which of the following is a geometric sequence

A. 6, 18, 54, 162
B. 1, 4, 5, 9, 14
C. 3, 6, 9, 12, 15
D. 3, 5, 8, 13, 21

Answer:

Step-by-step explanation:

∠J + ∠K + ∠L = 180   {Angle sum property of triangle}

8x + 6 + 2x + 2 + 4x + 4 = 180

8x + 2x + 8x + 6 + 2 + 4 = 180

Combine like terms.

14x + 12 = 180

Subtract 12 form both sides

14x = 180 - 12

14x = 168

Divide both sides by 14

x = 168/14

x = 12

∠L = 4x + 4

    = 4*12 + 4

    = 48 + 4

∠L = 52

Answer:

√161 yd

Step-by-step explanation:

Hi there!

We're given a right triangle (notice the right angle), the measure of one of the legs (one of the sides that make up the right angle) as 8 yd, and the hypotenuse (the side opposite to the right angle) as 15 yd.

We need to find x, which is the other leg in the triangle

If we are given 2 sides and need to find a third, we can use Pythagorean Theorem, which states that a²+b²=c² if a and b are legs and c is the hypotenuse

In this case, a=8, b=x, and c=15

So let's substitute those values into the formula

(8)²+x²=(15)²

raise everything to the second power

64+x²=225

subtract 64 from both sides

x²=161

take the square root of both x and 161

x=√161, x=-√161

-√161 cannot work in this case, as distance cannot be negative.

The question asks for the answer to be in simplified radical form, but √161 cannot be simplified down further

so the answer is √161 yd

Hope this helps! :)

Answer:

Step-by-step explanation:

-1 ≤ x < 3    Solution set = {-1, 0 ,1 , 2}

-2 < x < 2   Solution set  = {-1 , 0 , 1}

Integer values that satisfies both inequalities are -1 , 0 , 1

        I \\\\\\\\\   I                                                                                                          

      [-1]          -3                                                                                                                  I   \\\\\\\\\\\   I                                                                                                            -2              2                                                                                                            [tex]\displaystyle\bf x\in[-1;2)\\-1;0;\underline1\\\\Answer: 1[/tex]                                                                                                                                                                                                                                    

Answer:

a = 1000, p = 10

Step-by-step explanation:

Given

y = - 3lg x + lg a

in the form y = mx + c ( m is the slope and c the y- intercept )

From the graph

(a)

c = 3 , then

lg a = 3 , that is

a = 10³ = 1000

(b)

Replace x by p and y = 0 in the equation

0 = - 3lg p + 3 ( subtract 3 from both sides )

- 3 = - 3lg p ( divide both sides by - 3 )

1 = lg p

p = 10 [ [tex]log_{10}[/tex] 10 = 1 ]

Addition of a positive and negative number always means that you are going to subtract the number e. g. 4+-1 = 3. However, multiplication of a positive and negative number means the answer is always negative e. g. 5 x - 3 = - 15.

The addition of positive and negative number will always subtract with sign of maximum value.

The multiplication of positive and negative number will have a negative sign always.

When two numbers which have different sign are added, they will always be subtracted from each other. The sign will vary accordingly.

Example: Consider two number -5 and 4

= -5 + 4

= -1

Here, 5 is the larger value. So, the sign comes is negative.

Example: consider two number 5 and -4.

= 5 + (-4)

= 1

Here, 5 is the large number. So, the sign comes is positive.

When two numbers with opposite signs are multiplied, the answer is always a negative number.

Example; Consider two numbers 4 and -5.

On multiplication,

4×(-5) = -20

Thus, the multiplication of two numbers with different signs will always give a negative number.

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Answer:

They are parallel so also -4/3

Answer:

all real numbers

Step-by-step explanation:

got it right

Answer:

A

Step-by-step explanation:

it is all real numbers

brainiest please

Given:

The x- intercepts of a parabola are (0,-6) and (0,4).

The parabola crosses the y- axis at -120.

Lucas said that an equation for the parabola is [tex]y=5x^2+10x-120[/tex] and that the coordinates of the vertex are (-1, -125).

To find:

Whether Lucas is correct or not.

Solution:

The x- intercepts of a parabola are (0,-6) and (0,4). It means (x+6) and (x-4) are the factors of the equation of the parabola.

[tex]y=a(x+6)(x-4)[/tex]             ...(i)

The parabola crosses the y- axis at -120. It means the equation of the parabola must be true for (0,-120).

[tex]-120=a(0+6)(0-4)[/tex]

[tex]-120=a(6)(-4)[/tex]

[tex]-120=-24a[/tex]

Divide both sides by -24.

[tex]\dfrac{-120}{-24}=a[/tex]

[tex]5=a[/tex]

Substituting [tex]a=5[/tex] in (i), we get

[tex]y=5(x+6)(x-4)[/tex]

[tex]y=5(x^2+6x-4x-24)[/tex]

[tex]y=5(x^2+2x-24)[/tex]

[tex]y=5x^2+10x-120[/tex]

So, the equation of the parabola is [tex]y=5x^2+10x-120[/tex].

The vertex of a parabola [tex]f(x)=ax^2+bx+c[/tex] is:

[tex]Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]

In the equation of the parabola, [tex]a=5,b=10,c=-120[/tex].

[tex]-\dfrac{b}{2a}=-\dfrac{10}{2(5)}[/tex]

[tex]-\dfrac{b}{2a}=-\dfrac{10}{10}[/tex]

[tex]-\dfrac{b}{2a}=-1[/tex]

Putting [tex]x=-1[/tex] in the equation of the parabola, we get

[tex]y=5(-1)^2+10(-1)-120[/tex]

[tex]y=5-10-120[/tex]

[tex]y=-125[/tex]

So, the vertex of the parabola is at point (-1,-125).

Therefore, Lucas is correct.

Answer:

= 288π in2

Step-by-step explanation:

Volume of a sphere is given by;

V =(4/3)πr3

V = volume

r is radius

Therefore V = {(4/3) × π × (6^3)} in3

= 288π in2

Answer:

[tex]5 {x}^{2} - 11x + 6 \\ 5 {x}^{2} - (5 + 6)x + 6 \\ 5 {x}^{2} - 5x + 6x + 6 \\ 5x(x - 1) - 6(x - 1) \\ (5x - 6)(x - 1)[/tex]

Answer:

5.8

Step-by-step explanation:

Y e s .

Using the Distance formula and all.

The coordinates that describe the point D are: Option C: (0, 4)

The graph shows that the vertical axis is labelled as the y-axis while the horizontal axis is labelled as the x -axis.

Normally, the coordinate system of writing the given points of the graph is (x, y)

Thus, the point D on the graph is seem to be 4 units on the positive y-axis and 0 units on the positive x-axis and as such, we can say that the coordinates of point D are:

D(0, 4)

Read more about Graph Coordinates at: https://brainly.com/question/11337174

Complete question is:

Which of the following describes point D?

(-4, 0)

(0, -4)

(0, 4)

(4, 0)

Answer:

Step-by-step explanation:

Since the coordinates of P are (0, 1), this makes P the y-intercept of that line. The y-intercept exists where x = 0. And in the coordinate (0, 1), x does in fact equal 0.

Since the one coordinate given in Q is (?, 0), this means that Q is the x-intercept of the line. The x-intercept exists where y = 0. And in the coordinate (?, 0), y does in fact equal 0. So in order to solve for the x coordinate of Q, we plug in a 0 for y and solve for x:

3(0) - 4x = 12 and

-4x = 12 so

x = -3

Answer:

[tex] \rm Numbers = 4 \ and \ -3.[/tex]

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]

Hence the numbers are 4 and -3

Let integers be x and x-1

ATQ

[tex]\\ \sf\longmapsto 2x-1=1[/tex]

[tex]\\ \sf\longmapsto 2x=1+1[/tex]

[tex]\\ \sf\longmapsto 2x+2[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2}{2}[/tex]

[tex]\\ \sf\longmapsto x=1[/tex]

Now

[tex]\\ \sf\longmapsto x-1=1-1=0[/tex]

But

Integers can be x and 1-x as their sum is 1

[tex]\\ \sf\longmapsto x(1-x)=-12[/tex]

[tex]\\ \sf\longmapsto x- x^2=-12[/tex]

[tex]\\ \sf\longmapsto x^2-x-12=0[/tex]

[tex]\\ \sf\longmapsto x^2-4x+3x-12=0[/tex]

[tex]\\ \sf\longmapsto x(x-4)+3(x-4)=0[/tex]

[tex]\\ \sf\longmapsto (x-4)(x+3)=0[/tex]

[tex]\\ \sf\longmapsto x=4,-3[/tex]

Answer:

the volume of the cone is 60

Step-by-step explanation:

12×5=60

Answer:

Lo primero que debemos saber, es que la gráfica de pastel nos permite dividir a una población, la cual sería el 100%, en porcentajes menores que representan algo.

En este caso tenemos los porcentajes 20%, 50%, 10%  (notar que no suman 100%, entonces nos falta algún porcentaje)

Bueno, como sabemos el gráfico (el cual es un círculo) representa el 100%.

Y en un círculo, tenemos un ángulo de 360°

Entonces comenzamos con la equivalencia:

360° = 100%

Entonces, ¿a que grado corresponde el 50%? Planteamos la ecuación:

x = 50%

Si tomamos el cociente entre las ecuaciones:

x = 50% y  360° = 100%

obtenemos:

x/360° = 50%/100%

resolviendo para x, obtenemos:

x = (50%/100%)*360° = 0.5*360° = 180°

Para los otros porcentajes hacemos lo mismo.

Para el de 20% tenemos:

y = 20%

planteamos la ecuación:

y/360° = 20%/100%

y = 0.2*360° = 72°

Finalmente, para el de 10% tendremos:

z = 10%

planteando la ecuación como antes:

z/360° = 10%/100%

z = 0.1*360 = 36°

Asi, hemos encontrado los grados correspondientes para cada porcentaje.

Answer:

10

Step-by-step explanation:

use a^2+b^2=c^2

6^2+8^2=c^2

100=c^2

sqrt it and you get 10 for AC and AC=DB

Answer:

according to Pythagoras theorem, c²=a²+b²

|AC|²=|AD|²+|DC|²

|AC|²=6²+8²

|AC|²=36+64

|AC|²=100

√|AC|²=√100

|AC|=10

Answer:

El indicador mencionado en el enunciado indica que la suma de los resultados de las pruebas de razonamiento cualitativo de los estudiantes dividido por la población de los estudiantes arroja ese promedio.

El promedio indica el valor "central" del indicador, no estudia la dispersión de los resultados de las pruebas, es decir, como se distribuye la colección de indicadores.

Step-by-step explanation:

El indicador mencionado en el enunciado indica que la suma de los resultados de las pruebas de razonamiento cualitativo de los estudiantes dividido por la población de los estudiantes arroja ese promedio.

El promedio indica el valor "central" del indicador, no estudia la dispersión de los resultados de las pruebas, es decir, como se distribuye la colección de indicadores.  

Answer:

The answer is

[tex]4+ x[/tex]

Using the definition of linear equation,

[tex]y = 4 + x[/tex]

Is the answer.

Answer:

Step-by-step explanation:

Answer:

I don't understand your question.............!

Step-by-step explanation:

Step-by-step explanation:

[tex] \frac{2}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } = \frac{2(2 - \sqrt{3} )}{1} = 4 - 2 \sqrt{3} [/tex]

Answer:

Step-by-step explanation:

-x/8=12+11=23

-x=23*8=184

x=-184

x=-184Answer:

Step-by-step explanation:

Work Shown:

I'm assuming you meant to write 4p^3+8p^2+3p+6

If so, then we would have these steps

4p^3+8p^2+3p+6

(4p^3+8p^2)+(3p+6)

4p^2(p+2)+3(p+2)

(4p^2+3)(p+2)

Answer:

0.036

Step-by-step explanation:

See image below:)

the area is 32 and the length is 888

you use the formula w= a/l

so a= 32 and l= 888

The width is 0.036mm.

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

Here, given that,

the area is 32 and the length is 888

We use the formula w= A/l

so, A= 32 and l= 888

Then, width= w= 32/888

                         =0.036 mm.

Hence, width is 0.036mm

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Answer:

the answer is 3x2-10x+6=0

Answer:

A) 0.019

B) 0.563

Step-by-step explanation:

a) We will use Poisson distribution formula to solve this;

The formula is given as;

P(X = x) = ((e^-λ) × (λˣ))/x!

Mean is 1. Thus;

λ = 1 aircraft/hour.

Thus, the probability that more than three aircrafts will arrive within an hour is written as; P(X > 3)

Thus;

P(X > 3) = 1 - P(X ≤ 3)

Thus;

1 - P(X ≤ 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

Solving through online calculator, we have;

P(X > 3) = 1 - 0.98101

P(X > 3) = 0.01899

To 3 decimal places, we have; P(X > 3)= 0.019

b) Probability of one 1-hour interval not containing more than 3 arrivals is, let's first find;

P(X ≤ 3) = 1 - P(X > 3)

P(X ≤ 3) = 1 - 0.01899

P(X ≤ 3) = 0.98101

Since there are 30 one-hour intervals, then we have;

Probability that none of the thirty 1-hour intervals will contain more than 3 arrivals;

(P ≤ 3) = (0.98101)³⁰

(P ≤ 3) = 0.5626

Approximating to 3 decimal places, we have;

(P ≤ 3) = 0.563