Determine whether the following sequence is geometric. If so, find the common ratio,
1.-3.9. - 27,...

Answers

Answer 1

Answer:

Yes, the sequence is geometric

common ratio (r) = -3

Step-by-step explanation:

Given:

[tex]a_1=1[/tex][tex]a_2=-3[/tex][tex]a_3=9[/tex][tex]a_4=-27[/tex]

If a sequence is geometric, common ratio [tex]r[/tex]:

[tex]r=\dfrac{a_4}{a_3}=\dfrac{a_3}{a_2}=\dfrac{a_2}{a_1}[/tex]

Substituting the given values:

[tex]\implies \dfrac{a_4}{a_3}=\dfrac{-27}{9}=-3[/tex]

[tex]\implies \dfrac{a_3}{a_2}=\dfrac{9}{-3}=-3[/tex]

[tex]\implies \dfrac{a_2}{a_1}=\dfrac{-3}{1}=-3[/tex]

Therefore, as

[tex]\dfrac{a_4}{a_3}=\dfrac{a_3}{a_2}=\dfrac{a_2}{a_1}=-3[/tex]

the sequence is geometric with common ratio of -3


Related Questions

The amount of a radioactive substance remaining after t years is given by the function , where m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain? ; 13.5 mg ; 34.6 mg ; 0.2 mg ; 4.6 mg

Answers

The required equation f(10) = 13.52 mg remains.

We have given that ,

m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60

What is the fromula for he amount of a radioactive substance remaining after t years?

The amount of a radioactive substance remaining after t years is given by the function  

[tex]f(t)=m(0.5)^{t/h}[/tex]............ (1),

where m = initial mass and h= half-life in years.

Now, for Cobalt-60, h = 5.3 years, m = 50 mg and t = 10 years,

then from equation (1) we get,

[tex]f(10)=50(0.5)^{10/5.3}[/tex]

Therefore  the required equation  f(10) = 13.52 mg .

To learn more about the mass of radioactive substance visit:

https://brainly.com/question/25793075

Answer:

The required equation f(10) = 13.52 mg remains.

We have given that ,

m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60

What is the fromula for he amount of a radioactive substance remaining after t years?

The amount of a radioactive substance remaining after t years is given by the function  

............ (1),

where m = initial mass and h= half-life in years.

Now, for Cobalt-60, h = 5.3 years, m = 50 mg and t = 10 years,

then from equation (1) we get,

Therefore  the required equation  f(10) = 13.52 mg .

To learn more about the mass of radioactive substance visit:

brainly.com/question/25793075

The points represent the vertices of a polygon. Use a matrix to find the coordinates of the image after the given transformation. Graph the preimage and the image.

A(2, 3), B(–1, –4), and C(2, –2); a translation 1 unit left and 4 units down. 30 points

Answers

The translation of points A(2, 3), B(–1, –4), and C(2, –2), 1 unit left and 4 units down gives A'(1, -1), B'(-2, -8) and C'(1, -6)

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, reflection and dilation.

Given the points A(2, 3), B(–1, –4), and C(2, –2), the translation 1 unit left and 4 units down gives:

A'(1, -1), B'(-2, -8) and C'(1, -6)

The translation of points A(2, 3), B(–1, –4), and C(2, –2), 1 unit left and 4 units down gives A'(1, -1), B'(-2, -8) and C'(1, -6)

Find out more on transformation at: https://brainly.com/question/4289712

Graph the line that represents the equation .
y = -2/3 x + 1

i really need ive tried multiple times and got it wrong every time

Answers

I would try Desmond graphing calculator it helps a lot. Or try putting a point at 1 on the y axis and then from there go over 2 negatively and up three

Which statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFraction?.

Answers

As x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.

Given function is:

[tex]f(x) = \frac{2x}{1-x^{2} }[/tex]

What is a function?

A function f(x) is a rule which relates two variables where x and y are independent and dependent variables.

Divide the numerator and denominator of the given function by x.

[tex]f(x) = \frac{2}{\frac{1}{x} -x}[/tex]

[tex]\lim_{x \to \infty} f(x) \\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x}[/tex]

As we know that as x approaches the infinity 1/x approaches 0.

So, [tex]\\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x} = \lim_{x \to \infty} \frac{2}{-x}[/tex]

[tex]\lim_{x \to \infty} \frac{-2}{x} =0[/tex]

Therefore, as x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.

To get more about functions visit:

https://brainly.com/question/25638609

How to find the measure of an interior angle inside a regular polygon

Answers

Answer:

Step-by-step explanation:

[tex]\frac{180(n-2)}{n}[/tex] degrees, where n is the number of sides

The measure of an interior angle inside a regular polygon is given by;

[tex]\rm S = (n -2) \times 180[/tex].

What is the interior angle?

An interior angle of a polygon is an angle formed inside the two adjacent sides of a polygon. Or, we can say that the angle measures at the interior part of a polygon are called the interior angle of a polygon.

An Interior Angle is an angle inside a shape.

As per the angle sum theorem, the sum of all the three interior angles of a triangle is 180°.

Multiplying two less than the number of sides times 180° gives us the sum of the interior angles in any polygon.

The measure of an interior angle inside a regular polygon is determined by the following formula;

[tex]\rm S = (n -2) \times 180[/tex]

S = sum of interior angles and n = number of sides of the polygon.

To know more about interior angles click the link given below.

https://brainly.com/question/10638383

#SPJ4

Can someone help me please

Answers

first add the ratio numbers which is 12

[tex] \frac{2}{12} \times 6000 = 1000[/tex]

then divide 1000 with 175

=5.71

5.71×2.25

=12.85 ruro

can someone help me? it’s due in a few hours

Answers

Answer:

cars value decreases in value exponentially

Step-by-step explanation:

cant really read it but say that the cars value decreases in value exponentially and compare that to however the other cars decrease in value over time

Simplify this please
(5ab²c)^2

Answers

Answer:

25a^2b^4c^2

Step-by-step explanation:

step 1:

Remove the bracket by multiplying all the power inside the bracket with the power outside the bracket.

5^2a^2b^2x2c^2=25a^2b^4c^2

The surface area of a cube is 294 square inches. What is the length of a lateral edge?

Answers

Answer:

7 inches

Step-by-step explanation:

The surface area of a cube is denoted by: A = 6s², where s is the side length.

Here, we know that A = 294, so plug this into the formula to solve for s:

A = 6s²

294 = 6s²

s² = 49

s = √49 = 7

Thus, the answer is 7 inches.

Terrence measured an Italian restaurant and made a scale drawing. The scale of the drawing was 7 centimeters = 2 meters. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.

Answers

Answer:

200/7

Step-by-step explanation:

(2 meters)/(7 centimeters) or (2m/7cm)

1 meter = 100 cm

(2m/7cm)*(100cm/1m) = 200/7 (or   28.57) scale factor.

What are the roots of the polynomial equation x superscript 4 baseline x squared = 4 x cubed minus 12 x 12? use a graphing calculator and a system of equations. round noninteger roots to the nearest hundredth. –12, 20 –2.73, 2, 2.73 –1.73, 1.73, 2 –20, 12

Answers

The roots of the provided polynomial equation of 4 degree are 2,2,1.73,-1.73.

What is a factor of polynomial?

The factor of a polynomial is the terms in linear form, which are, when multiplied together, give the original polynomial equation as a result.\

To find the roots of a polynomial, equate these factors of a polynomial to zero.

The given polynomial equation is,

[tex]x^4+x^2=4x^3-12x+12[/tex]

Take all the terms left side of the equation,

[tex]x^4+x^2-4x^3+12x-12=0\\x^4-4x^3+x^2+12x-12=0[/tex]

The factor form of the polynomial on solving the above equation, we get,

[tex](x-2)(x-2)(x-1.73)(x+1.73)=0[/tex]

Equate all the factors to zero, to find the roots. The roots we get are,

[tex]2,2,1.73,-1.73[/tex]

Hence, the roots of the provided polynomial equation of 4 degree are 2,2,1.73,-1.73.

Learn more about factor of polynomial here;

https://brainly.com/question/24380382

Answer:

–1.73, 1.73, 2

Step-by-step explanation:

Which angles are complementary to each other?

Answers

Answer:

<1 and <2

Step-by-step explanation:

Complementary angles are two angles which their measure add up to 90 degrees.

There are only one angle pair that meet this requirement:

angle 2 and angle 1

Solve using area model. 53x95

Answers

53x95 = 5035!


hopes this helps! ^^

Answer:

5605

Step-by-step explanation:

PLEASE HELP ASAP!!
A population of zombies in Happy Town, USA doubles every week. The number of zombies in Happy Town is currently 75. How many more zombies will there be after an additional 4 weeks? (no commas just numbers)

Answers

Answer:

1200

Step-by-step explanation:

since the first week has 75 doubling it is 150 doubling that is 300 doubling that is 600 doubling that for the final week is 1200.

1200 more zombies will there be after an additional 4 weeks.

What is Sequence?

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members (also known as elements or phrases), just like a set. The length of the series is the number of elements (potentially infinite).

At initial the zombies are= 75

Now, the zombies doubles at every week.

So, After 1 st week the population of zombies are

= 75 x 2

= 150

Then, After 2 nd week the population of zombies are

= 150 x 2

= 300

Then, After 3 rd week the population of zombies are

= 300 x 2

= 600

Then, After 4th week the population of zombies are

= 300 x 2

= 1200

Learn more about Sequence here:

https://brainly.com/question/30262438

#SPJ2

Good afternoon, please help me with this question and if u get it correct ill give u the brainlest

Answers

Answer:

5/6

Step-by-step explanation:

it comes out originally like 10/12 but if your simplify it it's 5/6

Answer:5/6

Step-by-step explanation: 12-2 =10 so 10/12 which simplifies to 5/6

The length of a rectangular frame is represented by the expression 2x 10, and the width of the rectangular frame is represented by the expression 2x 6. Write an equation to solve for the width of a rectangular frame that has a total area of 140 square inches. 4x2 32x − 80 = 0 4x2 32x 60 = 0 2x2 32x − 80 = 0 x2 16x 60 = 0.

Answers

The equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.

What is the area of the rectangle?

The area of the rectangle is the product of its length and its breadth.

As it is given that the length of the rectangular frame is (2x+10), while the width of the rectangular frame is (2x+6). Also, it is mentioned that the area of the rectangular frame is 140 in².

Now we know the area is the product of length and breadth, therefore,

[tex]\rm \text{Area of rectangle} = length \times breadth[/tex]

[tex]140 = (2x+10)(2x+6)\\\\140 = 4x^2 + 12x + 20x + 60\\\\0=-140+4x^2 + 12x + 20x + 60\\\\4x^2 + 32 x -80=0[/tex]

Hence, the equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.

Learn more about the Area of Rectangle:

https://brainly.com/question/14383947

Answer:

A.)  4x2 + 32x − 80 = 0

Step-by-step explanation:

Just took the test

PLEASE HELP!! It's due tomorrow and I don't understand it..

Answers

Do you need help with a specific one or all of them?

Determine the solution to the system of equations below.

x - 3y = 1
3x-5y = 11

Pls answer for 50 brainlist!!

Answers

Answer:

[tex]\boxed{\sf{x=7 \quad y=2}}[/tex]

Step-by-step explanation:

To solve this problem, isolate it on one side of the equation.

x-3y=1 and 3x-5y=11

x-3y=1: x=1+3y

x=1+3y

Substitute.

x=1+3y= 3(1+3y)-5y=11

Solve.

3+4y=11

Subtract by 3 from both sides.

3+4y-3=11-3

Solve.

11-3=8

Rewrite the problem down.

4y=8

Divide by 4 from both sides.

4y/4=8/4

Solve.

8/4=2

y=2

x=1+3y

x=1+3*2

Solve.

PEMDAS stands for:

ParenthesisExponentsMultiplyDivideAddSubtract

1+3*2

Multiply.

3*2=6

Add.

1+6=7

x=7

Therefore, the correct answer is x=7 and y=2.

I hope this helps you! Let me know if my answer is wrong or not.

The school has $3,582 to spend on markers. Each package of markers costs $9. How many packages of markers can the school buy?​

packages

Answers

Answer:

398

Step-by-step explanation:

3582 / 9 = 398

Suppose that 25 students in an AP Statistics class independently do this exercise for homework and that all of their calculators are working properly. Find the probability that at least one of them makes a Type I error.

Answers

Using the binomial distribution, it is found that there is a 0.999977 = 99.9977% probability that at least one of them makes a Type I error.

What is the binomial distribution formula?

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.

In this problem:

There are 25 students, hence n = 25.70% do not commit any error, hence 30% do and p = 0.3.

The probability that at least one commits an error is given by:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{30,0}.(0.3)^{0}.(0.7)^{30} = 0.000023[/tex]

Then:

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.000023 = 0.999977[/tex]

There is a 0.999977 = 99.9977% probability that at least one of them makes a Type I error.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

15 POINTS

Write an equation in standard form for the given circle

A.) (x+3)^2 + (y+6)^2 = 16
B.) (x-3)^2 + (y+6)^2 = 16
C.) (x+3)^2 + (y-6)^2 = 16
D.) (x-3)^2 + (y-6)^2 = 16

Answers

Equation of a Circle: (x - h)^2 + (y - k)^2 = r^2

---Center = (h, k)

---Radius = r (this value will need to be squared in the final answer)

Center = (-3, -6)

---h = -3

---k = -6

Radius = 4

Equation: (x + 3)^2 + (y + 6)^2 = 16

Correct Answer: A

Hope this helps!

100 POINTS !! The trajectory of a potato launched from a potato cannon on the ground at an angle of 45 degrees with an initial speed of 70 meters per second can be modeled by the parabola f(x) = x − 0.002x2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the potato travels before hitting the ground. A.height: 125 m; distance: 500 m B.height: 250 m; distance: 22 m C. height: 500 m; distance: 125 m D. height: 22 m; distance: 250 m

Answers

Answer:

height: 125m; distance: 500m

Step-by-step explanation:

x = 250

f(x) = x − 0.002x2

f(x) = 250 − 0.002(250 )2

= 250 − 0.002(62,500)

= 250 − 125

= 125

250 times 2 = 500

[tex]\\ \rm\rightarrowtail y=x-0.002x^2[/tex]

So

Put 250

[tex]\\ \rm\rightarrowtail y=250-0.002(250)^2[/tex]

[tex]\\ \rm\rightarrowtail y=250-0.002(62500)[/tex]

[tex]\\ \rm\rightarrowtail y=250-125[/tex]

[tex]\\ \rm\rightarrowtail y=125m[/tex]

This is max height

Distance:-

2×height2×125500m

y = x + 2
5x - 4y = -3
Solving systems by equations

Answers

Answer: x = 5, y = 7

Step-by-step explanation:

1. First, put the variables together/rearrange:

y - x = 2 & 5x - 4y = -3

2. Cancel out variable x by multiply the first equation by 5:

5y - 5x = 10 & 5x - 4y = -3

3. Add equations:

y = 7

4. Then determine x by plugging y back into the first equation y = x + 2:

x = 5

Write a formula that shows the dependence of: the length of the side (a) of a cube on the surface area (S) of the cube

Write the formula for the parabola that has x-intercepts (-3-√2,0) and (-3+√2,0), and y-intercept (0,-5)

Answers

Answer:

Let a = side length of a cube

Let S = surface area of a cube

Area of a square = a²

Since a cube has 6 square sides:  S = 6a²

To make a the subject:

S = 6a²

Divide both sides by 6:

[tex]\sf \implies \dfrac{S}{6}=a^2[/tex]

Square root both sides:

[tex]\sf \implies a=\sqrt{\dfrac{S}{6}}[/tex]

(positive square root only as distance is positive)

-----------------------------------------------------------------------------------------------

[tex]\sf x=-3-\sqrt{2} \implies (x+[3+\sqrt{2}])=0[/tex]

[tex]\sf x=-3+\sqrt{2} \implies (x+[3-\sqrt{2}])=0[/tex]

Therefore,

[tex]\sf y=a(x+[3+\sqrt{2}]) (x+[3-\sqrt{2}])[/tex]  for some constant a

Given the y-intercept is at (0, -5)

[tex]\sf \implies a(0+3+\sqrt{2}) (0+3-\sqrt{2})=-5[/tex]

[tex]\sf \implies a(3+\sqrt{2}) (3-\sqrt{2})=-5[/tex]

[tex]\sf \implies a(9-2)=-5[/tex]

[tex]\sf \implies 7a=-5[/tex]

[tex]\sf \implies a=-\dfrac57[/tex]

Substituting found value of a into the equation and simplifying:

[tex]\sf y=-\dfrac57(x+[3+\sqrt{2}]) (x+[3-\sqrt{2}])[/tex]

[tex]\sf \implies y=-\dfrac57(x^2+6x+7)[/tex]

[tex]\sf \implies y=-\dfrac57x^2-\dfrac{30}{7}x-5[/tex]

Which ordered pair is a solution of...
x-y = -3
2x+y = 0

a. (-3,0)
b. (-1,2)
c. (0,0)
d. (1,4)

Answers

It’s B
Explanation: because it’s B

Answer:

the answer to your question is B

What would you drink to survive a extra 30 years?

A. Lean
B. Orange Juice
C. Mug

Answers

Lean bc I LOVE LEAN!!!

of the 64 students in grade five, 3/8 of them either walk or ride a bike to school. the rest take a bus. how many fifth graders take a bus to school?

Answers

Answer:

24

Step-by-step explanation:

I did this question before.

3. How many 3 digit all even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

Answers

Step-by-step explanation:

Only 3 numbers are possible at units place (2, 4 & 6) as we need even number.

But at tens & hundreds place all 6 are possible

Number of 3 digit even numbers

= 3x6x6 = 108

Answer:

36

Step-by-step explanation:

[tex]Solution:[/tex]

[tex]6\times6=36[/tex]

[tex]such\ as:[/tex]

[tex]11\ \ \ 22\ \ \ 33\ \ \ 44\ \ \ 55\ \ \ 66\\ 12\ \ \ 21\ \ \ 31\ \ \ 41\ \ \ 51\ \ \ 61\\ 13\ \ \ 23\ \ \ 32\ \ \ 42\ \ \ 52\ \ \ 62\\ 14\ \ \ 24\ \ \ 34\ \ \ 43\ \ \ 53\ \ \ 63\\ 15\ \ \ 25\ \ \ 35\ \ \ 45\ \ \ 54\ \ \ 64\\ 16+263646+56\\ 6+6+6+6+6+6\\ =36.[/tex]

I hope this helps you

:)

Find two integers having a product of positive 27 and a sum of negative 12.

Answers

I know you're looking for an answer but i'm doing a challenge where i have to answer 10 questions by the end of today, I'm sorry! :(

What is the word form for 407,219?
A
Four hundred seventy thousand and two hundred ninety
B
Four hundred seventeen thousand, two hundred nineteen
C
Four hundred seven thousand, two hundred nineteen
D
Four hundred seven thousand, two hundred and nineteen

Answers

Answer:

C or D Both basically

Step-by-step explanation:I read them

C -four hundred seven thousand, two hundred nineteen
Other Questions
The situation that arises when the norms of society are unclear or are no longer applicable is referred to as a. conformity. c. strain theory. b. anomie. d. conflict. please select the best answer from the choices provided a b c d What is the area of this rectangle?11.2 cm5.1 cm Make a title about this short paragraph and write a statement that is your own opinion about this paragraph Engaging in creative activities is one of the managing measure of adolescence? An umbrella policy would be most useful for people who want to:A. protect their wealth from any liability.B. reduce the cost of their insurance premiums.C. leave money to cover their funeral expenses.D. be prepared in the event of a long-term injury. The base of a triangle is (x - 3) inches. The height of a triangle is 4.5 inches. If the area is 27 square inches, what is the value of x? two or more substances combine to form a single new substance The volume of a right cone is 252pi units^3. If its height is 21 units, find its radius. The two conditional relative frequency tables below show the results of a survey asking students whether they are taking a foreign language or not.A 4-column table with 3 rows. The first column has no label with entries middle school, high school, total. The second column is labeled taking a foreign language with entries 0.34, 0.66, 1.0. The third column is labeled not taking a foreign language with entries 0.64, 0.36, 1.0. The fourth column is labeled total with entries 0.4, 0.6, 1.0.Table B: Frequency of Foreign-Language Studies by RowA 4-column table with 3 rows. The first column has no label with entries middle school, high school, total. The second column is labeled taking a foreign language with entries 0.68, 0.88, 0.8. The third column is labeled not taking a foreign language with entries 0.32, 0.12, 0.2. The fourth column is labeled total with entries 1.0, 1.0, 1.0.Which table could be used to answer the question "Assuming a student is taking a foreign language, what is the probability the student is also in high school?Table A, because the given condition is that the student is in high school.Table A, because the given condition is that the student is taking a foreign language. Table B, because the given condition is that the student is in high school. Table B, because the given condition is that the student is taking a foreign language What weighs more 5kg of feathers or 5kg of steel Could anyone please help me with these questions? PLEASE show all the work and I'll give u the brainiest.1. A circle has a diameter from (8,2) to (0,2). Find the coordinates of the center of the circle and find the area. Use 3.14 as pi.2. An amusement park just build a brand new Ferris wheel. But the Ferris wheel rolled 4 revolutions before coming to stop. The diameter of the Ferris wheel is 520 feet. What's the area of the circle? What led to the Greeks being independent-minded? Using the digits 1, 3, and 5 only once, write the greatestand least three-digit numbers you can. Solutions of monosodium phosphate and disodium phosphate are combined in equal volume to produce a buffer. Identify the combination that will produce the buffer with the highest buffer capacity a student sketched some art on an 8 inch x 10 inch piece if paper he wants to resize it to fit an 4 inch x 6 inch frame. What percent of the original sketch was still able to be included?(someone asked this question but all the answers were wrong, so I am letting you know that the correct answer is 83.3%) When evaluating a source for its usefulness, a writer is trying to determine if the source:A) was published recently.B) is relevant to his purpose and message.C) presents information fairly and is unbiased.D) All of the choices are correct. explain why not all solutions represented by inequation are always possible solutions in reality. A school gym has an area of 4,641 square feet and a perimeter of 284 feet. What are the dimensions of the gym? What are the two places in a cell where i could find dna? What combination led to the german defeat in the battle of stalingrad?.