Find the nth term an of the geometric sequence described below, where r is the common ratio.
a4 = -8, r= -2

The following system of equation can be solved by first substituting the dependent variable in the other equation . The solution yields x = -1.5 and y = 6.5 .

The two equations are given as -

4x-2y=7

3x-3y=15

First substituting the value of x from the first equation and then putting that value in the second equation for the following system of equation.

From first equation,

⇒ 4x = 7 + 2y

∴  x = (7 + 2y)/4

Putting this value of x in second equation,

⇒ 3*(7 + 2y)/4 - 3y = 15

⇒ 3*(7 + 2y) - 12y = 60

⇒ 21 + 6y - 12y = 60

⇒ -6y = 39

∴  y = -6.5

∴ x = (7 + 2y)/4 = -1.5

Thus x = -1.5 and y = -6.5

Therefore, the following system of equation can be solved by first substituting the dependent variable in the other equation . The solution yields x = -1.5 and y = 6.5 .

To learn more about system of equation, refer -

https://brainly.com/question/12526075

#SPJ9

Answer:

8/3 or 2(2/3) Textbooks to storybooks

Step-by-step explanation:

Textbooks:  (8 books)*(12 rupees/book) = 96 rupees

Storybooks:  (4 books)*(9 rupees/book) = 36 rupees

Total is 132 rupees

Ratio:  Textbook/Storybook = 96/36

96/36 = 8/3 or 2(2/3) Textbooks to storybooks

Answer:

  (c)  y = -3x +6

Step-by-step explanation:

The equation can be written in slope-intercept form when we know the slope and the y-intercept.

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . . where m is the slope and b is the y-intercept

The y-intercept is the y-value where the line crosses the y-axis. It is 6. This eliminates choices A and D, leaving choices ...

The line goes down to the right. This is a negative slope, eliminating choice B.

The equation of the line is y = -3x +6.

__

Additional comment

The line intersects the x-axis at x=2. This means the "rise" of the line is -6 units for a "run" of 2 units. The numerical value of the slope is ...

  m = rise/run = -6/2 = -3

Now, we know the parameters of the equation are m=-3, b=6, and the equation of the line is

  y =-3x +6

The diagonal of the rectangle solid is [tex]\sqrt{50[/tex]

The dimensions are given as:

3,4,5

The diagonal is calculated as:

[tex]d = \sqrt{3^2 + 4^2 + 5^2[/tex]

This gives

[tex]d = \sqrt{50[/tex]

Hence, the diagonal of the rectangle solid is [tex]\sqrt{50[/tex]

Read more about diagonal at:

https://brainly.com/question/654982

#SPJ1

Si triplicamos la cantidad de cada artículo, el subtotal será de 2 940 soles, el impuesto al consumo será de 529,20 soles y el total será de 3 469,20 soles.

En esta pregunta tenemos un recibo con una lista de productos, cantidades, precios unitarios y precios de compra, además de un impuesto que se aplica al consumo por concepto de los productos comprados y el total, el cual refleja tanto el subtotal como el concepto por impuestos.

En cuanto a la compra de una determinada cantidad para un artículo, el coste total respectivo es igual a producto del número de artículos por el precio unitario.

El subtotal se determina mediante la suma de los costes totales asociados a cada artículo y luego se le recarga con el impuesto al consumo. Por último, el total de compra es la suma del subtotal y los pagos tributarios.

Si triplicamos el número de cada artículo comprado, tenemos los siguientes costes para cada artículo:

Chompas de dralom

12 / 4 × 280 = 840

Chompas de Orlon

6 / 2 × 100

300

Chompas de lana de alpaca

15 / 5 × 600

1 800

El subtotal es 2 940 soles y el impuesto al consumo es 18 / 100 × 2 940 = 529,20 soles. Por tanto, el total es 3 469,20 soles.

Para aprender más sobre facturación: https://brainly.com/question/24267145

#SPJ1

The percentage change in volume from cylinder A to cylinder B; D: 100%

Formula for Volume of a Cylinder is;

V = πr²h

Thus, volume of Cylinder A is;

V_a = π * 7² * 5

V_a = 245π

Thus, percentage change in volume is;

[245π/(490π - 490π)] * 100%

Percentage change in volume = 100%

Read more about percentage change in volume at; https://brainly.com/question/9554871

#SPJ1

Answer:

100% increase

Step-by-step explanation:

I got it right on the test.

Answer:

60 ft^2

Step-by-step explanation:

Answer:

27.2

Step-by-step explanation:

V = (1/2)(2.6)(5.1)(4.1), which is 27.2 to the nearest tenth

The correct answer is identity

Using the law of cosines, it is found that the length of side AB is of AB = 13.

The law of cosines states that we can find the angle C of a triangle as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

in which:

For this problem, the parameters are:

C = 120, a = 8, b = 7.

Hence:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

[tex]c^2 = 8^2 + 7^2 - 2(8)(7)\cos{120^\circ}[/tex]

[tex]c^2 = 169[/tex]

[tex]c = \sqrt{169}[/tex]

c = 13.

Hence AB = 13.

More can be learned about the law of cosines at https://brainly.com/question/2491835

#SPJ1

Answer:

45 numbers

Step-by-step explanation:

The 10-digit numbers are from 10-99. We can manually analyze each tenth digit and see if we can find a pattern from it. First, 10-19 ~ 10 is the only number in the sequence where the tenth digit is greater than the unit digit (because 1 > 0). In every other case, 1 is less than or equal to the unit digit.

Next, 20-29 ~ 20 and 21 are the two numbers where the tenth digit is greater than the unit digit

30-39 ~ 30, 31, 32 follow the property

40-49 ~ 40, 41, 42, 43 follow the property

We can keep going, but we can see that there is a pattern. The number of numbers that correspond with the property for each set of 10 numbers is equal to the value of the tenth digit. We see that for the 40s, there are 4 numbers. For the 20s, on the other hand, there are 2 numbers. This pattern carries through:

50-59 ~ 5 numbers, 60-69 ~ 6 numbers, 70-79 ~ 7 numbers, 80-89 ~ 8 numbers, 90-99 ~ 9 numbers

We need to find how many 2-digit numbers total follow the property. We can just add our results together to get our answer:

1+2+3+4+5+6+7+8+9=45

A, C, D are correct. In this question the options that are correct are

We have first with legs height to be =529 m and 229 m;

second with legs height =529 m and 347 m.

Then tan x = 529/229

tan y = 529/347

We can see that tanx > tany

Hence x> y

We have alternate angles in the question. This makes x=v, y=w

For D

x > y while x = v

This tells us that v>y

Read more on this triangle here: https://brainly.com/question/11944448

#SPJ1

Answer:

acd

Step-by-step explanation:

Answer:

f[g(x)] = 6x + 47

Step-by-step explanation:

The expression f[g(x)] represents a composite function. You need to plug the function g(x) into the "x" value of the f(x) function. Then, you can simplify.

f(x) = 6x + 11               g(x) = x + 6

f[g(x)]                                                    <----- Composition expression

f[g(x)] = 6(x + 6) + 11                             <----- Plug g(x) into x

f[g(x)] = 6x + 36 + 11                             <----- Multiply terms in parentheses by 6

f[g(x)] = 6x + 47                                  <----- Add 36 and 11

Step-by-step explanation:

Answer: △JKL & △ MNP

Step-by-step explanation:

△JKL is similar because:

5 x 1.6 = 8

2.5 x 1.6 = 4

3.75 x 1.6 = 6

△MNP is also similar because:

4 x 2 = 8

2 x 2 = 4

3 x 2 = 6

Answer:

9

Step-by-step explanation:

See the attached image.

The coordinates of your position are (6, 0, -4).

the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation. Option B

Angle of elevation can be defined as the angle formed between a horizontal line and the line of sight up to an object with the image of the object located above the horizontal line.

It is the height greater than the height of the observer.

The opposite of the angle of elevation is the angle of depression which is formed with an observer

Words associated with the angle of elevation are;

The angle of elevation is the angle between the line of sight and the horizontal line.

Hence, the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation. Option B

Learn more about angle of elevation here:

https://brainly.com/question/19594654

#SPJ1

Sample is the 3 selected customers; And population is all customers

According to the statement

we have given that a shopkeeper asks 3 customers to taste the chocolate icecream.

And we have to identify the sample and population.

So, A definition of sample is that a

A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample.

And a Population is defines as the is a discrete group of people, animals or things that can be identified by at least one common characteristic for the purposes of data collection and analysis.

So, according to definition Sample is the 3 selected customers; And population is all customers.

Learn more about Sample here https://brainly.com/question/11073037

#SPJ4

Using the sine ratio, the length of the missing side is: 11.8.

The sine ratio is, sin ∅ = opposite/hypotenuse.

Given the following:

∅ = 24°

Opposite = x

Hypotenuse = 29

sin 24 = x/29

x = (sin 24)(29)

x = 11.8

Learn more about the sine ratio on:

https://brainly.com/question/2920412

#SPJ1

Comparing with the original expression, the value that will go into the green box is 5

Given the indices expression below;

[tex]\frac{4^{-5}}{4^4}[/tex]

Since 4^-5 is equivalent to 1/4^5, hence the given expression will be equivalent to;

[tex]\frac{1}{4^5\times4^4}[/tex]

Comparing with the original expression, the value that will go into the green box is 5

Learn more on exponent here: https://brainly.com/question/11975096

#SPJ1

Answer:

C. 4^6 / 5^6

Step-by-step explanation:

(4/5)^6

= 4^6 / 5^6

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{(\dfrac{4}{5})^6}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{(\dfrac{4}{5})^6}[/tex]

[tex]\mathbf{= \dfrac{4}{5}\times\dfrac{4}{5}\times\dfrac{4}{5}\times \dfrac{4}{5}\times\dfrac{4}{5}\times\dfrac{4}{5}}[/tex]

[tex]\mathbf{= \dfrac{4\times4\times4\times4\times4\times4}{5\times5\times5\times5\times5\times5}}[/tex]

[tex]\mathbf{= \dfrac{16\times16\times16}{25\times25\times25}}[/tex]

[tex]\mathbf{= \dfrac{256 \times 16}{625\times25}}[/tex]

[tex]\mathbf{= \dfrac{4,096}{15,625}}[/tex]

[tex]\mathbf{\approx \dfrac{4^6}{5^6}}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak{Option\ C. \dfrac{4^6}{5^6}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The angle measurements of angle B as represented in the diagram shown is 150°

An equation is an expression that shows the relationship between two or more numbers and variables.

From the diagram:

∠A = ∠B (alternate interior angles)

Hence:

8x - 10 = 3x + 90

x = 20

∠B = 3(20) + 90 = 150°

The angle measurements of angle B as represented in the diagram shown is 150°

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer: 17 campers attended last year

Step-by-step explanation:

Let x be the number that attended last year.

The number of campers this year (23) is equal to 2 times the number of last year (x), minus 11.

23 = 2x – 11

23 + 11 = 2x

34 = 2x

34/2 = x

17 = x

The probability of picking a red counter is therefore; 8/25.

Since the ratio of red to green is 2 :3 and there are 24 green counters, it follows that the number of red counters is;

x = (2/3)× 24 = 16 red.

The total of red and green is; 16 +24 = 40 which constitutes 80% of the total counters.

The total number of counters is therefore; 40/0.8 = 50 counters.

The probability of picking a red counter is therefore; 16/50 = 8/25.

Read more on ratios;

brainly.com/question/13513438

#SPJ1

25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path. This can be obtained by considering this as a right angled triangle.

Let x be the length between man and the pole, y be the distance between the tip of the shadow and the pole.

Then y - x will be the length between the man and the tip of the shadow.

Since two triangles are similar, we can write

[tex]\frac{y-x}{y} =\frac{6}{15}[/tex]

⇒15(y-x) = 6y

15 y - 15 x = 6y

9y = 15x

y = 15/9 x

y = 5/3 x

Differentiate both sides

dy/dt = 5/3 dx/dt

dy/dt is the speed of the tip of the shadow, dx/dt is the speed of the man.

Given that dx/dt = 5 ft/s

Thus dy/dt = (5/3)×5 ft/s

dy/dt = 25/3 ft/s

Hence 25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path.

Learn more about similar triangles here:

brainly.com/question/8691470

#SPJ4

The given analytical tools:

a. The single sample z-test analysis is appropriate for the data where the sample size is large and all data points are independent. Where the standard deviation is given(known).

b. The single sample t-test analysis is appropriate for the data where the sample size is small and the population variation or standard deviation is unknown.

This is a type of hypothesis test where the sample means and the population means are compared when the population variance or the standard deviation are given(known).

z = (X - μ)/(σ/√n)

Where X - sample mean, μ - population mean, σ - population standard deviation, and n - sample size.

Here the sample size is large and all data points are independent.

This is a type of parametric hypothesis test where the sample means and the population means are compared when the population variance or the standard deviation are not given(unknown).

t = (X - μ)/(s/√n)

Where X - sample mean, μ - population mean, s - sample standard deviation, and n - sample size.

Here the sample size is small.

Learn more about z-test and t-test analysis here:

https://brainly.com/question/27921714

https://brainly.com/question/14275602

#SPJ1

The linear function on a coordinate plane passes through (-5, -3) and (0, -4) is y = -1/5x-4

Linear function are functions that has a leading degree of 1. The equation of a linear function is expressed as y = mx + b

where

m is the slope

b is the intercept

Given the coordinates (-5, -3) and (0, -4)

Slope = -4+3/0+5
Slope = -1/5

The y-intercept of the line will be -4

Determine the equation

y = -1/5x-4

Hence the linear function on a coordinate plane passes through (-5, -3) and (0, -4) is y = -1/5x-4

Learn more on linear function here: https://brainly.com/question/15602982

#SPJ1

Answer:

Step-by-step explanation:

Given : 10 seat in first row, and the seat will increase 1 by 1 as we go above.... (as we go to the next row) - total rows - 38

Solve ; 38 rows, 10 seat in first row, 1 seat increases each row....

Extra seats - 37,

So,

37 x 10 = 370

TOTAL SEATS = 370

Answer:

  1083 seats

Step-by-step explanation:

The number of seats is an arithmetic series with first term 10 and common difference 1. We want to find the sum of 38 terms of the series.

The sum of n terms of an arithmetic series with first term a1 and common difference d is given by the formula ...

  Sn = (2a1 +d(n -1))(n/2)

The sum of the series of interest is ...

  S38 = (2(10) +1(38 -1))(38/2)

The total number of seats in the theater can be found by evaluating the expression for S38:

  S38 = (20 +37)(19) = 57×19 = 1083

There are 1083 seats in the theater.

Welcome to https://saigonstartravel.com/ Saigon Star Travel – Top Thương Hiệu Du Lịch Hàng Đầu Tại TP Hồ Chí Minh là Đơn vị tổ chức Tour du lịch trong nước & nước ngoài chuyên nghiệp, Dịch vụ Visa – Vé máy bay Nhanh chóng & Uy tín và Cho Thuê xe Du lịch từ 16-29-35-45 chỗ & Xe giường nằm Chất lượng.