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The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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Answer:

A) x=6

Step-by-step explanation:

6.5^2-2.5^2=x^2

42.25-6.25=x^2=36

x=6

Answer:

it is A-6 hope this helps

Step-by-step explanation:

The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. So the correct option is D.

Correlational method is a research technique used to explore the relationship between two or more variables. In this method, researchers collect data on the variables of interest and analyze their patterns of association. The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. This means that researchers are interested in exploring whether changes in one variable are associated with changes in another variable.

For instance, a researcher may be interested in exploring the relationship between stress and job performance. The researcher may collect data on the levels of stress and job performance in a sample of employees and then use statistical analysis to determine if there is a systematic relationship between the two variables. If the results show that higher levels of stress are associated with lower levels of job performance, then the researcher can conclude that there is a negative correlation between the two variables.

It is important to note that correlation does not imply causation. While a correlation between two variables indicates that they are related, it does not necessarily mean that changes in one variable are causing changes in the other variable. Therefore, researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

Therefore, the fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way, and researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

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9514 1404 393

Answer:

  (b)  24 m²

Step-by-step explanation:

After dilation by a factor of 2, the base is 2×3 m = 6 m, and the height is 2×4 m = 8 m. Then the area of the dilated triangle is ...

  A = 1/2bh

  A = 1/2(6 m)(8 m) = 24 m²

Answer:

A. 846 cm²

Step-by-step explanation:

1539 ÷ 19 = 81

√81 = 9

9 · 9 · 81 = 1539

A = 2(wl + hl + hw)

A = 2(19 · 9 + 9 · 9 + 9 · 19)

846 cm²

Answer:

3 toppings

Step-by-step explanation:

11.65

-7.90

3.75

3.75/1.25=3 toppings

After calculating the between group sum of squares and the within group sum of squares, the next step is to calculate the mean square between and the mean square within. This is achieved by dividing each sum of squares by its respective degrees of freedom. (Option D)

The term sum of squares is a statistical measure used in regression analysis to calculate the dispersion of data points. The sum of squares determines the deviation of data points from the mean value also known as variation. A higher sum of squares indicates higher variability while a lower result indicates low variability from the mean. It is used to determine the function that best fits i.e., which varies the least from the data. To calculate the sum of squares, subtract the data points from the mean, square the differences, and add them together. The mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable. Mean square is determined by sum of squares by its respective degrees of freedom.

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Answer:

Function 1 has the greatest rate of change.

Step-by-step explanation:

The rate of change is also known as the slope.

Slope is rise over run: change in y over change in x.

Function 1's slope: 3 / 2

Function 2's slope: (0 - (-4)) / (5 - (-5)) = 4/10 = 2/5

3/2 > 2/5

Function 1 has the greatest rate of change.

Answer:

D

Step-by-step explanation:

Answer:

D. (6, 9)

Step-by-step explanation:

B(2, 3) → B'(6, 9)

multiply by 3

Answer:

The equation of the line is; y = 0.5·x + 2

Step-by-step explanation:

The points that define the line CD = C(-2, 1) and D(10, 7)

The equation of the line can be presented in the form of the general equation of a straight line, y = m·x + c

Where;

m = The slope of the line = \(\dfrac{7 - 1}{10 - (-2)} = \dfrac{1}{2} = 0.5\)

c = The y-intercept

From the obtained slope, m = 0.5, using point D(10, 7), the equation of the line in point and slope form is therefore;

y - 7 = 0.5·(x - 10)

From the above equation of the line in point and slope form, we get the general form of the equation of the line as follows

y - 7 = 0.5·(x - 10) = 0.5·x - 5

y - 7 = 0.5·x - 5

y = 0.5·x - 5 + 7 = 0.5·x + 2

y = 0.5·x + 2

The equation of the straight line in general is y = 0.5·x + 2.

The fan blades will have rotated 180 degrees when vertex D reaches the point where vertex C is now.

When the two fan blades in the shape of equilateral triangles rotate clockwise around point P, the vertex D will reach the point where vertex C is now.
To determine the number of degrees the blades will have rotated, we need to know the number of degrees in a full rotation. A full rotation consists of 360 degrees.
Since both blades rotate together, they will cover the same number of degrees. Therefore, when vertex D reaches the point where vertex C is now, the blades will have rotated by half of a full rotation, which is 180 degrees.

In summary, the fan blades will have rotated 180 degrees when vertex D reaches the point where vertex C is now.

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Since B is invertible, it follows that A = -B/2 is also invertible. Thus, we have proven that A is invertible.

To prove that matrix A is invertible, we need to show that it has an inverse matrix. From the given equation:

\(2A^3 = I_n - 3A\)

Let's start by rearranging the equation:

\(2A^3 + 3A - I_n = 0\)

Now, let B = -2A. We can rewrite the equation as:

\(B^3 + 3/2 B + I_n = 0\)

We want to prove that A is invertible, which is equivalent to proving that B is invertible since A = -B/2.

Assume, for the sake of contradiction, that B is not invertible. This means that there exists a non-zero vector x such that Bx = 0.

Consider the equation \(B^3 + 3/2 B + I_n = 0.\)Multiply both sides of the equation by x:

\(B^3x + (3/2)Bx + I_nx = 0xB^3x + I_nx = 0\)

We can rearrange this equation as follows:

\((B^3 + I_n)x = 0\)

Since x is non-zero and B^3 + I_n = 0, we have:

\(B^3x = -IxB^3x = -x\)

Now, let's consider the eigenvectors of B. Suppose v is an eigenvector of B with eigenvalue λ. We have:

Bv = λv

We can raise both sides to the power of 3:

\(B^3v = λ^3vSince B^3x = -x, we have:λ^3v = -x\)

This implies that \(λ^3\) is an eigenvalue of B corresponding to the eigenvector -x. However, since x is non-zero and \(λ^3v = -x,\)it means that -λ^3 is also an eigenvalue of B corresponding to the eigenvector x.

Now, consider the polynomial p(t) = \(t^3 + 1.\)The eigenvalues of B are roots of this polynomial. We have shown that both λ^3 and -λ^3 are eigenvalues of B, which means that p(t) has at least two distinct eigenvalues.

However, this contradicts the fact that a square matrix can have at most n distinct eigenvalues. Since B is an n × n matrix, it can have at most n distinct eigenvalues. Therefore, our assumption that B is not invertible must be false.

Since B is invertible, it follows that A = -B/2 is also invertible. Thus, we have proven that A is invertible.

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Answer:

y= -\(\frac{3}{2} \\\) +2    

y=2

Step-by-step explanation:

1. 3x+2y=4      subtract 3x on both sides to isolate 2y

  -3x    =-3x

   2y=-3x+4

2. 2y=-3x+4    divide both sides by 2 to isolate y

   2      2

y=-\(\frac{3}{2\\}\) +2            this is the equivalent equation

To solve for y.

1. substitute 0 for x

 y= -\(\frac{3}{2}\)(0) + 2

2. anything multiplied by 0 is 0

y=2

2 hours will pass before they meet.

"Information available from the question"

In the question:

Aaron starts riding a bike at a rate of 3 mi/h on a road toward a store 20 mi away.

Zhang leaves the store when Aaron starts riding his bike, and he rides his bike toward Aaron along the same road at 2 mi/h.

Now, According to the question:

Total distance = 20mi

Aaron starts riding a bike at a rate of  = 3mi/h

Zhang rides his bike toward Aaron along the same road at  = 2mi/h

Let y be the number of hours for them to meet.

The expression is given as

3y + 2y = 20

solving for y, we have

5y = 20

y = 20/5

y = 4hrs

Therefore, 2 hours will pass before they meet.

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The equation of the plane passing through the points \((0, 6, 6), (6, 0, 6), and (6, 6, 0)\) is \(36x + 36y + 36z = 432\).

To find the equation of the plane passing through the points \((0, 6, 6), (6, 0, 6), and (6, 6, 0)\), we can use the point-normal form of the equation of a plane.

Step 1: Find two vectors in the plane.

Let's find two vectors by taking the differences between the given points:

Vector v₁ = \((6, 0, 6) - (0, 6, 6) = (6, -6, 0)\)

Vector v₂ = \((6, 6, 0) - (0, 6, 6) = (6, 0, -6)\)

Step 2: Find the normal vector.

The normal vector is perpendicular to both v₁ and v₂. We can find it by taking their cross product:

Normal vector n = v₁ \(\times\) v₂ = \((6, -6, 0) \times (6, 0, -6) = (36, 36, 36)\)

Step 3: Write the equation of the plane.

Using the point-normal form, we can choose any point on the plane (let's use the first given point, \((0, 6, 6)\)), and write the equation as:

n · (x, y, z) = n · (0, 6, 6)

Step 4: Simplify the equation.

Substituting the values of n and the chosen point, we have:

(36, 36, 36) · (x, y, z) = (36, 36, 36) · (0, 6, 6)

Simplifying further:

\(36x + 36y + 36z = 0 + 216 + 216\\36x + 36y + 36z = 432\)

Therefore, the equation of the plane passing through the given points is:

\(36x + 36y + 36z = 432\)

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The correct answer is answer choice- A.

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

See the attached worksheet. The use of a filled or unfilled circle on a number indicates whether that actual number is included (solid circle) or not included (empty circle)  A solid bar between two points telss us these points are all included.  

 -3<x<3 does not have an equality ("=") for ether +3 nor -3.  The the line between those points would be solid (all points are allowed).  Either 3 would be an empty circle.  

Option A seems to have these features.

Answer:

30/40 and 12/16 are equivalent fractions.

As per the given measurement, the scale drawing of the barn is attached below.

The term scale drawing is defined as a real object with accurate sizes reduced or enlarged by a certain amount.

Here we have given that a  barn is 40 feet wide by 100 feet long.

Here we have given in the question that if you draw a line that is 1/2 an inch on paper its proportional to 10 feet long on the house.

Which means that 1 inch would be 20, then 1.5 would be 30 feet, and then 2 inches would be 40.

Here we have given the proportion would be written as,

=> 2 in: 40 ft

As we know that if we make the ratios equal, then we have,

=> 1/20 = x/40

When we simplify this then we get the value of x as 2

Similarly, for the another one,

=> 1/20 = x/100

Now, we have to multiply both sides by 100:

=> 100/20 = x

Therefore, the value of x is 5.

Hence the scale drawing of the house would be 2 inches wide and 5 inches long.

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Answer:

Step-by-step explanation:

The answer is B, if we were to plug all the values of x with its corresponding value of y into the equation, everything matches up

Hope that helps

Answer:

125 over 343 as a fraction and 0.364431 as a decimal

Step-by-step explanation:

hope this helps dont know if its right

Answer:

125/343

Step-by-step explanation:

Answer:

55 pages per hour

Step-by-step explanation:

You divide 165 by 3 = 55

Answer:

Step-by-step explanation:

13.48x − 200 < 256.12

Using the addition property , add 200 to both sides

That's

13.48x + 200 - 200 < 256.12 + 200

13.48x < 456.12

Divide both sides by 13.48

\( \frac{13.48x}{13.48} < \frac{456.12}{13.48} \\ x < \frac{456.12}{13.48} \\ \: \: \: x < 33.83679\)

We have the final answer as

x < 33.84 to the nearest hundredth

Hope this helps you

Answer: A: 3 square feet per minute

Step-by-step explanation:

The square feet more that Paula can shovel in 1 minute more than Melinda is 3 square feet per minute.

30x + + 30y = 450 equation 1

20x + 25y = 345 equation 2

Where:

x = square feet shovelled by Melinda

y = square feet shovelled by Paula

The first step is to multiply equation 1 by 20 and equation 2 by 30

600x + 600y = 9000 equation 3

600x + 750 y = 10,350 equation 4

Subtract equation 3 from equation 4

150y = 1350

Divide both sides by 150

y = 9 square meters

Substitute for y in equation 1

30x + 30(9) = 450

30x + 270 = 450

30x = 450 - 270

30x = 180

x = 6 square meters

9 - 6 = 3 square meters

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Answer:

47

Step-by-step explanation:

You need to get c by itself

First add 25 to both sides of the equation

2c-25=69

    +25    +25

The 25s on the left side cancel and 69+25 is 94

2c=94

Divide by 2 to get the value of c

c=47

The number of bars he sold is 47

The estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

To estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints, we can use the right Riemann sum method.

The width of each rectangle, Δx, is given by the interval width divided by the number of rectangles.

In this case, Δx = (π/2 - 0)/4 = π/8.

To calculate the right endpoint values, we evaluate f(x) at the right endpoint of each rectangle.

For the first rectangle, the right endpoint is x = π/8.

For the second rectangle, the right endpoint is x = π/4.

For the third rectangle, the right endpoint is x = 3π/8.

And for the fourth rectangle, the right endpoint is x = π/2.

Now, let's calculate the area for each rectangle by multiplying the width (Δx) by the corresponding height (f(x)):

Rectangle 1: Area = f(π/8) * Δx = 5cos(π/8) * π/8

Rectangle 2: Area = f(π/4) * Δx = 5cos(π/4) * π/8

Rectangle 3: Area = f(3π/8) * Δx = 5cos(3π/8) * π/8

Rectangle 4: Area = f(π/2) * Δx = 5cos(π/2) * π/8

Now, let's calculate the values:

Rectangle 1: Area = 5cos(π/8) * π/8 ≈ 0.2887

Rectangle 2: Area = 5cos(π/4) * π/8 ≈ 0.3142

Rectangle 3: Area = 5cos(3π/8) * π/8 ≈ 0.2887

Rectangle 4: Area = 5cos(π/2) * π/8 ≈ 0

Finally, to estimate the total area, we sum up the areas of all four rectangles:

Total Area ≈ 0.2887 + 0.3142 + 0.2887 + 0 ≈ 0.8916

Therefore, the estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

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Answer:maybe 9 but if not is 8 and the seond is 321

Step-by-step explanation: