Which of the following is a geometric sequence? a. 5,-25,125,-625 b.2,4,16,48 c. 13,16,19,22 d. 100,50,0,-50

Answer:

The sequence has first term 7 and common difference is 8.

So the sequence is f(n)=7 + 8(n-1)

Step-by-step explanation:

Let a be the first term.

Let a+d be the second term where d is the common difference.

Then a+2d is the third....

And a+(n-1)d is the nth term.

Adding these terms we get:

an+(n-1)(n)/2×d

For the first term of this sum I seen we had n amount of a's and for the second term I used the well known identity sum of the first n positive integers is n(n+1)/2.

Let's simplify:

an+(n-1)(n)/2×d

Distribute:

an+(n^2d/2)-(nd/2)

Find common denominator:

(2an/2)+(n^2d/2)-(nd/2)

Combine terms into one:

(2an+n^2d-nd)/2

Reorder terms:

(n^2d+2an-nd)/2

Regroup terms:

(n^2d+(2a-d)n)/2

We want the following sum though:

4n^2+3n

This means d/2=4 (so d=8) and (2a-d)/2=3.

So plug d=8 into second equation to solve for a.

(2a-8)/2=3

2a-8=6

2a=14

a=7

The sequence has first term 7 and common difference is 8.

So the sequence is f(n)=7 + 8(n-1).

Answer:

A=5h(B+b)

A/5h=B+b

A/5h - b= B

Answer:

c

Step-by-step explanation:

took the test so i assume its this question

Answer:

25827165

Step-by-step explanation:

from the question that we have here

the total population = 54 students

the sample size = 6 students

So given this information carol has to pick the total samples from the 54 students that we have here

the total ways that she has to do this

= 54 combination 6

= 54C6

= [tex]\frac{54!}{(54-6)!6!}[/tex]

= 25827165

this is the total number of possible samples that could occur given the total population of 54 students.

The sine curve equation, y = 10·sin(x·π/24), that models the entrance of the

tunnel with a cross section that is the shape of half of a sine curve and the

height of the tunnel at the edge of the road, (approximately 7.07 ft.) are

found by applying the following steps

(a) The equation for the sine curve is y = 10·sin(x·π/24)

(b) The height of the tunnel at the edge of the road is approximately 7.07 feet

The reason for the above answers are presented as follows;

(a) From a similar question posted online, the missing part of the question

is, what is the height of the tunnel at the edge of the road

The known parameters;

The shape of the tunnel = One-half sine curve cycle

The height of the road at its highest point = 10 ft.

The opening of the tunnel at road level = 24 ft.

The unknown parameter;

The equation of the sine curve that fits the opening

Method;

Model the sine curve equation of the tunnel using the general equation of a sine curve;

The general equation of a sine curve is y = A·sin(B·(x - C) + D

Where;

y = The height at point x

A = The amplitude = The distance from the centerline of the sine wave to the top of a crest

Therefore;

The amplitude, A = The height of half the sine wave = The height of the tunnel = 10 ft.

D = 0, C = 0 (The origin, (0, 0) is on the left end, which is the central line)

The period is the distance between successive points where the curve passes through the center line while rising to a crest

Therefore

The period, T = 2·π/B = 2 × Opening at the road level = 2 × 24 ft. = 48 ft.

T = 48 ft.

We get;

48 = 2·π/B

B = 2·π/48 = π/24

By plugging in the values for A, B, C, and D, we get;

y = 10·sin((π/24)·(x - 0) + 0 = 10·sin(x·π/24)

The equation of the sine curve that fits the opening is y = 10·sin(x·π/24)

(b) The height of the tunnel at the edge of the road is given by substituting

the value of x at the edge of the road into the equation for the sine curve

as  follows;

The width of the shoulders = 6 feet

∴ At the edge of the road, x = 0 + 6ft = 6 ft., and 6 ft. + 12 ft. = 18 ft.

Therefore, we get;

y = 10 × sin(6·π/24) = 10 × sin(π/4) = 5×√2

y = 10 × sin(18·π/24) = 10 × sin(3·π/4) = 5×√2

The height of the, y, tunnel at the edge of the road where, x = 6, and 18 is y = 5·√2 feet ≈ 7.07 ft.

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The horizontal distance from the base of the skyscraper out to the ship is 349.8feet

The angle situated above the hill is known as  the angle of depression

Given the following parameters

Height of the harbor = 824 feet

Angle of depression = 67degrees

According to SOH CAH TOA identity:

tan 67 = opp/adj
tan 67 = 824/d

d = 824/tan67
d = 349.8 feet

Hence the horizontal distance from the base of the skyscraper out to the ship is 349.8feet

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Answer:

1 + 7n

Step-by-step explanation:

7-(3n+6)+10n​

7 - 3n - 6 + 10 n

1 - 7n

Answered by Gauthmath

Answer:

G(-1) = -2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify

G(x) = 5x + 3

Step 2: Evaluate

Answer:

G = -2

Step-by-step explanation:

Plug in -1 for x.

5(-1) + 3

-5 + 3

-2

G = -2

Answer:

11.2

Step-by-step explanation:

yz = 11.2

since the corresponding arc of yz and xy are same, their measures will ba same too

Answered by GAUTHMATH

Answer:

11.2

Step-by-step explanation:

good luck!

Answer:

175731 is one of the answers of the 6 digit number

some others are:

275732

375733

475734

575735

675735

775734

875732

The 6-digit number is 175731.

The place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, use your places values, such as tens and hundreds. It is possible to employ enlarged notation or compensation. Using regrouping techniques, you can make the problem easier by compensating for addition.

Let the number would be ABCDEF

Given the condition that the value of its thousands of digits is 5,000.

So C = 5

Given the condition that the value of its hundreds of digits is 700.

So D = 7

Given the condition that Its tens digit is 2 less than the thousand digits.

So E = 5-2 = 3

Given the condition that Its hundred thousand digits is the same as the hundred digits.

So B = 7

Therefore, all possible answers:

275732

375733

475734

575735

675735

775734

875732

Hence, the 6-digit number is 175731

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Answer:

-1 <x < 7

(-1,7)

Step-by-step explanation:

open circle on the left means the number is greater than

-1 <x

Open circle on the right means the number is less than

x < 7

Since both statements are true. we combine them

-1 <x < 7

open circles means parentheses, closed circles mean brackets

Answer:

Step-by-step explanation:

Triangular cross-section.

Answer:

it is a triangle cross-section

hope this answer helps you

Plz make me a brainlist

Answer:

2110

Step-by-step explanation:

4100-1990=2110

Answer:

-6/5

Step-by-step explanation:

- 2/3 (2 - 1/5)

Distribute

-2/3 *2 -2/3 *(-1/5)

-4/3 + 2/15

Get a common denominator

-4/3 *5/5 +2/15

-20/15 +2/15

-18/15

Simplify

-6/5

Answer:

given

f(x).4x+5

fog(x).8x+13

now

fog(x):8x+13

4x+5(g(x)):: 8x+13

g(x):: 8x+13/4x+5

Answer:

g(x) = 2x + 2

Step-by-step explanation:

One is given the following information:

One is asked to find the following:

Remember, (f o g (x)) is another way of representing a composite function. A more visual way of representing this composite function is the following (f(g(x)). In essence, one substitutes the function (g(x)) into the function (f(x)) in places of the varaible (x). Thus, represent this in the form of an equation:

f(g(x)) = 8x + 13

Substitute the given infromation into the equation:

4(g(x)) + 5 = 8x + 13

Solve for (g(x)) in terms of (x). Remember to treat (g(x)) as a single parameter:

4(g(x)) + 5 = 8x + 13

Inverse operations,

4(g(x)) + 5 = 8x + 13

4(g(x)) = 8x + 8

g(x) = (8x + 8) ÷ 4

g(x) = 2x + 2

Answer:

(0, 3)

Step-by-step explanation:

y = 3 is the horizontal tangent to y = x^2+3, and passes the parobala at (0, 3)

Answer:

statistics are when data analyzed in order to make decisions about the population behind the data.

The correct answer to the question is Statistics (Option D).

What is statistics?

Statistics is a field of study in mathematics which deals with raw data. It is a tool which refines the data to produce meaningful results and a pathway to better understanding of it.

Some examples of raw data can be population sample which loves to see a particular TV show or a sample of students getting so and so marks in Math test.

Data is analyzed mainly by three different measure of central tendency that is mean, median and mode.

Therefore, Statistics the correct answer.

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Answer:

1/3

Step-by-step explanation:

common ratio is

9÷27=1/3

3÷9=1/3

1÷3=1/3

therefore common ratio is 1/3

Answer: 1/3

Step-by-step explanation:

Let us confirm that this is a geometric sequence. 9/27 = 1/3 and 3/9 = 1/3. Thus, the common ratio is 1/3.

The angle of 30.283° in a degree-minute-second format will be 30° 16' 58". Then the correct option is C.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

The angle is given below.

⇒ 30.283°

Convert 30.283° into a degree-minute-second format. Then we have

⇒ 30° (0.83 x 60')

⇒ 30° 16.98'

⇒ 30° 16' (0.98 x 60'')

⇒ 30° 16' 58"

The angle of 30.283° in a degree-minute-second format will be 30° 16' 58". Then the correct option is C.

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Answer:

40

Step-by-step explanation:

Let x represent the mystery number.

Create an equation to represent the situation, then solve for x:

0.85x - 5 = 29

0.85x = 34

x = 40

So, the mystery number is 40.

Answer: y = -3/2x + 5

Step-by-step explanation:

Slope-intercept form: y = mx + b

y = -3/2x + 5

Answer:

y = -3/2x + 5 totally

Step-by-step explanation:

9514 1404 393

Answer:

  50

Step-by-step explanation:

The number you choose depends on the location you consider to be zero height.

If we consider the surface of the pool to be zero height, and "up" to be the positive direction for measuring height, then the appropriate number for the original 50-ft height is 50.

Answer:

[tex]\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 6} = -9[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Calculus

Differentiation

Basic Power Rule:

Derivative Rule [Quotient Rule]:                                                                           [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle V = \frac{1}{3} \pi x^2y[/tex]

[tex]\displaystyle V = 324 \pi[/tex]

[tex]\displaystyle x = 6[/tex]

[tex]\displaystyle y = 27[/tex]

Step 2: Differentiate

Step 3: Evaluate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

1^1 + 0^1 =1

Step-by-step explanation:

sin^2 theta + cos^2 theta = 1

sin^2 (pi/2)   + cos^2  (pi/2)  =1

1^1 + 0^1 =1

Answer:

a=1, b=-2,c=-1

Step-by-step explanation:

1*(x)+(-2)*y+(-1)*1. a=1, b=-2,c=-1

angle G

sin inverse (21/29) = 46.4

GH

c^2 - b^2 = a^2

29^2 - 21^2 = a^2

a = √(29^2 - 21^2)

GH = 20

therefore ans is B) <G = 46.4º, <I = 43.6º, GH = 20

the answer is on the photo