Find the 11th term of the geometric sequence 1, 3, 9, ....

Answers

Answer 1

Answer:

So lets calculate, we know that the common multiplier is 3. So we can use the geometric sequence formula.

(ar)^(n-1)

So we have 1*3 = 3. 3 to the power of 11-1 = 10. So our answer is 3^10 or 59049. Thats the answer

59049

Answer 2

The 11th term of the geometric progression is 59049

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 ,

The first term of the geometric progression is a = 1

The common ratio r = second term / first term

                                 = 3/1

                                 = 3

The number of terms n = 11

So , the equation to calculate the nth term of a GP is

aₙ = arⁿ⁻¹

Substituting the value of a , n and r  we get

a₁₁ = ar¹¹⁻¹

a₁₁ = ar¹⁰

a₁₁ = 3¹⁰

a₁₁ = 59049

Therefore the value of a₁₁ is 59049

Hence , The 11th term of the geometric progression is 59049

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Related Questions

The names of 5 boys and 5 girls are in a hat. What is the probability of first drawing a girl’s name and then a boy’s name from the hat?

Answers

Answer:

9/20

Step-by-step explanation:

The probability of drawing a girl's name is 0.5, since there are 5 girls in 10 kids here.  If that girl's name is not replaced, then the probability of drawing a boy's name is 5/9, since there are still such names but the total number of names is now 9.

Thus, the probability of this joint event is (0.5)(9/10) = 4.5/10 = 9/20

Answer:

so drawing a girls name from the hat would be 5/10 since 5 girls are there out of 10 students in total. After, you pick the girls name the total number of student names would become 9 and since there are 5 guys, you get a 5/9 probability

Find the area of the shaded region. Can I have the steps explained please?

Answers

Answer:

76.3 cm²

Step-by-step explanation:

step 1

area of circle= πr²= 3.14*5²= 78.6 cm²

step 2

area of 60° sector= 60/360*area of circle= 1/6*78.6= 13.1 cm²

step 3

Area of equilateral triangle = √3/4a²= √3/4*5²= 10.83 cm²

step 4

Area of circle - area of sector + area of triangle=  78.6 - 13.1 + 10.8= 76.3 cm²

The day after her birthday party 1/3 of Emma’s birthday cake is left is the remaining cake is shared equally among Emma her brother Owen and their mother and father what fraction of the original Kikoo each of them get

Answers

Answer:1/4

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

1/3 ÷ 4

1/3 x 1/4 = 1/12

What’s the answer to this ??

Answers

Answer:

Option C

Step-by-step explanation:

zero's are

(2, 0) and (0, -2)

y= x-2, x<3

(3, 2) and (4,3)

y=x-1, x≥3

These are covered in Option C

cos (x/2) = -sqrt2/2 in (0,360) looking for two values ?? Can someone please help me I can’t seem to figure out how to solve this problem, I’m looking at other examples but I’m still confused please help

Answers

Answer:

135° and 225°

Step-by-step explanation:

basically you want to find the value of x between 0 and 360 in this equation

cos x/2 = -(√2)/2

assume x/2 as n, so

cos n = -(√2)/2

n = 45°

then remember the quadrant system

0-90 1st quadrant, all is POSITIVE

90-180 2nd quadrant, only SIN has positive value

180 - 270 3rd quadrant, only TAN has positive value

270 -360 4th quadrant, only COS positive here.

so if you try to find negative value look into 2nd and 3rd quadrant that related 45° to x-axis (0°or 180°)

so the value of x is

180 - 45 = 135° (2nd quadrant) and

180 + 45° = 225° (3rd quadrant)

A sequence is defined by the recursive function f(n + 1) = –10f(n). If f(1) = 1, what is f(3)?

Answers

Answer:

f(3) = 100

Step-by-step explanation:

Using the recursive formula and f(1) = 1 , then

f(2) = - 10 f(1) = - 10 × 1 = - 10

f(3) = - 10 f(2) = - 10  × - 10 = 100

Answer:

100

Step-by-step explanation:

How are the equations of a parabola, ellipse, and hyperbola created?

Answers

Answer:

ellipses and hyperbolas as a simple form has the x-axis as principal axis and the origin (0,0) as center. If it's a circle, c = 0 so a2 = b2. And for the parabola, the standard form has the focus on the x-axis at the point (a, 0) and the directrix the line with equation x = −a.

(I'm sorry I got most of this from google) :(

Simply the expression [tex]\frac{x-7}{3} - \frac{5-x}{2}[/tex]

Answers

Answer: [tex]\frac{5x-29}{6}[/tex]

Step-by-step explanation:

To simplify the equation, we can just subtract the 2 fractions. First, we need to make sure they have a common denominator.

[tex]\frac{2(x-7)}{6} -\frac{3(5-x)}{6}[/tex]

Now that the fractions have the same denominator, we can distribute the numerator and subtract.

[tex]\frac{2x-14}{6} -\frac{15-3x}{6} =\frac{2x-14-15+3x}{6} =\frac{5x-29}{6}[/tex]

how to find the distance from a velocity-time graph?

Answers

Answer:

Calculating the distance travelled

Calculate the total distance travelled by the object - its motion is represented by the velocity-time graph below.

Here, the distance travelled can be found by calculating the total area of the shaded sections below the line.

½ × base × height.

½ × 6 × 2 = 12 m 2

(10 – 6) × 2 = 8 m 2

Answer:

Calculate the total distance travelled by the object - its motion is represented by the velocity-time graph below.

Here, the distance travelled can be found by calculating the total area of the shaded sections below the line.

½ × base × height.

½ × 4 × 8 = 16 m 2

(10 – 4) × 8 = 48 m 2

Step-by-step explanation:

Suck at maths! HELP!

Answers

Answer:

Step-by-step explanation: you can use a protractor if you have 1 or seeing as the bottom left is 65, the bottom right will be the same, mostly a guess but half 65 and try that.

A=50
Explanation as it is an isosceles triangle it ads up to 180
65+65=130
180-130=50

which expression is equivalent to 7/12?

Answers

if i understand correctly what you mean by this question the answer could be

14/24

28/48

you can just keep multiplying the top and the bottom by the same number to get an equivalent fraction

im sorry if i understood the question wrong, i hope this helped a little bit

Disclaimer: The options are missing. The options to the question are:

A.7x1/12; B.7/7x12/12; C.1/7x7/12; D.12x1/7

The expression equivalent to 7/12 is 7x1/12. So, option A. is the right choice.

What are equivalent fractions?

Two fractions are said to be equivalent fractions when they both give the same value in their reduced or simplest form.

How do we solve the given question?

We are asked to find the expression equivalent to 7/12 from the given options.

To solve the question, we reduce all the options to their simplest form. The option = 7/12 will be our answer.

A. 7 * 1/12 = 7/12B. 7/7 * 12/12 = 1*1 = 1C. 1/7 * 7/12 = 1/12D. 12 * 1/7 = 12/7

As we can see only option A. 7 * 1/12 = 7/12 in its simplest form, so it is the right option.

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-7/10+7/15+1/-20+-9/10+11/15+11/-20
what is the answer please help me .....!!!!

Answers

Answer:

-1

Step-by-step explanation:

-7/10+7/15+1/-20+-9/10+11/15+11/-20

= -7/10 + -9/10 + 7/15 + 11/15 + 1/-20 + 11/-20

= -16/10 + 18/15 + 12/-20

= -8/5 + 6/5 + -3/5

= (-8+6-3)/5

= -5/5

= -1

The interior angles of a triangle are 42°,56° and 2x°. Find the value of x.

Answers

Answer:

41 degrees

Step-by-step explanation:

Since the sum of the interior angles of a triangle will always be 180 degrees:

42+56+2x=180

2x=82

x=41

Hope this helps!

Answer:

X=41°

[tex]solution \\ 42 + 56 + 2x = 180(sum \: of \: angle \: in \: triangle) \\ or \: 98 + 2x = 180 \\ or \: 2x = 180 - 98 \\ or \: 2x = 82 \\ or \: x = \frac{82}{2} \\ x = 41[/tex]

hope this helps...

Good luck on your assignment...

Which expression can be used to find the sum of the polynomials? (9 – 3x2) + (–8x2 + 4x + 5)

Answers

Answer:

- 11x² + 4x + 14

Step-by-step explanation:

Given

(9 - 3x²) + (- 8x² + 4x + 5) ← distribute both parenthesis by 1

= 9 - 3x² - 8x² + 4x + 5 ← collect like terms

= - 11x² + 4x + 14 ← sum of the polynomials

Answer:

D.)[(-3x^2)+(-8x^2)]+4x+[9+5]

Step-by-step explanation:

The reason this is right is because I took the quiz.


I need help .... can y’all help me

Answers

6. C.

7. B.

8. B.

9. B.

10. C

PLEASE HELP!!! this is really dependant on my final grade !

Answers

Answer:
x-intercept: (-2, 0)
y-intercept: (0, -2.5)

Explanation:
To solve this problem you must graph the equation. I attached an image of it graphed. There you can see the x- and y-intercepts.

Gisele worked as a carpenter for how many hours and worked as a blacksmith for how many hours last week? please help

Answers

Answer: She worked as a carpenter for 12 hours and a blacksmith for 18 hours.

Step-by-step explanation:

18*25 = 450

12*20 = 240

240 + 450 = 690

12 + 18 = 30.

Triangle L N P has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N R, L P, and Q M. The length of line segment N S is 7 x minus 3 and the length of line segment S R is 5 x minus 3. What is the length of segment NS? 1 unit 2 units 4 units 6 units

Answers

Answer:

6 units

Step-by-step explanation:

Given: Triangle L N P has centroid S.

[tex]NS=7x-3, SR=5x-3[/tex]

To find: NS

Solution:

Centroid is the point of intersection of the medians of the triangle such that it divides each of the median in ratio [tex]2:1[/tex]

So,

[tex]NS:SR=2:1\\\frac{NS}{SR}=\frac{2}{1} \\[/tex]

Put [tex]NS=7x-3, SR=5x-3[/tex]

[tex]\frac{7x-3}{5x-3}=\frac{2}{1}\\ 7x-3=10x-6\\10x-7x=-3+6\\3x=3\\x=1[/tex]

Therefore,

[tex]NS=7x-3=7(1)-3=4\,\,units\\SR=5x-3=5(1)-3=2\,units[/tex]

So,

[tex]NS=NS+SR=4+2=6\,\,units[/tex]

Answer:

The answer is 4

Step-by-step explanation:

It asks for the length of NS not the length of NR

YEAR 9 MATHS- PLEASE HELP
The shape A has been reflected on the line drawn to give shape B.
State the equation of the line.

Answers

Answer:

y=2

Step-by-step explanation:

since the line is horizontal, on the point 2 on the y axis, the equation is 2. If, however the line were to be diagonal, it would have been different, as would it if the line were vertical(in which case, the equated would start x =)

Hope this helps

Answer: y =2

Step-by-step explanation:

Find the surface area of a cylinder with a diameter of 4 cm, and a height of
8 cm. (use 3.14 for Pi) *

Answers

Answer:

125.66

Step-by-step explanation:

Simplify 3x(2x + 4y)

Answers

Answer:

[tex]6x^2+12xy[/tex]

Step-by-step explanation:

By the distributive property:

[tex]3x(2x+4y)= \\\\3x(2x)+3x(4y)=\\\\6x^2+12xy[/tex]

Hope this helps!

What is the decimal multiplier to increase by 99%?

Answers

Answer:To work out the multiplier, first add or subtract the percentage from 100, then convert to a decimal. Example: we want to add 20% to £110. To work out the multiplier, add 20 to 100, to get 120, and then change it to a decimal (divide by 100) to get 1.2.

Step-by-step explanation:

The decimal multiplier of a number to increase by 99% will be 1.99.

What is the percentage?

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

Let's consider the number x.

To increase it by 20% we need to find 20% of it so 0.20x

Now, add this 20% to x so that it will increase by 20% as,

0.20x + x = 1.20x

Thus,to increase the number by 20% we need to multiply 1.20

Similarly to increase a number by 99% we need to multiply with 1.99.

Hence "The decimal multiplier of a number to increase by 99% will be 1.99".

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Since slope is calculated using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction, the slope of both lines is equivalent to ________. It is given that the lines are parallel, and we calculated that the slopes are the same. Therefore, parallel lines have the same slopes.

Answers

Answer:

The product of these slopes is [(d-b)/(c-a)] × [(c-a)/(-d+b)] = -1

Proved: This product shows that the slopes are negative reciprocals

Question:

The complete question as seen on brainly ( question ID = 13270010):

Determine the missing information in the paragraph proof.

Given: Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular. Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).

Prove: The slopes of perpendicular lines are negative reciprocals.

The slopes of lines PQ and P’Q’ can be determined using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction

The product of these slopes is ________. This product shows that the slopes are negative reciprocals. It is given that the lines are perpendicular and we have shown that the slopes of the lines are negative reciprocals.

Step-by-step explanation:

Line PQ contains the points (a, b) and (c, d)

Line P’Q’ contains the points (–b, a) and (–d, c)

The two lines are said to be perpendicular.

For two lines are said to be perpendicular, the product of the slope of the two lines must be equal to -1.

Let's determine if it's true for this two lines.

Find attached the the diagram and explanations.

The product of these slopes is [(d-b)/(c-a)] × [(c-a)/(-d+b)] = -1

This product shows that the slopes are negative reciprocals

Answer:5

Step-by-step explanation:

Mary is paid 7.5% commission on all of her sales. She had sales of $2300 for the month of December. How much commission did Mary make?

Answers

Answer: $172.50

Step-by-step explanation:

$2300 x 0.075 = $172.50

You can double check quickly because you know 10% of 2300 is $230, so 5% is $115.  The answer is halfway between the 5% and 10% numbers, so you know it is reasonable.

Dr.Chavez drew a rectangle on a coordinate plane to estimate the size of a lake. Each unit represents 1 mi. The coordinates of the rectangle are the origin, (0,7.65), (12.8, 7.65) and (12.8,0). Based on the information, what is the perimeter of the lake?

Answers

Answer:

40.9 mi

Step-by-step explanation:

The four points will make the rectangle, and each pair of points in sequence will create a side of the rectangle. So, to find the length of each side, we need to find the distances between each pair of points in sequence:

distance between (0,0) and (0, 7.65) -> |7.65 - 0| = 7.65 mi

distance between (0,7.65) and (12.8, 7.65) -> |12.8 - 0| = 12.8 mi

distance between (12.8, 7.65) and (12.8, 0) -> |0 - 7.65| = 7.65 mi

distance between (12.8, 0) and (0, 0) -> |0 - 12.8| = 12.8 mi

So the perimeter is 7.65 + 12.8 + 7.65 + 12.8 = 40.9 mi

Answer:

40.9 mi

Step-by-step explanation:

will make it simple and short

in a surveying measurements with coordinates, we always take it from the Zero. So each coordinates must be subtracted from Zero to get the length of each point.

therefore the perimeter = 0 + 7.65 + 12.8 + 7.65 + 12.8 + 0 = 40.9 mi

What is the vertical asymptote for the reciprocal of y=8x-4

Answers

Answer:

The vertical asymptote for the reciprocal of y=8x-4 is [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given Equation : [tex]y = 8x-4[/tex]

Reciprocal of given equation =[tex]\frac{1}{y}=\frac{1}{8x-4}[/tex]

Now to find the vertical asymptote

[tex]\frac{1}{y}=\frac{1}{8x-4}[/tex]

Equate denominator to 0

8x-4=0

8x=4

[tex]x=\frac{4}{8}[/tex]

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

So, The vertical asymptote is[tex]\frac{1}{2}[/tex]

Hence the vertical asymptote for the reciprocal of y=8x-4 is [tex]\frac{1}{2}[/tex]

Four different positive integers have a product of 110.
What is the sum of the four integers?

Answers

Answer:32.09

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

To Find Out What are the four Positive Integers, Let's Prime Factorize 110:

110 = 1 × 2 × 5× 11

This means these are the four positive integers by multiplying which results in 110.

Now, The sum of these integers:

=> 1+2+5+11

=> 19

Can somebody help me with this ?? :)

Answers

Answer:

(-3, -4)

Step-by-step explanation:

6 units down from point F will be x: 2, y: -4

5 units left from there will be x: -3, y: -4

Daniel, Clarence, and Matthew split a $20.20 dinner bill so that Daniel pays half of what Clarence pays. If Daniel pays $6.06, what is the ratio of Clarence's pay to Matthew's pay?

Answers

Answer:

grgrtgdegtrt

Step-by-step explanation:

etetetetrdgtfrrgdergdrg

Is the real number rational or irrational? rational irrational

Answers

Answer:

rational

Step-by-step explanation:

Answer:

Rational.

Step-by-step explanation:

A real number is rational.

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