14}+\frac{-1}{7}) ^{2} - (\frac{-1}{7})^{2})[/tex] .

Complete the square

y = -14 ( [tex](x -\frac{1}{7}) ^{2} +\frac{19}{14}- (\frac{-1}{7})^{2})[/tex].

y = -14 ( [tex](x-\frac{1}{7}) ^{2} -\frac{131}{7}[/tex]

Standard form of parabola vertex form y  = a(x - h)²+ k,

Where, ( h, k)  are vertex

On comparing a = -14 , h= [tex]\frac{1}{7}[/tex], k =  [tex]\frac{131}{7}[/tex]

Therefore, vertex (  [tex]\frac{1}{7}[/tex], [tex]\frac{131}{7}[/tex]).

Option: C is the correct answer.

    C     The mean will increase, and the median will stay the same.

We know that the mean of scores is the average value of the scores of  the score obtained by 4 friends.

i.e. it is the ratio of sum of scores of 4 friends to the total number of person i.e. 4.

Hence, if the score of any of the person will increase then the mean will also increase

( Since, the denominator remains the same and the numerator is increasing so , the resultant value will increase )

Also, we know that the median of the score lie between the data set, i.e. the change in the score of the last score won't affect the median :

Since, here we have  4 data points and the median lie between the 2nd and 3rd data point so change in the 4th data point won't affect the median.

Hence, increasing Adam's high score affect the mean and median as:

Mean will increase and Median remains the same.

The mean and median will increase as Adam's high score rises, while the median will remain unchanged. Then the correct option is C.

Mean is simply defined as the average of the given set of numbers. The mean is considered one of the measures of central tendencies in statistics.

The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.

A group of 4 friends likes to bowl together, and each friend keeps track of his all-time highest score in a single game.

Their high scores are all between 180 and 220, except for Adam, whose high score is 250.

Adam then bowls a great game and has a new high score of 290.

If any of the individuals' scores improve, the mean will improve as well.

We also observe that the median of the scoring lies inside the data set, implying that a change in the last score will have no effect on the median.

Because we have four data sets and the median is between the second and third, a change in the fourth data point will have no effect on the median.

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To determine if a formula represents a length, area, or volume, consider the units used in the formula.

When determining if a formula represents a length, area, or volume, you need to consider the units used in the formula. Length is typically measured in units such as meters or feet. Area is measured in square units, such as square meters or square feet. Volume is measured in cubic units, such as cubic meters or cubic feet.

For example, suppose you have a formula that involves only one variable and it includes units such as meters. This formula would most likely represent a length. If the formula involves two variables and includes units like square meters, then it represents an area. And if the formula involves three variables and includes units like cubic meters, then it represents a volume.

It's important to pay attention to the units to determine whether a formula represents a length, area, or volume.

To solve the equation 8/x + 1/5 = 3/x, we multiply the entire equation by 5x to get rid of the fractions to get 40 + x = 15. Solving for x we get x = -25.

To solve the given rational equation 8/x + 1/5 = 3/x, we first need to find a common denominator to combine the fractions. Hence, we multiply the entire equation by 5x to get rid of the denominators:

5 * 8 + x = 15

which simplifies to

40 + x = 15.

Then by subtracting 40 from both sides to solve for x, we get:

x = -25.

That is the solution to the rational equation.

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The rational equation 8/x + 1/5 = 3/x is solved by finding a common denominator, simplifying the equation and then factoring the resulting polynomial to find the roots.

To solve the given rational equation 8/x + 1/5 = 3/x, we first find a common denominator for the fractions. Seeing x and 5, we can take the common denominator as 5x.

Next, we rewrite each term with the common denominator: (40/5x) + (x/5x) = (15/5x). This simplifies to 40/5x + x/5x - 15/5x = 0. Simplifying further we have 8/x - 3/x + 1/5 = 0.

After setting the equation to zero, one may notice that this equation can be solved by bringing the terms together and then trying to factorize the resulting polynomial. The solution of the equation are the roots of the factored polynomial.

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Answer:

C. Compressed horizontally by a factor of 1/3, horizontal shift right 2, vertical shift up 3

Step-by-step explanation:

If a function f(x) is transformed and make f(kx),

f(x) is compressed horizontally by the factor 1/k if k > 1

f(x) is stretched horizontally by the factor 1/k if 0 < k < 1

Also, if f(x) is transformed and make f(x+a),

f(x) is shifted right if a < 0

f(x) is shifted left if a > 0,

Now, if f(x) gives f(x) + k after transformation,

f(x) is shifted vertically k unit up if k > 0,

f(x) is shifted vertically k unit down if k < 0,

Here, the parent function,

[tex]f(x) = x^2[/tex]

transformed function,

[tex]g(x)=(3x-6)^2+3=(3(x-2))^2+3[/tex]

Thus, by the above explanation,

f(x) is compressed horizontally by a factor of 1/3, horizontal shift right 2, vertical shift up 3.

Option C is correct.

If the flux of a vector field through a closed surface is zero, this implies that the divergence of the field is zero everywhere. This condition can be used to determine some constants of the vector. In the provided equation, we can determine one of the constants a, c or m if we know the other two.

The subject matter of this question is within vector calculus, a field of mathematics used in physics and engineering. The question talks about the flux of a vector field f through a closed surface which is given to be zero.

When the flux through any closed surface is zero, it implies that the divergence of the vector field f is zero everywhere. This condition allows us to determine some of the coefficients of the components of f. In this case, we have: f = (ax + by + 4z) i + (x + cz) j + (9y + mx) k

The operation that gives the divergence of a vector field in three-dimensional Cartesian coordinates is given by the dot product of the del operator with the vector field. This means:

div f = ∂/∂x(ax+by+4z) + ∂/∂y(x+cz) + ∂/∂z(9y+mx) = a + c + m

For the flux of f through the surface to be zero, the divergence of f needs to equal zero, that is a + c + m =0. Therefore, for a given set of a, c, and m, we can determine one of them knowing the others.

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Answer:

x = 100 is equivalent to z = -1.75

Step-by-step explanation:

Answer:

1-P(z<1.75) D in EDG

Step-by-step explanation:

For the second part !!

Answer:

c

Step-by-step explanation:

edge 2020

Answer:

The correct answer is C.

Step-by-step explanation:

Answer:

Part A : 2 snacks

Part B : Solution to both the inequality and the problem situation ⇒ 1 , 2

             Solution to the inequality only ⇒ -4 , 3/4 , 2.3

             Not a solution ⇒ 2.5

=================================================================

Step-by-step explanation:

Part A :

Janelle  has $20 to spend

She spends $8 on a ticket, so , the remaining = 20 - 8 = $12

Each snack costs $4.99

So, the number of snacks =

the integer of ( 12 / 4.99 ) = integer of (2.4) = 2 snacks

Part B:

Inequality that represents this situation: 20 ≥ 8 + 4.99x

Solve for x

∴ 20 - 8 ≥ 4.99 x

12 ≥ 4.99 x

divide both sides by 4.99

∴ (12/4.99) ≥ x

∴ x ≤ 2.4048

The given options are : -4 , 3/4 , 2.3 , 2.5 , 1 , 2

So,

Solution to both the inequality and the problem situation ⇒ 1 , 2

solution to the inequality only ⇒ -4 , 3/4 , 2.3

Not a solution ⇒ 2.5

Answer:

Solutions to Both:

1

2

Solutions to the Inequality Only;

3/4

-4

2.3

Not a Solution:

2.5

Step-by-step explanation:

Out of a class of 40 students, 28 passed their maths test. The fraction of the class that passed the test is 28/40, which simplifies to 7/10.

The class consists of 40 students. The problem mentions that 28 of these students passed their maths test. To find the fraction of the class that passed, we have to compare the number of students who passed with the total number of students in the class. This is done by dividing the number of students who passed the test by the total class size. So, the fraction of the students who passed is 28/40. However, this fraction can be simplified by dividing both the numerator (28) and the denominator (40) by their greatest common divisor, which is 4. The result is 7/10. Therefore, the fraction of the class that passed the maths test is 7/10.

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The problem involves determining the dimensions of a rectangular pen using given fencing length and area. Two possible solutions were found: the dimensions of the pen could be 30 yards by 35 yards, or 100 yards by 15 yards.

The manager at Clark's Country Pet Resort is trying to construct a rectangular pen for dogs with a fixed amount of fencing and a desired area.

Given that the length of the fencing is 130 yards and the area must be 1050 square yards, we can solve this problem by applying algebra and the principles of rectangle properties.

Consider 'l' to be the length of the rectangle and 'w' to be the width of the rectangle. We know that the perimeter of a rectangle is 2l + 2w. Given the total length of fencing available is 130 yards, it can be formulated as 2l + 2w = 130.

The area of a rectangle is given by l*w. As we know the area is 1050 square yards, it can be written as l*w = 1050.

We now have a pair of equations which we can solve simultaneously to find the values of 'l' and 'w'.

From the first equation, we can express 'w' as (130 - 2l) / 2. Putting this into the area equation gives us l * (130 - 2l) / 2 = 1050. Solving for 'l' we get two possible solutions: l = 30 yd or l = 100 yd. By substituting these values back into the first equation, we get the corresponding values of 'w' which are 35 yd and 15 yd respectively.

Thus, the dimensions of the pen could be either 30 yd by 35 yd or 100 yd by 15 yd.

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