1) A comet that passes through the solar system just once has a path that is modeled by a conic section. Astronomers discover a comet whose path is modeled by the following equation, with the Sun at one focus. What type of conic section is the comet's path?
x^2/2,500-y^2/37,500=1

2) What are the vertices of the comet's path? (Hint: Examine the general formula for the path and identify the numbers that determine the vertices.)

3) At its closest point to the Sun, this comet is ____ million miles from the Sun. (Enter only the number.)
Hint: Subtract the vertex from the focus

The height of the telephone pole is approximately 20.79 feet, calculated using tangent function with a 30° angle.

To find the height of the telephone pole, we can use trigonometry. We'll use the tangent function since we have the opposite side and the adjacent side of the right triangle formed by the person, the pole, and the ground.

Let [tex]\( h \)[/tex] be the height of the pole.

We have the tangent of the angle:

[tex]\[ \tan(30^\circ) = \frac{h}{36} \][/tex]

Now, we can solve for [tex]\( h \):[/tex]

[tex]\[ h = 36 \times \tan(30^\circ) \][/tex]

Let's calculate:

[tex]\[ h = 36 \times \tan(30^\circ) \]\[ h = 36 \times 0.5774 \] (rounded value of tan(30°))\[ h \approx 20.7864 \][/tex]

So, the height of the telephone pole is approximately 20.79 feet.

Answer:

Part 4) Right triangle

Part 5) Kite

Step-by-step explanation:

Part 4) What kind of triangle is made by connecting the points A(0, –6), B(3, –6), and C(3, –2)?

Using a graphing tool    

see the attached figure N [tex]1[/tex]

The triangle of the figure is not equilateral------> The triangle does not have three equal sides

The triangle of the figure is a right triangle------>The triangle  has an angle of [tex]90\°[/tex]

The triangle of the figure is not isosceles------> The triangle does not have two equal sides

The triangle of the figure is not a right and isosceles

Part 5) What type of quadrilateral is formed by connecting the points [tex](0, 9), (3, 6), (0, 1), and (-3, 6)[/tex]?                

Using a graphing tool    

see the attached figure N [tex]2[/tex]        

The figure is not a rhombus------> All sides are not congruent  

The figure is not a trapezoid-----> has not parallel sides

The figure is a kite------> Two disjoint pairs of consecutive sides are congruent and the diagonals meet at a right angle

Answer:      U7L7

Polygons in the coordinate plane

1.D

2.A

3.D

4.B

5.C

Step-by-step explanation:

Answer:

its c on edge babes, yw <3

Step-by-step explanation:

Grant should remove approximately 7.33 gallons of water to obtain a 24% ammonia solution from the initial 16% ammonia solution.

Let x be the number of gallons of water that Grant needs to remove.

The equation you can use to represent this situation is based on the principle of maintaining the amount of ammonia in the solution:

The amount of ammonia in the original solution = The amount of ammonia in the final solution

The amount of ammonia in the original solution is the product of the initial concentration (16%) and the initial volume (22 gallons).

The amount of ammonia in the final solution is the product of the desired concentration (24%) and the final volume (22 - x gallons, where x is the amount of water removed).

So, the equation becomes:

0.16 * 22 = 0.24 * (22 - x)

Now, you can solve this equation for "x" (the number of gallons of water to remove) to achieve the desired concentration:

0.16 * 22 = 0.24 * (22 - x)

3.52 = 5.28 - 0.24x

Now, isolate the variable "x" by subtracting 3.52 from both sides:

0.24x = 5.28 - 3.52

0.24x = 1.76

Now, divide both sides by 0.24 to solve for "x":

x = 1.76 / 0.24

x ≈ 7.33

To know more about ammonia solution click here :

https://brainly.com/question/1642219

#SPJ12

To find the arithmetic means in the given sequence, we fill in the missing numbers using the average of the numbers before and after them. The arithmetic means in the given sequence are 160, 175, and 190.

To find the arithmetic means in the given sequence, we need to fill in the missing numbers.

Given sequence: 145, __, __, __, 205.

The arithmetic mean is the average of two numbers. We can find the missing numbers by taking the average of the numbers before and after them.

First, let's find the missing number between 145 and 205. The average of 145 and 205 is 175. So, the missing numbers are:

145, 175, 175, 175, 205.

To find the last missing number, we can take the average of the two numbers after it: (175 + 205) / 2 = 190.

So, the arithmetic means in the given sequence are 160, 175, and 190.

https://brainly.com/question/34270619

#SPJ2

The solution to the first problem is that Julia can watch up to 3.5 more hours of TV this week. The solution to the second problem is that you need to watch 30 more movies to earn a free movie pass. An example of an equation with infinitely many solutions is x = x.

19. To represent this scenario as an inequality, we let T be the amount of television Julia can still watch this week. Since she can watch no more than 5 hours per week and she has already watched 1.5 hours, we subtract 1.5 from 5. So we have the inequality T + 1.5 <= 5. Subtracting 1.5 from both sides gives us the inequality T <= 3.5. So Julia can watch 3.5 more hours of TV this week.

20. Let m be the number of movies you need to watch to get a free movie pass. Each movie gives you 2 advantage points and you currently have 40 points. The equation to model this situation is 2m + 40 = 100. Subtracting 40 from both sides gives 2m = 60. Dividing by 2 gives m = 30. So you need to watch 30 more movies to get a free movie pass.

21. An equation with infinitely many solutions is one where all the terms on one side can be made identical to all the terms on the other side. A simple example is x = x. For every value of x, the equation holds, meaning it has an infinite number of solutions.

https://brainly.com/question/29731212

#SPJ3

In the diagram, the pair of angles ∠1 and ∠7 form a pair of alternate exterior angles.

Here is the reason:

Within the graph, ∠1 and ∠7 are on the inverse sides of transversal t and exterior lines a and b. Subsequently, they are a combination of substitute outside points.

The other answer choices are not correct since:

Laplace transformation is the transformation in the integral form which convert a function of a real variable to a complex variable.

The Laplace transform of the given function is,

[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]

Laplace transformation is the transformation in the integral form which convert a function of a real variable to a complex variable.

Given information-

The function given in the problem is,

[tex]t^{2}\sin(2t)[/tex]

By the Laplace transform we can write that,

[tex]L[t^{2}\sin(2t)]=(-1)^2\dfrac{d^2}{ds^2}L(\sin 2t)\\L[t^{2}\sin(2t)]=\dfrac{d}{ds}\;\dfrac{d}{ds}\dfrac{2}{s^2+4}\\L[t^{2}\sin(2t)]=\dfrac{d}{ds}\left [\dfrac{-4s}{(s^2+4)^2} \right ]\\[/tex]

Solve further to get the final result,

[tex]L[t^{2}\sin(2t)]=\left [\dfrac{(s^2+4)^2(-4)+4s(s^2+4)\times2s}{(s^2+4)^2} \right ]\\[/tex]

Simplify the above equation as,

[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]

Hence, the Laplace transform of the given function is,

[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]

Learn more about the Laplace transform here; https://brainly.com/question/17062586

Answer:

1

Step-by-step explanation:

6 Is rounded to 10 like 0.6 is rounded to 1

The final equation is vf = [tex]\frac{(m1v1 + m2v2)}{(m1 + m2)}[/tex]

The given equation represents the conservation of momentum, which can be written as :

m1v1 + m2v2 = (m1 + m2) vf

To solve for vf, follow these steps :

Answer:

Its D) 8t + 16 = 200

Answer:  The correct option is (d) [tex]8t+16=200.[/tex]

Step-by-step explanation:  Given that Benito is selling T-shirts for $8 each for his school fund-raiser and he has sold 16 T-shirts till now.

We are to find the number of T-shirts that he still need to sell to reach his goal of $200 in sales.

The number of T-shirts still he needs to sell is represented by t.

The, according to the given information, we have

[tex]8(t+16)=200\\\\\Rightarrow 8t+128=200\\\\\Rightarrow 8t=200-128\\\\\Rightarrow 8t=72\\\\\Rightarrow t=\dfrac{72}{8}\\\\\Rightarrow t=9.[/tex]

So, the number of T-shirts that he still needs to sell is 9.

Now, we can see from the above steps of solution for t that options (a), (b) and (c) gives the correct value of t, but from option (d), we get

[tex]8t+16=200\\\\\Rightarrow 8t=200-16\\\\\Rightarrow 8t=184\\\\\Rightarrow t=23\neq 9[/tex]

So, option (d) does NOT solve for the correct value of t.

Thus, (d) is the correct option.

Answer:

Option 2 is correct.

Step-by-step explanation:

In the given graph x-axis represents the numbers and y-axis represent the frequency.

Number         Frequency              Cumulative frequency

100                        14                              14

200                       6                               20   (20<36)

300                       18                              38  (38>36)

400                       12                              50

500                       2                               52

600                       12                              64

700                       8                               72

Total                     72          

Mode is the number which has highest frequency. From the above table it is noticed that the highest frequency is 18 at 300. Therefore mode of the data is 300.

Sum of frequency is 72, which is an even number.

[tex]Median=\frac{n}{2}\text{th term}[/tex]

[tex]Median=\frac{72}{2}\text{th term}[/tex]

[tex]Median=36\text{th term}[/tex]

We have to find the number whose cumulative frequency is more than 36 but preceding cumulative frequency is less than 36.

Median of the graph is 300.

Since the value of median and mode are same, therefore

[tex]median=mode[/tex]

Option 2 is correct.

The trains will meet at 6:40 P.M. after traveling at different speeds towards each other.

The trains will meet at 6:40 P.M.

To calculate the time when the trains will meet, we need to determine the time it takes for the second train to cover the distance that the first train has already covered.

The first train covers the 200-mile distance in 200 / 75 = 2.67 hours, which is 2 hours and 40 minutes.

The second train leaves at 5:00 P.M., so adding 2 hours and 40 minutes gives us 7:40 P.M. as the time the second train reaches the meeting point.

By then, the first train has been traveling for 3 hours and 40 minutes, making the meeting time 6:40 P.M.

Answer:

Step-by-step explanation:

Yes

The correct option is:

4(3x² + 1)(x – 5)

To find the completely factored form of the expression 12x³ – 60x² + 4x – 20, we can first factor out the greatest common factor, which is 4.

4(3x³ – 15x² + x – 5)

Next, we can factor the quadratic expression 3x³ – 15x² + x – 5 by grouping:

4[3x²(x – 5) + 1(x – 5)]

4(3x² + 1)(x – 5)

Therefore, the completely factored form of 12x³ – 60x² + 4x – 20 is:

4(3x² + 1)(x – 5

So, the correct option is:

4(3x² + 1)(x – 5)

You made a typo in your question.

The equation should be y = 2x - 3.

y = 2(-1) - 3

y = -2 - 3

y = - 5

Answer:

Option C. (n + 1)/(n +2).

Step-by-step explanation:

The given sequence is 2/3, 3/4, 4/5, 5/6, 6/7.

and we have to find the general term of the given sequence.

Since first term of the sequence is 2/3

So numerator can be represented as (n + 1) and the denominator as (n + 2)

Therefore the general term will be (n + 1)/(n + 2)

Option C is the answer.

Final answer:

The number that, when multiplied by itself 4 times equals 81, is 3, as 3 to the fourth power (3^4) is 81.

Explanation:

To find what number multiplied by itself 4 times equals 81, we need to find the fourth root of 81. The fourth root is the same as raising a number to the 0.25 power. To calculate manually, we may take two square roots in succession, since the square root of a number squared is the original number. The square root of 81 is 9, and the square root of 9 is 3, thus the fourth root of 81 is 3. Indeed, 34 = 3 × 3 × 3 × 3 = 81.

we know that

The standard form of the equation of the line is

[tex] Ax + By = C [/tex]

we have

[tex] y = \frac{1}{6}x + 4 [/tex]

Multiply by [tex] 6 [/tex] both sides

[tex] 6y = x+24 [/tex]

Subtract x both sides

[tex] -x+6y = 24 [/tex]

therefore

the answer is

the equation of the line in standard form is equal to

[tex] -x+6y = 24 [/tex]

Answer: The explicit rule for the sequence will be

[tex]a_n=15.5-2.5n[/tex]

Step-by-step explanation:

Since we have given that

[tex]13,10.5,8,5.5,3,0.5.....[/tex]

Here,

a = first term = 13

d = common difference

[tex]a_2-a_1 = 10.5-13=-2.5[/tex]

Since it forms an A.P. ;

[tex]a_n=a+(n-1)d\\\\a_n=13+(n-1)(-2.5)\\\\a_n=13-2.5n+2.5\\\\a_n=15.5-2.5n[/tex]

Hence, the explicit rule for the sequence will be

[tex]a_n=15.5-2.5n[/tex]

Answer:

[tex]a_n[/tex]  [tex]= 15.5-2.5n[/tex]

Step-by-step explanation:

c The probability that event A occurs, given that event B occurs, is 83%.