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

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 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:

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.

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Answer:

A.)  4x2 + 32x − 80 = 0

Step-by-step explanation:

Just took the test

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

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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

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 .

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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 .

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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

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.

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.

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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! :(

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

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.

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

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.

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Answer:

–1.73, 1.73, 2

Step-by-step explanation:

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

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

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

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]

What would you drink to survive a extra 30 years?

A. Lean
B. Orange Juice
C. Mug

Answers

Lean bc I LOVE LEAN!!!

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.

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!

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

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?

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)

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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.

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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.

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

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.

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