What is 681x239 please help

Por restricciones de longitud no es posible resumir las respuestas asociadas a esta pregunta, invitamos cordialmente a leer la explicación para mayores detalles sobre el análisis de secciones cónicas.

Según la geometría analítica, existen cinco tipos de secciones cónicas: (i) Circunferencia, (ii) Parábola, (iii) Elipse, (iv) Hipérbola, (v) Recta. 2) a) La ecuación estándar de la circunferencia se caracteriza con el centro (h, k) y la longitud del radio (r):

(x - h)² + (y - k)² = r²

(x - 2)² + (y + 1)² = 4²

b) La longitud del radio de la circunferencia se obtiene por el teorema de Pitágoras sobre la longitud del segmento CP:

r = √[(4 - 1)² + (6 - 3)²]

r = √(3² + 3²)

r = 3√2

(x - 1)² + (y - 3)² = 18

3) a) El eje focal forma parte del eje de simetría de la parábola. La ecuación estándar de la parábola es:

4 · p · x = y²      

Donde p es la distancia entre el foco y el vértice.

Si tenemos que (x, y) = (2, 4), entonces la ecuación de la parábola es:

4 · p · 2 = 4²

p = 2

8 · x = y²

Las coordenadas del foco de la parábola son de la forma (x, y) = (h + p, k):

F(x, y) = (2, 0)

Ahora se determinan los extremos del lado recto: (x = 2)

8 · 2 = y²

y = ± 4

Los extremos del lado recto son (2, 4) y (2, - 4), cuya longitud de segmento es 8 unidades.

b) El eje focal forma parte del eje de simetría de la parábola. La ecuación estándar de la parábola es:

4 · p · x = y²      

Si tenemos que (x, y) = (6, 3), entonces la ecuación de la parábola es:

4 · p · 6 = 3²

p = 8 / 3

(32 / 3) · x = y²

Las coordenadas del foco son F(x, y) = (8 / 3, 0).

Ahora se determinan los extremos del lado recto: (x = 6)

(32 / 3) · 6 = y²

y = ± 8

Los extremos del lado recto son (6, 8) y (- 6, - 8), cuya longitud de segmento es 16 unidades.

4) a) Tenemos una ecuación estándar de la forma 4 · p · y = x². A continuación, hallamos todas las variables requeridas:

x² = 8 · y

p = 2

Directriz: y = - 2, Foco: F(x, y) = (0, 2), Longitud del lado recto: 4

b) Tenemos una ecuación estándar de la forma 4 · p · x = y². A continuación, hallamos todas las variables requeridas:

y² = - (3 / 2) · x

p = - 3 / 8

Directriz: x = 3 / 2, Foco: F(x, y) = (- 3 / 2, 0), Longitud del lado recto: 3.

5) En esta parte debemos manipular algebraicamente las ecuaciones hasta su forma estándar para determinar los datos requeridos de cada caso. La ecuación estándar de la elipse tiene el siguiente problema:

(x - h)² / a² + (y - k)² / b² = 1      

Donde:

a) 81 · x² + 144 · y² = 11664

x² / 144 + y² / 81 = 1

x² / 12² + y² / 9² = 1

Longitud del semieje mayor: 12

Longitud del semieje menor: 9

c = √(12² - 9²)

c ≈ 7.937

Coordenadas de los focos: F₁ (x, y) = (- 7.937, 0), F₂ (x, y) = (7.937, 0)

Vértices: V₁ (x, y) = (- 12, 0), V₂ (x, y) = (12, 0)

Longitud del lado recto

144 · y² = 11664 - 81 · x²

y² = (11664 - 81 · x²) / 144

y = ± (1 / 12) · √(11664 - 81 · x²)

y = ± (1 / 12) · √(11664 - 81 · 7.937²)

y = ± 6.750

La longitud del lado recto es 13.5.

b) 36 · x² + 25 · y² = 3600

x² / 10² + y² / 12² = 1

Longitud del semieje mayor: 12

Longitud del semieje menor: 10

c = √(12² - 10²)

c ≈ 6.633

Coordenadas de los focos: F₁ (x, y) = (0, - 6.637), F₂ (x, y) = (0, 6.637)

Vértices: V₁ (x, y) = (0, - 12), V₂ (x, y) = (0, 12)

Longitud del lado recto

36 · x² = 3600 - 25 · y²

x² = 100 - (25 / 36) · y²

x = √[100 - (25 / 36) · y²]

x = √[100 - (25 / 36) · 6.637²]

x = ± 8.331

La longitud del lado recto es 16.662.

Para aprender más sobre secciones cónicas: https://brainly.com/question/16156916

#SPJ1

The angle that represents an exterior angle of the given triangle is: D. ∠CAB.

An exterior angle of a triangle is the angle that is located outside a triangle on an extended adjacent side of the triangle.

In the image given, and considering the options we have, ∠CAB is located outside a triangle ABF on an extended adjacent side CF of the triangle.

Therefore, the answer is: D. ∠CAB.

Learn more about the exterior angle of a triangle on:

https://brainly.com/question/17972372

#SPJ1

Answer:

  (a)  6 x (21 ÷ 3) + 8

Step-by-step explanation:

The first step in translating English to math is to understand the English.

The quotient of 21 and 3 is written (21 ÷ 3). Six times that quotient is ...

  6×(21÷3)

When 8 is added to this, it becomes ...

  6 × (21 ÷ 3) + 8

Answer:

Step-by-step explanation:

Initial volume of mixture is 100 ml with oil to water ratio of 1 : 4.

First, let's find the volume of each component.

If the oil is x then water is 4x according to ratio and their sum is 100 ml:

So, we have 20 ml of oil and 80 ml of water.

Now, let's added volume of oil be y. Then we have the ratio:

So, we have 40 ml of oil and 80 ml of water.

Lastly, let's added water be z. Then we have the ratio:

We must add 40 ml of water.

Answer: False

Step-by-step explanation:

If the function has a negative slope, then it will decrease.

The ratio between 40,000 and 200 is 200 : 1

The numbers are given as:

40,000 and 200

Express as ratio

Ratio = 40000 : 200

Divide each number by 200

Ratio = 200 : 1

Hence, the ratio between 40,000 and 200 is 200 : 1

Read more about ratio at:

https://brainly.com/question/2328454

#SPJ1

Considering the probability of success of 0.8 in the Bernoulli trial, the probability of failure is of 0.2.

The probability of failure in a Bernoulli trial is one subtracted by the probability of a success.

In this problem, the probability of a success is of 0.8, hence the probability of failure is:

pF = 1 - 0.8 = 0.2.

More can be learned about Bernoulli trials at https://brainly.com/question/16931609

#SPJ1

Answer: (5,1)

Step-by-step explanation:

Adding the equations gives 2d=10, and thus d=5.

So, it follows e=1.

Therefore, the solution is (5,1).

The solution is (5,1)

Given that d+e =6 and d-e =4

We need to find the solution of the given equations

Elimination method is used to eliminate a variable in an equation to find the value of another variable

Now here ,

We we will solve the equation i.e

d+e = 6

d-e = 4

Solving this equation We get,

2d = 10

Therefore,

d= 5

Now substituting the value of d in equation d+e =6

therefore,

5+e =6

Therefore e = 1

Hence the solution is (5,1)

Learn more about Elimination method here

https://brainly.com/question/22440227

#SPJ1

The two-column proof that proves that ∠O ≅ ∠R using the SSS and CPCTC theorems is shown in the image attached below.

The side-side-side congruence theorem (SSS) states that when three sides of a triangle are congruent to the corresponding three sides of another triangle, then both triangles are considered congruent to each other.

The CPCTC theorem states that when two triangles are proven to be congruent by any triangle congruent theorem, then all the corresponding parts of the congruent triangle are congruent. This implies that the corresponding sides and angles of both triangle are equal or congruent.

We are asked to prove that ∠O ≅ ∠R.

With the given image, we would draw segment UP. Thus, based on the reflexive property, UP ≅ UP (one pair of congruent sides).

We are given two pairs of corresponding sides already, which are: UO ≅ UR and PO ≅ PR.

This means that triangles OUP and RUP have three pairs of corresponding congruent sides. Therefore, ΔOUP ≅ ΔRUP.

Applying the CPCTC theorem, ∠O ≅ ∠R.

The two-column proof is attached in the image below.

Learn more about the Side-side-side Congruence Theorem (SSS) on:

https://brainly.com/question/4280133

#SPJ1

Answer: Option (3)

Step-by-step explanation:

Since the parabola has a vertical axis of symmetry, we can eliminate Options (1) and (4).

To see whether options (2) or option (3) is correct, we can substitute in [tex]x=-1[/tex] and see if we get y=3.

Doing this with option (2), we get y = -3, so it is wrong.

Doing this with option (3), we get y = 3, as required.

So, option (3) is correct.

Answer: SAS

Step-by-step explanation:

There are two pairs of congruent angles and the pair of angles formed by these sides are congruent.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

In the given figure, one angle and two adjacent sides of Triangle AFB is equal to corresponding angle and sides of the Triangle DFC.

So, we can conclude that,

Triangle AFB and Triangle DFC are congruent by :

[tex] \qquad \large \sf {Conclusion} : [/tex]

See below for the algebraic expressions of the scenarios.

The given parameters are:

Scenario 1

Represent the speed with x.

So, we have:

Speed = Distance/Time

The time is given as:

Time = 10 minutes

Since he did not stop at all;

The speed is

x = 2400/10

Multiply both sides by 10

10x = 2400

The above expression represents the scenario 1.

Scenario 2

Represent the speed with x, and time with t

So, we have:

Speed = Distance/Time

The time to reach halfway is given as:

Time = 6 minutes

He stopped for 1 minute, before continuing at the same initial speed

So, the total time it 13 minutes

The speed is represented as:

x = 2400/13

Multiply both sides by 13

13x = 2400

The above expression represents the scenario 2.

Scenario 3

Represent the speed with x, and time with t

So, we have:

Speed = Distance/Time

The time to reach halfway is given as:

Time = 6 minutes

He stopped for 1 minute, before continuing at twice the initial speed

So, the total time is

t = 6 + 1 + 1/2 * 6 minutes

t = 10 minutes

The speed is represented as:

x = 2400/10

Multiply both sides by 10

10x = 2400

The above expression represents the scenario 3.

Read more about algebraic expressions at:

https://brainly.com/question/19245500

#SPJ1

Answer:

363 (d)

Step-by-step explanation:

Sum = (a1+an)(n)/2

n = (an-a1)/d +1 = 11

Plug into the sum formula.

Sum = 363

[tex]\begin{array}{c|c|c|c} p & q & \neg q & p \land \neg q \\ T & T & F & F \\ T & F & T & T \\ F & T & F & F \\ F & F & T & F \end{array}[/tex]

[tex]\begin{array}{c|c|c|c} t & s & \neg t & \neg t \implies s \\ T & T & F & T \\ T & F & F & T \\ F & T & T & T \\ F & F & T & F \end{array}[/tex]

[tex]\begin{array}{c|c|c}p\land \neg q & \neg t \implies s & (p \land \neg q) \implies (\neg t \implies s) \\T & T & T \\ T & F & F \\ F & T & T \\ F & F & T \end{array}[/tex]

The given logical statement is false when [tex]p\land\neg q[/tex] and [tex]\neg t\implies s[/tex] are true and false, respectively.

The point that describes the intersection of line m and line n is; Point W

Intersection of the two lines is defined as the point where the two lines cross or meet each other.

It is given that the lines m and n intersect each other, which means that they must be intersecting each other at some point.

From the figure, it can be seen that in plane A, the lines m and n intersect each other at point W, thus point W is the point of intersection of the two line m and n.

Read more about Intersection of Planes at; https://brainly.com/question/10955258

#SPJ1

The probability of inductees who are female will be 0.155.

Question: What proportion of inductees have been female or have included female members?

From the information, 303 groups or individuals and forty-seven of the inductees have been female or have included female members.

Therefore, the proportion will be:

= 47/303

= 0.155

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

volume = (1/3) * π * r² * h

= 1/3* 22/7 * (3.5*3.5) * 5 ( 22/7 is the value of π)

=64.1

Answer:

If you need a pi in your answer: 20.417 [tex]\pi[/tex] (rounded to the nearest thousanth)

If you don't: 64.141 (rounded to the nearest thousanth)

Step-by-step explanation:

The formula of the volume of a cone: [tex]V = \pi r^2\frac{h}{3}[/tex]

--> V = Volume, r = Radius, h = Height

In other words, the volume of the cone is the area of the circle x height x 1/3 x pi.

Since the radius of the cone is 3.5, you square that number.

--> (3.5)^2 = 12.25

The height is 5, so h/3 will be 5/3.

The volume = [tex]\pi[/tex] x 12.25 x 5/3

--> 20.416666... [tex]\pi[/tex]

--> 64.14085....

The amount of the radioactive material in the vault after 140 years is 210 pounds

We have that the function is given as a model;

f(x) = 300(0.5)x/100

Where

Let's substitute the value of 'x' in the model

f(x) = 300(0.5)x/100

[tex]f(x) = \frac{300(0.5) * 140}{100}[/tex]

[tex]f(x) =\frac{21000}{100}[/tex]

f(140) = 210 pounds

This mean that the function of 149 years would give an amount of 210 pounds rounded up to the nearest whole number.

Thus, the amount of the radioactive material in the vault after 140 years is 210 pounds

Learn more amount radioactive decay here:

https://brainly.com/question/11117468

#SPJ1

Triangle XYZ was translated 2 units left and 1 unit up to form triangle X'Y'Z'. It was then rotated 180° about the origin to form triangle X''Y''Z''  

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

Triangle XYZ was translated 2 units left and 1 unit up to form triangle X'Y'Z'. It was then rotated 180° about the origin to form triangle X''Y''Z''  

Find out more on transformation at: https://brainly.com/question/4289712

#SPJ1

A state uses a combination of three letters (A-Z) followed by three digits (0-9) for their license plates. So, there are 17576000 license plates can be made.

Given that, license plates consists of 3 letters followed by 3 digits.

Let the numbers on license plates be N

Let the letters on license plates be L

So, the license plate consisting of 3 letters and 3 digits will be LLLNNN.

Letters can be anything from A to Z.

There are 26 letter combinations for the first letter. That is applicable for the following 2 letters.

So, the combination for letters = 26×26×26 = 17576

Numbers can be anything from 0 to 9.

There are 10 combinations for each place.

So, the combination for numbers = 10×10×10 = 1000

Now, the combination for letters and numbers= 17576×1000

                                                                        =  17576000

Therefore, 17576000 license plates can be made.

Learn more about Combinations on

https://brainly.com/question/11732255

#SPJ1

The volume of the rectangular solid is: 11,960 units³.

The formula to find the volume of a rectangular solid is: (length)(width)(height).

Given the dimensions as:

Volume = (20)(23)(26)

Volume of the rectangular solid = 11,960 units³.

Learn more about about the volume of rectangular solid on:

https://brainly.com/question/15116803

#SPJ1

[tex]f(x) = 7x {}^{2} - 3x {}^{4} [/tex]

The intensity at a distance of 14 feet is 18.29 ft

The intensity (I) of a light source is inversely proportional to the square of the distance (d) from the source.

Light intensity refers to the strength or amount of light produced by a specific lamp source

The light intensity is measured in terms of lumens per square foot or lumens per square meter.

Therefore,

I ∝ 1 / d²

Hence,

I = k / d²

where

Therefore,

k = Id²

k = 16 × 16

k = 256

Hence,

I = 256 / 14

I = 18.2857142857

I = 18.29 ft

Therefore, the intensity at a distance of 14 feet is 18.29 ft

learn more on intensity here: https://brainly.com/question/25926665

#SPJ1

The correct product of (6x - 2)(6 x + 2) is 36x^2 - 4

The expression is given as:

(6x - 2)(6 x + 2).

The above expression is a difference of two squares.

And this is represented as

(a - b)(a + b)= a^2 - b^2

So, we have

(6x - 2)(6 x + 2) = (6x)^2 - 2^2

Evaluate

(6x - 2)(6 x + 2) = 36x^2 - 4

Hence, the correct product of (6x - 2)(6 x + 2) is 36x^2 - 4

Read more about difference of two squares at:

https://brainly.com/question/3189867

#SPJ1

Complete question

What is the product?

(6x - 2)(6 x + 2).

x=regular selling price

X×80/100=380

= X×8/10=380

= 8X=380×10=3800

X=3800/8

X=475

the regular selling price is 475

Before the 20% discount, the TV's regular selling price was $475 as per the concept of percentage.

Let's denote the regular selling price of the plasma TV as "x". When the TV was marked down by 20%, the sale price became $380.

To find the regular selling price, we can set up an equation using the information given:

Sale Price = Regular Selling Price - (Discount Percentage × Regular Selling Price)

$380 = x - (0.20x)

Now, let's solve for "x" (the regular selling price):

$380 = x - 0.20x

$380 = 0.80x

To isolate "x," we divide both sides of the equation by 0.80:

x = $380 / 0.80

x = $475

The regular selling price of the plasma TV is $475.

Therefore, before the 20% discount, the TV's regular selling price was $475. After the discount, the sale price was reduced to $380, which is 20% less than the regular price.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ3

Answer: x / 5 = 16

x = 80

The key feature that the function of f(x) and g(x) has in common is the domain.

The domain of a function is the set of input or argument values for which the function is valid and well defined. The range is the set of the dependent variable for which a function is defined.

From the given information, we are to find the domain, range, x-intercept, and, y-intercept of the given equation:

[tex]\mathbf{f(x) = -4^x+5}[/tex]

[tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex]

For [tex]\mathbf{f(x) = -4^x+5}[/tex];

The domain of a function [tex]\mathbf{-4^x+5}[/tex] has no undefined points or constraints. Thus, the domain is -∞ < x < ∞.

For [tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex]

The domain of a function [tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex] has no undefined points or constraints. Thus, the domain is -∞ < x < ∞.

Learn more about the domain and range of a function here;

https://brainly.com/question/26098895

#SPJ1

The point of intersection for the pair of linear equations is (-5.5, -4.8)

Linear equations are equations that have constant average rates of change, slope or gradient

The pair of linear equations is given as:

x + y = 0.7

y = 3x + 11.7

Substitute y = 3x + 11.7 in x + y = 0.7

x + 3x + 11.7 = 0.7

Evaluate the like terms

2x = -11

Divide both sides by 2

x = -5.5

Substitute x = -5.5 in y = 3x + 11.7

y = 3*-5.5 + 11.7

Evaluate

y = -4.8

So, we have

x = -5.5 and y = -4.8

Express the above points as an ordered pair, to determine the point of intersection

(x, y) = (-5.5, -4.8)

Hence, the point of intersection for the pair of linear equations is (-5.5, -4.8)

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1