6,9, 27/2,....
Find the 6th term.

Answers

Answer 1

Answer: 45.563

Step-by-step explanation:

Answer 2

The 6th term of the geometric progression is given by a₆ = 729 / 16

What is Geometric Progression?

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the 6th term of the geometric progression be a₆

Now , the first term of the GP is a₁ = 6

Let the second term of the GP be a₂ = 9

So , the common ratio of the GP is r = second term / first term

Substituting the values in the equation , we get

The common ratio r = 9/6 = 3/2

Now , the 6th term of the geometric progression a₆ = arⁿ⁻¹

On simplifying the equation , we get

The 6th term of the geometric progression a₆ = 6 ( 3/2 )⁵

The 6th term of the geometric progression a₆ = 6 ( 243 / 32 )

The 6th term of the geometric progression a₆ = 729 / 16

Hence , the 6th term of the GP is 729/16

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Related Questions

how much time is required for a 5.75 mgmg sample of 51cr51cr to decay to 0.700 mgmg if it has a half-life of 27.8 days? express the time in days to one decimal place.

Answers

The time is required for a 5.75 mg sample of 51cr to decay to 0.700 mg is 99.4 days

What is decay constant?

A property of unstable radionuclides that spontaneously decay at various rates to a more stable atomic configuration is the radioactive decay constant (λ); The higher the decay constant, the faster the parent radionuclide depletes over time.

Decay constant k = ln(2) / half life

= ln(2) / 27.8

= 0.024933 day⁻¹

For first order decay:

ln(M / M₀)  = -kt

where M is mass remaining at time t and  M₀ is initial mass.

ln(0.700/5/75) = -0.024933 * t

Time, t = 99.4 days

Hence, time is required for a 5.75 mg sample of 51cr to decay to 0.700 mg is 99.4 days.

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Find the slope of the line that passes through (5, 8) and (2, 4).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Answer:

4/3

Step-by-step explanation:

4-8/2-5

-4/-3

4/3

hopes this helps

Answer: 4/3 is the slope

You rent an apartment that costs \$1600$1600 per month during the first year, but the rent is set to go up 9.5% per year. What would be the rent of the apartment during the 9th year of living in the apartment? Round to the nearest tenth (if necessary).

Answers

The rent of the apartment during the 9th year of living in the apartment is $362

What would be the rent of the apartment during the 9th year of living in the apartment?

It should be noted that based on the information given, the person rent an apartment that costs $1600 per month during the first year, but the rent is set to go up 9.5% per year.

This will be:

= $1600 × (1 + 9.5%)^9

= $1600 × 1.095^9

= $1600 × 2.2632

= $3620

The rent is $3620.

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In circle L with m/KLM = 60°, find the angle measure of minor arc KM.

Answers

Answer:

minor arc KM = 60°

Step-by-step explanation:

the measure of an arc is equal to the measure of the central angle that subtends it , then

arc KM = ∠ KLM = 60°

Consider the vector field F(x,y,z)=⟨−7y,−7x,9z⟩. Show that F is a gradient vector field F=∇V by determining the function V which satisfies V(0,0,0)=0.V(x,y,z)=

Answers

The gradient of the vector field F(x , y , z) = ⟨−7y , −7x , 9z⟩ be

F'(x , y , z) = < 0 , 0 , 9 > i.e. F'(x , y , z) = 9k.

Given, a vector field F(x , y , z) = <-7y , -7x , 9z>.

we have to find the gradient of the vector field F = ∇V.

Also, the function V satisfies the condition V(0 , 0 , 0).

As, we know to find the gradient of the vector field F(x , y , z) we differentiate the vector field or differentiate the vector field partially.

F(x , y , z) = <-7y , -7x , 9z>

F(x , y , z) = -7yi - 7xj + 9zk

On differentiating, we get

F'(x , y , z) = <d(-7y)/dx , d(-7x)/dy , d(9z)/dz>

F'(x , y , z) = < 0 , 0 , 9 >

F'(x , y , z) = 9k

So, the gradient of the vector field F(x , y , z) be, 9k

Hence, the gradient of the vector field F(x , y , z) be

F'(x , y , z) = < 0 , 0 , 9 >

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Since 1992, the value of homes in a neighborhood has doubled every 16 years. The
value of one home in the neighborhood was $136,500 in 1992.

a. What is the value of this home, in dollars, in the year 2000? Explain your
reasoning.
b. Write an equation that represents the growth in housing value as a function of
time in t years since 1992.

c. Write an equation that represents the growth in housing value as a function of
time in d decades since 1992.
d. Use one of your equations to find the value of the home, in dollars, 1.5 decades
after 1992.

Answers

a. To find the value of the home in the year 2000, we need to find how many 16-year intervals have passed between 1992 and 2000. Since 2000 is 8 years after 1992, we have that $\frac{8}{16} = \frac{1}{2}$ 16-year intervals have passed. This means that the value of the home has doubled once since 1992, so it is now worth $136,500 * 2 = $273,000.

b. The growth in housing value as a function of time in t years since 1992 can be represented by the equation $V(t) = 136,500 * 2^{\frac{t}{16}}$, where $V(t)$ is the value of the home in t years after 1992 and 2 is the factor by which the value has doubled every 16 years.

c. The growth in housing value as a function of time in d decades since 1992 can be represented by the equation $V(d) = 136,500 * 2^{\frac{d * 10}{16}}$, where $V(d)$ is the value of the home in d decades after 1992 and 2 is the factor by which the value has doubled every 16 years.

d. To find the value of the home 1.5 decades after 1992, we can use the equation $V(d) = 136,500 * 2^{\frac{d * 10}{16}}$. Plugging in $d = 1.5$, we get $V(1.5) = 136,500 * 2^{\frac{1.5 * 10}{16}} = 136,500 * 2^{0.9375} = $351,284.375.

-(7x-8)=2-5x please I need help

Answers

Answer:

x = 3.

Step-by-step explanation:

To solve this equation, we first need to get all the terms containing the variable x on one side of the equation and all the constants on the other side. We can do this by adding 8 to both sides of the equation. This will give us:

$$-(7x-8) + 8 = 2-5x + 8$$

Next, we can simplify the left side of the equation by combining the two terms:

$$-7x + 8 + 8 = 2-5x + 8$$

This gives us:

$$-7x + 16 = 2-5x + 8$$

Now, we need to get all the x terms on one side and all the constants on the other side. We can do this by adding 5x to both sides of the equation:

$$-7x + 16 + 5x = 2-5x + 8 + 5x$$

This gives us:

$$-2x + 16 = 2 + 8$$

We can simplify the left side of the equation by combining the two terms:

$$-2x + 16 = 10$$

Now, we need to get all the x terms on one side and all the constants on the other side. We can do this by subtracting 16 from both sides of the equation:

$$-2x + 16 - 16 = 10 - 16$$

This gives us:

$$-2x = -6$$

To solve for x, we need to divide both sides of the equation by -2:

$$\frac{-2x}{-2} = \frac{-6}{-2}$$

This gives us:

$$x = 3$$

Therefore, the solution to the original equation is x = 3.

Find the area of a polygon with vertices A(–3, 1), B(–3, 4), C(7, 1), D(7, 4)

Answers

The area of the given polygon is 30 square units.

How to calculate the area of a triangle with coordinates of its vertices?

The area of a triangle can be calculated using the formula 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)] where (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the coordinates of its vertices. This formula is also useful in finding the area of any polygon with given coordinates.

The area of the given polygon can be calculated by the expression of the area of triangle as 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)].

The given polygon can be divided into two ΔABC and  ΔACD,

Then, the area is given as follows,

Area of ΔABC +  Area of ΔACD

= 1/2|[-3(4 - 1) + -3(1 - 1) + 7(1  - 4)]| + 1/2|[-3(1 - 4) + 7(4 - 1) + 7(1 - 1)]|

= 1/2 × 30 + 1/2 × 30

= 30

Hence, the area of the given polygon is 30 square units.

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i need help with my Math homework please​

Answers

Answer:

Step-by-step explanation:

15% of 3,000 is 450

Can Someone Solve This By Using The Formula a^2+b^2=c^2

Answers

Answer: 72 cm

Step-by-step explanation:

78 is the hypotenuse, so that it will be the c

30^2 + b^2 = 78^2

900 + b^2 = 6084

b^2 = 5184

b= 72cm

12. If g(x) = -4²-3r + 2, determine g(−2).
C

Answers

Answer:

Step-by-step explanation:

The diameter of the hubcap of a tire is 46 cm find the area in square centimeters of this hubcap write your answer in the terms of pi 

Answers

Answer:

[tex]529\pi[/tex] cm²

Step-by-step explanation:

[tex]d=46 \implies r=23 \\ \\ A=\pi r^2=\pi (23^2)=529\pi[/tex]

What does the bar in a fraction mean?

Answers

Answer:

A fraction bar separates the numerator and denominator of a fraction. It indicates that a division of the numerator by the denominator will be performed.

Step-by-step explanation:

In math, a fraction bar can be defined as a visual representation of fractions that helps in comparing fractions and carrying out operations with fractions. Fraction bars or fraction strips are a part-to-whole representational model. Each part of a fraction bar represents one unit out of a whole.

Answer:To separate the top and bottom numbers.

Step-by-step explanation:In math, a fraction bar can be defined as a visual representation of fractions that helps in comparing fractions and carrying out operations with fractions.

which expression represents w^-7 · w³ written in simplest form

Answers

Answer:

1/w^4

Step-by-step explanation:

please answer question 10

Answers

Answer: A song costs 0.99$, and an album 9.99$

Step-by-step explanation:

14.94=5x+1y

22.95=3x+2y

29.88=10x+2y

22.95=3x+2y

subtract

6.93=7x

x=0.99$

y=9.99

PLEASE HELP WITH THIS GEOMETRY!!!!! 50 POINTS & BRAINLIEST

Answers

Answer:

angle L= 55 degrees

Angle Lmk= 62 degrees

Step-by-step explanation:

we will find Lmk first by subtracting 118 by 180
180-118

62

Now the sum of all the three angles of any triangle equal 180

so we can set all these angles equal to find x

(6x-9)+(4x+7)+62=180

10x-2+62=180

10x+60=180

     -60. -60

10x=120

/10.  /10

x=12

4(12)+7

48+7

55

Hopes this helps have a wonderful day

Lisa works two jobs to pay for college. She tutors for $20 per hour and also works as a library assistant for $12 per hour. Due to her class and study schedule, Lisa is only able to work up to 18 hours per week but must earn at least $200 per week. If T represents the number of hours Lisa tutors and L represents the number of hours she works as a library assistant, which system of inequalities represents this scenario?

Answers

Answer:

20T+12L[tex]\geq[/tex]200

T+L[tex]\leq[/tex]18

Step-by-step explanation:

HELP ME!! I will give brainly

Answers

Answer:

-4

Step-by-step explanation:

First find the slope of the original line

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } \\\frac{1-0}{4-0} \\\frac{1}{4}[/tex]

Slope = 1/4

Then take it's negative reciprocal to get the slope of the perpendicular line by dividing 1 by the slope and then changing the sign

-4  

find x in the equation
x = 2
x = −2
x equals 392 over 9
x equals negative 392 over 9

Answers

Answer:

x= -2

Step-by-step explanation:

5x+1/3=1/3x-9

-1/3x.      -1/3x

4 2/3x+1/3= -9

           -1/3.  -1/3

4 2/3x= -9 1/3

14/3x= -28/3

/14/3.    /14/3

x= -28/3*3/14

x= -84/42

x= -2

hopes this helps please mark brainliest

Answer:

x = -2

Step-by-step explanation:

5x + 1/3 = 1/3x - 9

5x - 1/3x + 1/3 = -9

5x * 3                           15x

       --               >           --              (remember -> 5x is the same as 5/1x)

       3                            3

15x/3 - 1/3x + 1/3 = -9

14x/3 + 1/3 = -9

14x+1/3       = -9              (14x + 1 is ALL over 3)

Now multiply by 3 on both sides to cancel out the denominator since 3 is the denominator.

14x + 1 = -27

14x = -28

(divide by 14 to both sides)

x = -2

Find the slope of the line passing through the points (8, 4) and (8, -9).
slope:
Find the slope of the line passing through the points (-7, 5) and (5, 5).
slope:

Answers

Answer:

Step-by-step explanation:

Slope is "rise over run" or change is y values divided by change in x values

the change is x values is zero. 8-8=0. Anything divided by zero is infinity.

the slope is infinite. The line connecting the 2 points is a vertical line, x=8.

Vertical lines have infinite slope.

A senior accounting major at midsouth state university has job offers from four cpa firms. To explore the offers further, she asked a sample of recent trainees from each firm: how many months did you work before receiving a raise in salary? using the following anova table, is there a difference in the mean number of months before receiving a raise among the four firms? use the 0. 01 level of significance. Analysis of variance source df ss ms f p factor 3 25. 89 8. 63 4. 27 0. 031 error 11 22. 21 2. 02 total 14 48. 10 required: a. What are the null and alternate hypotheses? b. What is the test statistic? (round your answer to 2 decimal places. )

Answers

A) Reject H0 if F > 5.417.

B) We conclude that the average number of months before a raise was granted varied between the four CPA firms at the 0.05 level of significance but are unable to rule out the null hypothesis.

Given,

a) According to the table, the values for df1 and df2 are 3 and 15, respectively. Furthermore, a significance cutoff of = 0.01 is offered.

An additional f-value of 1.75 is given.

Given the significance level of = 0.01 and the corresponding values of df1 and df2 from the f-distribution table, we have;

F-critical 5.417

Normally, we reject H0 if F > 5.417.

We conclude that we do not rule out H0 at the 0.01 level of significance in this case because F is 1.75 5.417.

b) Using the values of df1 = 3 and df2 = 15 for 0.05 level of significance from the second linked table, we have

F-critical has a value of 3.2874.

The f-value is once more less than this significant one.

As a result, we cannot conclude that the average number of months until a raise was granted varied among the four CPA companies at the 0.05 level of significance and reject the null hypothesis.

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Which point is a solution to the system of inequalities graphed here?
y ≤ 2x + 2
y2-5x + 4

Answers

Both equations are satisfying by substituting (5, 0) in the system of inequalities.

What is a system of inequalities?

"A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system."

Given

System of inequalities graphed equation

y ≤ 2x + 2.................(1)

y ≥ -5x + 4................(2)

Substituting the point (5, 0) in equations 1 and 2

y ≤ 2x + 2

⇒ 0 ≤ 2(5) + 2

⇒ 0 ≤ 27

It is true

y ≥ -5x + 4

⇒ 0 ≥ -5(5) + 4

⇒ 0 ≥ -25 + 4

⇒ 0 ≥ -21

It is also true

In this option, Both equations are satisfying by substituting (5, 0)

Both equations are not satisfying by substituting (0, 5)

Hence, Both equations are satisfying by substituting (5, 0) in the system of inequalities given.

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Please help me. Write each proof
Please help please

Answers

What do you need help with take a picture of the question you need help with


Javier wants to prove that the base angles of an isosceles triangle are congruent. To do this, he draws triangle ABC,
with AB = BC. He will then prove that ZA and C are congruent by dividing triangle ABC into two triangles and
using triangle congruence.
Which of the following must be part of Javier's proof?
drawing a line parallel to AC through the midpoints of AB and BC
drawing a line parallel to BC through the midpoints of AB and AC
drawing a line perpendicular to AC through point B
drawing a line perpendicular to BC through point A

Answers

Answer:

C. Drawing a line perpendicular to [tex]\overline{AC}[/tex] through point [tex]B[/tex]

Step-by-step explanation:

The triangles formed by the perpendicular can be proved congruent by HL, and thus [tex]\angle A \cong \angle C[/tex] by CPCTC.

What is the equation for the line in slope-intercept form? enter your answer in the box.

Answers

The equation for the line in slope-intercept form y=-4x+5

1. We will, first of all, Determine the slope by counting down and over from one place to another. Let's start at (-2,13) and work our way down (0,5)

If at all you are concerned about miscounting, you can use the slope formula, which is y2-y1/x2-x1.

5-13/0--2 \s = -8/2

The gradient is -4.

2. Determine where the line intersects the y-axis to obtain the y-intercept. It crosses it at 5 here.

3. Write the equation in slope-intercept form, y=mx+b, where mx is the slope and b is the y-intercept.

y=-4x+5

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Find the coordinates
(Simplify your answer.)
A (-6x, 4y)
D
B (-2x, -4y)
of midpoint D.
W
Midpoint Formula
X1+X2
Y1+y2
yı+y2)
2
M = (x¹+x²,
D = ([?],
C (8x, -2y)
Enter

Answers

The coordinates of midpoint D from the given triangle ABC is (-4x, 0).

What is the midpoint of a line segment?

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.

The formula to find the midpoint of line segment is (x, y) = [(x1+x2)/2, (y1+y2)/2]

From the given figure, the coordinates are A(-6x, 4y) and B(-2x, -4y) and C(8x, -2y)

D(x, y)=[(-6x-2x)/2, (4y-4y)/2]

= (-4x, 0)

Therefore, the coordinates of midpoint D is (-4x, 0).

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If you can buy 2 bags of chips for $125. How many bags of chips can you get with $9,455 dollars? $7,600?
$1,000,000? Use a Ratio, ratio table, or equation to solve.

Answers

By using $9,455 dollars we can get 151 bags of chips and $7,600 dollars we can get 122 bags of chips and 16000 bags for $1,000,000 dollars.

What is Ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that you can buy 2 bags of chips for $125.

We need to find how many bags of chips we can get by $9,455 dollars,

$7,600 dollars and $1,000,000 dollars.

2/125=x/9455

Apply cross multiplication

2×9455=125x

18900=125x

Divide both sides by 125

x=151

So 151 bags we can get by using $9,455 dollars.

Now for $7,600 dollars.

2/125=x/7,600

2(7600)=125x

15200=125x

x=121.6 =122

So 122 bags we can get by using $7,600 dollars.

Now for $1,000,000

2/125=x/1,000,000

2000000=125x

Divide both sides by 125

16000=x

16000  bags for $1,000,000

Hence, 151 bags we can get by using $9,455 dollars, 122 bags we can get by using $7,600 dollars and 16000  bags for $1,000,000

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Consider the inequalities -2r<10 and -6<-2x

Answers

The value of the variable 'x' is less than 3 and the value of the variable 'r' is greater than negative 5.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequalities are given below.

-2r < 10 and -6 < -2x

The value of the variable 'r' is given as,

-2r < 10

2r > -10

r > - 10/2

r > - 5

The value of the variable 'x' is given as,

-6 < -2x

2x < 6

x < 6 / 2

x < 3

The value of the variable 'x' is less than 3 and the value of the variable 'r' is greater than negative 5.

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how many points does a team get when a player makes a shot from more than 25 feet away?

Answers

Answer:

e

Step-by-step explanation:

Please help asap. Anything helps!!!

Answers

Answer: 2x

Step-by-step explanation:

Ok I’ll take these one at a time

Picture 1:
You are given that two sides are congruent and you are given two angles in terms of x. You should know that all angles of a triangle must add up to 180, and if a triangle has two equal side lengths, it must have two equal angles. The equal angles will always be next to each other and the congruent sides. So because you know that all sides add up to 180, you can add all of the angles and set them equal to 180. This yields this equation:
(2x+2) + (2x+2) + (3x+1) = 180
7x + 5 = 180
7x = 175
x = 25˚

Picture 2:
This one might seem complicated being an hourglass-like shape, but just remember that all it is is 2 triangles. So lets start with the upper triangle. You know that the two sides are equal, so the two unknown angles in that triangle must also be equal. Using the fact that all three angles of any triangle will always add to 180, you can solve using the equation:
x + x + 55 = 180
2x=125
x=62.5
So angles 1 and 2 both equal 62.5
Now, the lower triangle.
If two triangles are stacked on top of each other with the same lines making up the angle, the angle must be the same. I didn’t do a very good job of explaining, but this phenomenon is known as “vertical angles” and you can search it up for a better explanation. So you know angle 3 is 55˚. The outside angle, 105, is on a straight line with angle 4, and you know that all straight lines have an angle of 180 degrees. So 180-105 will give you angle 4 which would be 75˚. Now you have two of the three angles of the bottom triangle, so because they must all add up to 180, you know that 180-75-55=50˚ so angle 5 is 50˚

Picture 3:
So once again you must apply the fact that triangles add up to 180˚ to set the sum of the three angles of the triangle equal to 180 yielding this formula:
(2x+13) + (3x) + (57) = 180
5x + 70 = 180
5x = 110
x = 22
To find y, you must remember that all straight lines are a 180 degree angle, and because you know a part of it, 57, you can do 180-57 to find y which makes y = 123
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