Consider any conic section and discuss an application of the conic that you find
most interesting. Include an example of a mathematical equation that models
the application. Also, describe why you think this application is relevant and
beneficial to society.

PLEASE HELP ME COME UP WITH AN EQUATION USING A CONIC SECTION! Just one that I could put into a calculator.

28.68235294117647 days (29 days ) will be taken by nate and his family to take a cross country trip of 2438 miles .

Divide is the polar opposite of multiply. You get four in each group when you divide twelve into three equal groups then multiply three groups of four to create twelve. Determining how many equal groups are formed or how many individuals are in each group following a fair distribution is the fundamental goal of splitting.

speed  = 85miles / day

distance = 2438

time = 2438 / 85 = 28.68235294117647 days

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Answer:

10, 12 and 11

Step-by-step explanation:

On each median , the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint.

TZ = 2 × ZX = 2 × 5 = 10

UY = UZ + ZY = 8 + 4 = 12

ZW = \(\frac{1}{3}\) × VW = \(\frac{1}{3}\) × 33 = 11

Answer:

One Triangle

Step-by-step explanation:

It would be one triangle because a traingle has 3 sides.

Answer:

8? not sure tho....

Step-by-step explanation:

Answer:

The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect. In other words, the point of concurrency of the bisector of the sides of a triangle is called the circumcenter. It is denoted by P(X, Y). The circumcenter is also the centre of the circumcircle of that triangle and it can be either inside or outside the triangle.

Step-by-step explanation:

Steps to find the circumcenter of a triangle with vertices are:

Calculate the midpoint of given coordinates, i.e. midpoints of AB, AC, and BC

Calculate the slope of the particular line

By using the midpoint and the slope, find out the equation of the line (y-y1) = m (x-x1)

Find out the equation of the other line in a similar manner

Solve two bisector equations by finding out the intersection point

Calculated intersection point will be the circumcenter of the given triangle

Answer

\(168in^{2}\)

Step-by-step explanation:

SA=2(wl+hl+hw)

2·(6·2+9·2+9·6)

=168

Answer:

370 stores

Step-by-step explanation:

Given data

initial number of stores P= 200

r= 8%

t= 1999-2007=  8 years

Let us apply the compound interest expression to find the final amount of stores

A= P(1+r)^t

A= 200(1+0.08)^8

A= 200(1.08)^8

A= 200*1.85

A=370

Hence the number of stores in 2007 is 370 stores

Answer:

Step-by-step explanation:

If f: rn → rm is a linear map, then its derivative is simply the map itself. This is because a linear map is a function that preserves vector addition and scalar multiplication.

In other words, if we take two vectors in the domain and add them together, and then apply the linear map, it is the same as applying the linear map to each vector separately and then adding the results. Similarly, if we multiply a vector in the domain by a scalar and then apply the linear map, it is the same as multiplying the result of applying the linear map to the original vector by the same scalar.
Formally, we can express this idea using the concept of a Jacobian matrix. The Jacobian matrix of a function describes the rate at which the function changes near a particular point. For a linear map, the Jacobian matrix is simply the matrix that represents the map. This means that the derivative of f is the matrix A such that f(x) = Ax for all x in rn.
To see why this makes sense, consider the simplest case of a linear map from R1 to R1, given by f(x) = ax, where a is a constant. The derivative of this function is f'(x) = a, which is just the constant coefficient of the linear map. More generally, the derivative of a linear map f: rn → rm is the matrix A such that f(x) = Ax for all x in rn.

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Answer:   x = 41

Step-by-step explanation:

4x - 68 = 2x + 14         [since alternate interior angles are equal]

4x - 2x = 14 + 68

       2x = 82

         x = 41

Answer:

x=41

Step-by-step explanation:

this problem can be solved using the alternate interior angles converse theorem, which states that if two coplanar lines are cut by a transversal so that a pair of alternate inerior angles are congruent, then the two lines are parallel.

4x-68=2x+14

2x-68=14 <- subtract 2x from both sides

2x=82 <- add 68 to both sides

x=41 <- divide both sides by 2

check:

4(41)-68=96

2(41)+14=96

Answer:

BRAINLIEST PLEASE!

Step-by-step explanation:

Use Pythagorean theorem to solve this problem.

IN THIS CASE THE LADDER IS THE HYPOTENUSE OF THE TRIANGLE.

ladder^2 = building^2 + distance^2

where "ladder" is the length of the ladder (14 feet), "building" is the height of the building (which we don't know yet), and "distance" is the distance between the base of the ladder and the building (2 feet).

Substituting the values we know, we get:

14^2 = h^2 + 2^2

Simplifying and solving for h, we get:

h^2 = 14^2 - 2^2

h^2 = 196 - 4

h^2 = 192

h = sqrt(192)

h ≈ 13.856

Therefore, the height of the building is approximately 13.856 feet.

Answer:

0 Joules (No work)

Step-by-step explanation:

The amount of work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force applied to the car is 100 newtons, but the car does not move, so the distance over which the force is applied is 0 meters.

Therefore, the amount of work done on the car is 100 newtons * 0 meters = 0 joules. This means that no energy has been transferred to or from the car as a result of the force applied to it.

Answer:

The slope is 3/4

Step-by-step explanation:

Answer:

1/4x+27/4

Step-by-step explanation:

Here's the equation: -4y+x=-27

We'll need to isolate y on one side

subtract x from both sides

-4y=-x-27

divide everything by -4

y=1/4x+27/4

So you can substitute 1/4x+27/4 for y.

hope this helps!

She needs 3 3/4 cups more

Step-by-step explanation:

(I think you accidently put the 18 3/4 part twice) but anyways if you add 3/4 and 1/2 you get 1 and 1/4 that will be important later then you do 18 + 6 = 24 and then add your 1 and 1/4 to get a total of 25 1/4 then you just minus that from 29 and get 3 and 3/4

Hope this Helps!

Answer:

Step-by-step explanation:

y=m₁x+b₁   ║   y=m₂x+b₂   ⇔    m₁ = m₂

{Two lines are parallel if  their slopes are equal}

Changing to slope-intercept form:

2x - 3y = 9         {subtract 2x from both sides}

-3y = -2x + 9        {divide both sides by (-3)}

y = ²/₃x - 3     ⇒    m₁=²/₃   ⇒   m₂=²/₃

The line y=²/₃x+b passes through point (6, 7) so the equation:

7 = ²/₃×6 + b  is true

7 = 4 + b

b = 3

Therefore equation in  slope-intercept form:

                                                     y = ²/₃x + 3

The equation of the line passing through the point (6, 7) parallel to the line is y = 2/3x + 3

The equation in slope - intercept form :

2x - 3y = 9

-3y = 9 - 2x

Divide both sides by - 3

y = - 3 + 2/3x

Using the points (6, 7)

7 = c + 2/3(6)

7 = c + 12/3

7 = c + 4

c = 7 - 4 = 3

c = 3

The equation of the parallel line is thus :

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Answer: y= 4^3-7

Step-by-step explanation:

Answer:

We know that there are 5,569,500 strings of length 14 over the alphabet {a, b, c, d} that have exactly three a's or exactly three b's or both

Step-by-step explanation:

We can use the principle of inclusion-exclusion to count the number of strings of length 14 over the alphabet {a, b, c, d} that have exactly three a's or exactly three b's or both.

First, let's count the number of strings with exactly three a's. We can choose the positions for the three a's in ${14 \choose 3}$ ways, and for each choice, we can fill the remaining 11 positions with any of the three remaining letters (b, c, or d) in $3^{11}$ ways. Therefore, the number of strings with exactly three a's is ${14 \choose 3} \times 3^{11}$.

Similarly, the number of strings with exactly three b's is ${14 \choose 3} \times 3^{11}$.

To count the number of strings with both three a's and three b's, we can choose the positions for the three a's in ${14 \choose 3}$ ways, and choose the positions for the three b's among the remaining 11 positions in ${11 \choose 3}$ ways. Then, we can fill the remaining 8 positions with any of the two remaining letters (c or d) in $2^8$ ways. Therefore, the number of strings with both three a's and three b's is ${14 \choose 3} \times {11 \choose 3} \times 2^8$.

By the principle of inclusion-exclusion, the total number of strings with exactly three a's or exactly three b's or both is:

(

14

3

)

×

3

11

+

(

14

3

)

×

3

11

−

(

14

3

)

×

(

11

3

)

×

2

8

(

3

14

​

)×3

11

+(

3

14

​

)×3

11

−(

3

14

​

)×(

3

11

​

)×2

8

Simplifying this expression gives:

2

×

(

14

3

)

×

3

11

−

(

14

3

)

×

(

11

3

)

×

2

8

2×(

3

14

​

)×3

11

−(

3

14

​

)×(

3

11

​

)×2

8

Plugging in the values gives us:

2

×

(

14

3

)

×

3

11

−

(

14

3

)

×

(

11

3

)

×

2

8

=

5

,

569

,

500

2×(

3

14

​

)×3

11

−(

3

14

​

)×(

3

11

​

)×2

8

=5,569,500

Therefore, there are 5,569,500 strings of length 14 over the alphabet {a, b, c, d} that have exactly three a's or exactly three b's or both

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Answer:

\( \sqrt{3(1 + \sqrt{3)} } = 2.86\)

Step-by-step explanation:

\(1. \: \sqrt{3 + 3 \sqrt{3} } \\ 2. \: \sqrt{3(1 + \sqrt{3)} } = 2.86\)

Answer:

1.   E:  20a - 18

2.  D:  42

3.  G:  17b + 3

4.  I:  105

CODE: EDGI

Step-by-step explanation:

Question 1

Perimeter of a rectangle = 2W + 2L

(where W is the width and L is the length)

Given:

Perimeter = 2(2a + 3) + 2(8a - 12)

                 = 4a + 6 + 16a - 24

                 = 20a - 18

Question 2

When a = 3

⇒ perimeter = 20(3) -18

                     = 60 - 18

                     = 42 centimeters

Question 3

The dashes on the side lengths mean those sides are equal in length.

⇒ perimeter = (7b - 2) + (7b - 2) + (3b + 7)

                     = 17b + 3

Question 4

When b = 6

⇒ perimeter = 17(6) + 3

                     = 102 + 3

                     = 105 meters

Answer:

Step-by-step explanation:

You want to know the domain and range of the relation {(-1, 5). (3, 4), (2, 5), (-1, -3)}, and whether it is a function.

The domain is the list of x-values in the (x, y) pairs. We conventionally eliminate duplicates and put them in order.

  { -1, 2, 3} . . . . domain

The range is the list of y-values in the (x, y) pairs. Again, duplicates are eliminated, and they are put in order.

  {-3, 4, 5} . . . . range

The mapping diagram is a visual aid that has domain values on the left, range values on the right, and arrows showing how the domain values map to the range values. Such a diagram is attached.

If there are multiple arrow tails extending from any given domain value, the relation is not a function. This relation maps -1 to multiple values, so it is not a function.

The interest earned increases with higher principal amounts, higher interest rates, and longer time periods.

Principal (P) | Interest Rate (r) | Time Period (t) | Interest Earned (I)

$1,000 | 2% | 1 year | $20

$5,000 | 4% | 2 years | $400

$10,000 | 3.5% | 3 years | $1,050

$2,500 | 1.5% | 6 months | $18.75

$7,000 | 2.25% | 1.5 years | $236.25

To calculate the interest earned (I), we can use the simple interest formula: I = P * r * t.

For the first row, with a principal of $1,000, an interest rate of 2%, and a time period of 1 year, the interest earned is calculated as follows: I = $1,000 * 0.02 * 1 = $20.

For the second row, with a principal of $5,000, an interest rate of 4%, and a time period of 2 years, the interest earned is calculated as follows: I = $5,000 * 0.04 * 2 = $400.

For the third row, with a principal of $10,000, an interest rate of 3.5%, and a time period of 3 years, the interest earned is calculated as follows: I = $10,000 * 0.035 * 3 = $1,050.

For the fourth row, with a principal of $2,500, an interest rate of 1.5%, and a time period of 6 months (0.5 years), the interest earned is calculated as follows: I = $2,500 * 0.015 * 0.5 = $18.75.

For the fifth row, with a principal of $7,000, an interest rate of 2.25%, and a time period of 1.5 years, the interest earned is calculated as follows: I = $7,000 * 0.0225 * 1.5 = $236.25.

These calculations show the interest earned for different savings principals, interest rates, and time periods.

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Answer:

8 + 6x < 44

Step-by-step explanation:

x = the number of games played

Step-by-step explanation:

Let the 5 even integers be x-4,x-2,x,x+2,x+4

Hence, x-4+x-2+x+x+2+x+4=530

Hence, 5x=530

Hence, x=530/5

Hence,x=106

so.. the integers are 102,104,106,108,110

The most appropriate method for creating an estimate of the percent of district residents who support the building of a new middle school would be  v. A one-sample z-interval for a population proportion.

In this case, the superintendent wants to estimate the proportion (percentage) of district residents who support the building of a new middle school. To achieve this, a random sample of district residents can be selected, and the proportion of residents in the sample who support the new middle school can be calculated.

Since the sample size is relatively large (as it is a large school district), the sampling distribution can be assumed to follow a normal distribution. Therefore, a one-sample z-interval for a population proportion is suitable for estimating the proportion of district residents who support the new middle school.

Using this method, a confidence interval can be constructed around the sample proportion, providing an estimate of the true proportion of district residents who support the new middle school, along with a measure of uncertainty.

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Answer:

so u will pay 3.82 and u will save 15.26 dollars

Step-by-step explanation:

Answer:

14.40$

Step-by-step explanation:

Answer:

option d

Step-by-step explanation:

(-3m⁴)(6m⁶)

-18m¹⁰

With a down payment of $15,000, an annual income of $90,000, and a 30-year mortgage rate of 5%, you should be able to afford a house with a median price of $350,000 in your area.

To determine how expensive of a house you can afford, we need to consider several factors, including your income, down payment, mortgage rate, and the median house price.

First, let's calculate the loan amount. Subtracting your down payment of $15,000 from the median house price of $350,000 gives us a loan amount of $335,000.

Next, we need to calculate your monthly mortgage payment. To do this, we will use the 30-year mortgage rate of 5%. Converting this annual rate to a monthly rate, we get 0.05/12 = 0.0042.

Using an online mortgage calculator, we can determine that the monthly mortgage payment for a $335,000 loan at a 5% interest rate is approximately $1,794.

To determine how much you can afford, we need to consider your income. Assuming an annual income of $90,000, we can estimate your monthly income by dividing it by 12, which gives us $7,500.

As a general rule, lenders typically recommend that your monthly mortgage payment should not exceed 28% of your monthly income. In your case, 28% of $7,500 is $2,100.

Since your estimated monthly mortgage payment of $1,794 is below $2,100, you should be able to afford a house with a median price of $350,000, given your income, down payment, and mortgage rate.

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