Determine whether the geometric series 27 + 18 + 12 + 8 + ... converges or diverges, and identify the sum if it exists.

Answer:

a₂₁ = 638

Step-by-step explanation:

substitute n = 21 into the explicit formula

a₂₁ = - 2 + 32(21 - 1) = - 2 + 32(20) = - 2 + 640 = 638

Answer:

x = 3y + 4

Step-by-step explanation:

add 4 to both sides

simplify

Answer:

Step-by-step explanation:

For there to be no solution, the graphs must never intersect.

An equation is formed of two equal expressions. The graphs that indicate that the equation has no solution are the first graph from the top row and the last graph from the second row.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of a pair of equations is the point at which the graph of the two functions intersects each other. The number of times the two graphs intersect is the number of solutions to the pair of equations.

Since there are only two graphs where the graphs do not intersect.

Thus, the graphs that indicate that the equation has no solution are the first graph from the top row and the last graph from the second row.

Learn more about Equation:

https://brainly.com/question/2263981

#SPJ1

Answer:

5/4 is the correct answer for this question

To plot more the points, we move up one and right two.

The ratios are given as:

(1, 0.5), (2, 1), and (5, 2.5)

Calculate the slope (m) using:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{1 - 0.5}{2 - 1}[/tex]

Evaluate

[tex]m = \frac{0.5}{1}[/tex]

This gives

[tex]m = \frac{1}{2}[/tex]

The above means

Vertical : Horizontal = 1 : 2

This means a vertical movement of 1, followed by an horizontal movement of 1

Hence, to plot more the points, we move up one and right two.

Read more about equivalent ratios at:

https://brainly.com/question/13513438

#SPJ1

Complete question

Three equivalent ratios are shown on the graph. On a coordinate plane, points (1, 0.5), (2, 1), and (5, 2.5) are plotted. Starting on one of the plotted points, how can you plot more equivalent ratio points?

Graph fourth shows a system of equations with a solution at (2, -1) option fourth is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is

Which graph shows a system of equations with a solution at (2,-1)?

The graph is in the picture, please refer to the attached picture.

As we can see in the graph there are two graphs of a function shown.

The first one is a parabola and the second one is a linear graph.

From the graph, the intersection point of the two groups is at (2, -1)

The intersection point is shown in graph fourth.

Thus, graph fourth shows a system of equations with a solution at (2, -1) option fourth is correct.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ1

Answer:

Graph 4

Step-by-step explanation:

The equation of the perpendicular line as required is; y = 2x -3.

Since the line in discuss is perpendicular to the given line whose slope is; -1/2. It therefore follows that the slope of the line to be determined is;

m = -1/(-1/2) = 2.

The equation of the required line can therefore be written as;

2 = (y-7)/(x-2)

2x -4 = y -7

Hence, y = 2x -3 is the equation of the line.

Read more on equation of a perpendicular line;

https://brainly.com/question/7098341

#SPJ1

The amount of money in the account if compounded quarterly at 6% after 9 years is $22,217

A = P(1 + r/n)^nt

= 13,000(1 + 0.06/4)^4×9

= 13,000(1 + 0.015)^36

= 13,000(1.015)^36

= 13000(1.709)

= $22,217

Learn more about compound interest:

https://brainly.com/question/24924853

#SPJ1

Answer:

12 yd^2 (c)

Step-by-step explanation:

A=1/2bh

= 1/2 x 8 x 3

=12 yd^2

Hope it helps!!!

Answer: 12 yd^2

Step-by-step explanation:

Area=[tex](1/2) *base*height\\[/tex]

here

base= 8yd

height =3 yd

putting values

area=(1/2)*(8)*(3)

area=12 yd^2

Answer: 9

Step-by-step explanation:

 Given:

n², n = 3

  Plug-in:

(3)²

  Square 3:

3 * 3 = 9, so (3)² = 9

  Simplify:

9

Answer:

B

Step-by-step explanation:

In order the angles <C and <F are shared, then <B and <E, then the side equaling 10. This together proves that this triangle is congruent because of AAS (angle,angle,side) a triangle congruency rule.

Answer:

f(x)=x²-3x-10

Step-by-step explanation:

\begin{gathered}f(x) = x {}^{2} - 3x - 10 \\ to \: find \: x \: intercept \:o r \: zero \: substitute \: f(x) = 0\: \\ 0 = x {}^{2} - 3x - 10 \\ x {}^{2} - 3x - 10 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5\end{gathered}

f(x)=x

2

−3x−10

tofindxinterceptorzerosubstitutef(x)=0

0=x

2

−3x−10

x

2

−3x−10=0

x

2

+2x−5x−10=0

x(x+2)−5x−10=0

x(x+2)−5(x+2)=0

(x+2).(x−5)=0

x+2=0

x−5=0

x=−2

x=5

therefore the zeros of the equation are x₁=-2,x₂=5

Select a random sample of 35 unmarried and 15 married subjects

A researcher who wishes to study the effects of a prenatal breastfeeding education program on the length of time African-American inner-city women breastfeed infants learns that 70% of women in the target population are unmarried.

To achieve stratified random sampling in a sample of 50 subjects, the researcher will:

Select a random sample of 35 unmarried and 15 married subjects.

hence, Select a random sample of 35 unmarried and 15 married subjects.

Learn more about random sampling here https://brainly.com/question/5432563

#SPJ4

Answer:

The unknown length = 12 units.

Step-by-step explanation:

The small and large triangles are similar because of the parallel lines.

So

6 / (6+4) = x / 20

10x = 120

x = 12.

Answer:

5c-9h

Step-by-step explanation:

1) 7c-4h-2c-5h

2) 5c-4h-5h

3) 5c-9h

Answer:

Step-by-step explanation:

ur mother

The y-intercept = 127 and the slope = -10

The function is given as:

y = 127 - 10x

A linear function is represented as:

y = c + mx

Where

c = the y-intercept

m = slope

This means that:

y-intercept = 127

slope = -10

The y-intercept implies that, the initial amount of water is 127 ounces and the slope implies that the water leaks by 10 ounces per minute

Read more about linear functions at:

https://brainly.com/question/15602982

#SPJ1

Complete question

The amount of water in a leaky bucket is given by the linear function y = 127 - 10x, where y is in ounces and x is in minutes. Find and interpret the slope and y-intercept of the linear equation.

A disadvantage of debt consolidation is you can pay more money in the long term.

Debt consolidation is when a person takes out a new loan in order to pay off an existing loan. Debt consolidation increases the money you pay in the long term because you would still have to pay for the new debt incurred.

To learn more about debt consolidation, please check: https://brainly.com/question/14309069

#SPJ1

Answer: Option 2 or B. AAS

Step-by-step explanation:  B. AAS

Trust me!

If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful.

If you found any of my answers helpful please like and subscribe I mean "heart", friend me and/or choose my answer as Brainliest. I would appreciate it!   Good luck everyone!  :)

When two angles and the non-included side of one triangle are congruent to other triangle the by AAS congruency they are congruent. Therefore, option B is the correct answer.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

AAS, two angles and one side of a triangle are equal to two angles and one side of another triangle then they are congruent.

Therefore, option B is the correct answer.

To learn more about the congruent theorem visit:

https://brainly.com/question/24033497.

#SPJ5

Answer:

you would get about 6:20 of sleep

you would have gotten at least 6 hours of sleep and 20 mins

Step-by-step explanation:

Answer:

x-7y

Step-by-step explanation:

7x-9y-6x+2y

Combine like terms

7x -6x    -9y +2y

x       -7y

x-7y

Answer:

x -7y

Step-by-step explanation:

7x - 9y - 6x + 2y

Rearrange so like terms are together (these are terms that are similar such as 5b and 7b; 7 and 1)

7x - 6x - 9y + 2y

Group into brackets one-by-one and solve

(7x-6x) -9y + 2y

x -9y + 2y

x (-9y + 2y)

x -7y

Note that 1x, 1b, 1z etc are simply written as their variable eg x, b and z

The solutions by suitable arrangement are:

a)4x2984x250

By suitable arrangement, we would arrange this as

(4 x 250) x 2984

= (1000 * 2984)

= 2,984,000

b. b) 495+114+205

By suitable arrangement we would have:

(495 + 205) + 114

= 814

c. The factors of 13965 are all of the numbers that can divide this number.

They are: 1, 3, 5, 7, 15, 19, 21, 35, 49, 57, 95, 105, 133, 147, 245, 285, 399, 665, 735, 931, 1995, 2793, 4655, and 13965

Read more on the factors of a number here:

https://brainly.com/question/2058395

#SPJ1

The answers are D.)3, B.) Values were not subtracted from each side, and A.) The substitution property of equality

A straight line is a combination of endless points joined on both sides of the point.

We have;

UX=WZ

VW=XY

In line 3 the statement does not justify.

Because values were not subtracted from each side.

The reason should be substitution property of equality.

Thus, the answers are D.)3, B.) Values were not subtracted from each side, and A.) The substitution property of equality

Learn more about the straight line here:

brainly.com/question/3493733

#SPJ1

Answer:

I just got it right on the test

Step-by-step explanation:

The logarithmic form of  13² = 169 is ㏒₁₃ 169 = 2

Using the logarithmic rule , we have that

㏒ₙn = bⁿ

Given 13² = 169

It is important to  note that it can be written either in the logarithmic form or in the index form.

In this case, we have written in the index form as .

㏒₁₃ 169 = 2

Thus, the logarithmic form of  13² = 169 is ㏒₁₃ 169 = 2

Learn more about logarithm form here:

https://brainly.in/question/51458041

#SPJ1

The complete factor of the given expression is 2x(x-2y)(x+5)

Given the following expression shown below

2x^3 + 10x^2 − 4x^2y − 20xy

Factor out the GCF

2x^2(x+5)-4xy(x+5)

Group

(2x^2-4xy)(x +5)

2x(x-2y)(x+5)

Hence the complete factor of the given expression is 2x(x-2y)(x+5)

Learn more on factoring here: https://brainly.com/question/24734894

#SPJ1

All the points which are at the distance of PQ from the center of the circle will be located on the circle.

A circle is a closed shape created by following a moving point on a plane while maintaining a constant distance from another point.

According to the given question, the circle named A has it's center at the point P and has a point Q on the circumference of the circle, so any point at the distance of PQ from the center of the circle will lie on the circumference of the circle.

Learn more about circles on:

https://brainly.com/question/24375372

#SPJ4

Answer:

Points S, T, and W

Hope this helps!

Step-by-step explanation:

The proportion shows that the time taken to do the same job by Mrs. Squirrel is 6 hours.

From the information given, the ratios are:

Turtle / Squirrel = Squirrel / Pigeon

3/x = x/(1/48)

x² = 1/16

x = 1/4

The number of days will be:

= 1/4 × 24

= 6 hours.

Learn more about proportion on:

brainly.com/question/24372153

#SPJ1

For the triangle ABC, if B or C is an obtuse angle, then a = b cos C + c cos B  according to the law of sines and the addition formula.

For a triangle ABC with angles ∠A, ∠B, and ∠C and with sides a, b, and c

Thus, we can write,

sinA/a = sinB/b = sinC/c

or

a/sinA = b/sinB = c/sinC

It is given that in a ΔABC,

The ∠B or ∠C is an obtuse angle.

So, ∠A = 180° - (B + C)

⇒ sin A = sin (180° - (B + C))

⇒ sin A = sin (B + C) (since we know that sin(180° - θ) = sinθ)

From the addition formula,

sin (B + C) = sin B cos C + sin C cos B

⇒ sin A = sin (B + C)

⇒ sin A = sin B cos C + sin C cos B

From the law of sines,

a/sinA = b/sinB = c/sinC = K

⇒ aK =sin A, bK = sin B, cK = sin C

On substituting,

⇒ sin A = sin B cos C + sin C cos B

⇒ aK = bK cos C + cK cos B

⇒ K(a) = K(b cos C + c cos B)

∴ a = b cos C + c cos B

Hence it is proved.

Learn more about the law of sines here:

https://brainly.com/question/2807639

#SPJ1