What is the value of x in the geometric sequence x, 3, — ‚ .A. -27B. -9C. -1D. -3

What Is The Value Of X In The Geometric Sequence X, 3, .A. -27B. -9C. -1D. -3

Answers

Answer 1

Recall that in a geometric sequence, whenever we take one value of the sequence and divide it by the next number of the sequence, we would get a constant number unique to that sequence. If we take the first and second numbers and calculate the ratio, we get

[tex]\frac{x}{3}[/tex]

if we do that with the second and third numbers, we get

[tex]\frac{3}{\text{ -}\frac{1}{3}}=\text{ -}\frac{3\cdot3}{1\cdot1}=\text{ -9}[/tex]

this two numbers should be equal. So we get

[tex]\frac{x}{3}=\text{ -9}[/tex]

if we multiply both sides by 3, we get

[tex]x=3\cdot\text{ -9= -27}[/tex]

so option A is the correct option.


Related Questions

Which are the better statistics to use to compare the team scores

Answers

Step 1

We are given two team scores

Required; Which are the better statistics to use to compare the team scores

Step 2

The box plot displays the 5 number summary

-Minimum data value

-Maximum data value

-Median

-First Quartile, and

Third Quartile

The Interquartile Range (IQR) of the data can also be calculated by finding the difference between the First Quartile, and the third Quartile.

The Interquartile Range (IQR) helps us to determine the variability of the data set. The IQR is often seen as a better measure of spread than the range as it is not affected by outliers.

The median that is gotten from the box pot measures the center tendency of the data. The median is the most informative measure of central tendency for skewed distributions or distributions with outliers.

Therefore, the better statistics to use for comparing the scores of the teams are;

Median and IQR​.

what is the equivalent expression for:

m - (8 -3m)

Answers

4m-8 that’s your answer

Each relationship below compares the shaded portion the part to the entire figure the whole complete the table 6'60'600'32

Answers

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a portion of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Percent refers to one hundred percent.

A decimal is a number divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of full and partially whole quantities.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.

A ratio displays the multiplicity of two numbers. A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations.

Percentage  Decimal  Fraction                       Ratio

6%                  0.06        6 / 100                       6:100

60%                0.6          60 / 100                    60:100

600%              6             600 / 100 = 6 / 1         6:1

32%               0.32         32 / 100                     32:100

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Given the following: P(A)=0.28, P(B)=0.64, P(B|A)= 0.37, calculate P(A and B)

Answers

By definition of conditional probability you know that

[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]

Now, replace the values that you have and solve for P(A and B)​

[tex]\begin{gathered} P(B|A)=\frac{P(A\cap B)}{P(A)} \\ 0.37=\frac{P(A\cap B)}{0.28} \\ \text{ Multiply by 0.28 on both sides of the equation} \\ 0.37\cdot0.28=\frac{P(A\cap B)}{0.28}\cdot0.28 \\ \text{ Therefore,} \\ 0.1036=P(A\cap B) \end{gathered}[/tex]

A board 172 inches wide is cut to three-fourths of its original width

Answers

Answer: 129 inches

Step-by-step explanation:

172 inches x 3/4 original with = 129 inches

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 4.3% per hour. How many hours does it take for the size of the sample to double? Note this is a continuous exponential growth model. Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answers

Answer:

16.12 hours

Explanation:

A continuous exponential growth model is given below:

[tex]P(t)=P_oe^{rt}[/tex]

• The growth rate, r = 4.3% = 0.043

,

• t = time in hours

,

• Po = Initial population

,

• P(t) = Present population

We want to find the number of hours it takes the population to double. That is if the initial population, Po = 1

• The present population, P(t) = 1 x 2 = 2.

Substitute these values into the model above to get:

[tex]2=1(e^{0.043t})[/tex]

Since natural logarithm(ln) is the inverse of exponential, take the natural logarithm of both sides to remove the exponential operator.

[tex]\begin{gathered} \ln (2)=\ln (e^{0.043t}) \\ \ln (2)=0.043t \end{gathered}[/tex]

Divide both sides by 0.043.

[tex]\begin{gathered} \frac{\ln (2)}{0.043}=\frac{0.043t}{0.043} \\ t=\frac{\ln(2)}{0.043} \\ t\approx16.12 \end{gathered}[/tex]

It will take 16.12 hours for the size of the sample to double.

A family has 6 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 6 girls if it is known the family has at least one girl.

Answers

The probability that the family has 6 girls if it is known the family has at least one girl is; 3.125%

What is the Probability?

We are told that each child has the same chance of being a boy or a girl and as such we can say that probability is 1 in 2, or 0.50 or 50%.

Since the family must have at least one girl, if we assume that the first child is a girl, the the probability of the second child being a girl is 50%.

The probability of the other 5 children all being girls is:

(1/2) * (1/2) * (1/2) *(1/2) * (1/2) = 1/32.

This Probability expressed as a decimal or percentage represents a probability that we have as; 1/32 = 0.03125 = 3.125%.

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Select the table that represents a linear function. (Graph them if necessary.)
OA. x 0 1 2 3
y 2 3 6 11
OB. x 0 1 2 3
y 1 3 9 27
OC. x 0123
y 0149
OD. x 012
3
y 39 15 21

Answers

Answer:

The last table represents a linear function.

As x increases by 1 unit, y increases by a constant of 6 units

The equation of the function is

y = 6x + 3

Step-by-step explanation:

a cylinder shaped popcorn

Answers

Answer

Option C is correct.

Volume = 1,413 in³

Explanation

The volume of a cylinder is given as

Volume = πr²h

where

π = pi = 3.14

r = radius of the cylinder = ½ (Diameter) = ½ (10) = 5 inches

h = height of the cylinder = 1.5 feet = 1.5 (12 inches) = 18 inches

The conversion from feet to inches was done using 1 feet = 12 inches

So, we can calculate the volume now

Volume = πr²h

Volume = (3.14) × (5²) × (18)

Volume = 1,413 in³

Hope this Helps!!!

Give a parametric representation of the parabola y = (x+7)^2 -5

Answers

We have to find the parametric representation of the parabola y = (x+7)² - 5, which is represented in vertex form.

Parametric representations use a third variable on which we define x and y.

We will call this variable t.

We can start with defining t as:

[tex]\begin{gathered} t=x+7 \\ \Rightarrow x(t)=t-7 \end{gathered}[/tex]

We then have already x in function of t.

Then, we can use the definition of t to find y(t):

[tex]\begin{gathered} y(t)=(x(t)+7)^2-5 \\ y(t)=(t-7+7)^2-5 \\ y(t)=t^2-5 \end{gathered}[/tex]

We then have x and y defined in function of t.

Answer: we can represent the parabola in a parametric form as

x(t) = t-7

y(t) = t² - 5

the numberof blocks has 9 in the ones places.The number in the hundreds place is one more than the number in the tens place. Those two numbers equal 11. How many blocks are there?

Answers

Based on the given information, we can express the following

[tex]\begin{gathered} h=1+t \\ h+t=11 \end{gathered}[/tex]

Because the digit of hundreds is 1 more the tens, and they sum 11. Let's combine the function to find t

[tex]\begin{gathered} h+t=11 \\ 1+t+t=11 \\ 2t=11-1 \\ t=\frac{10}{2}=5 \end{gathered}[/tex]

So, the digit of tens is 5.

Let's find the hundreds.

[tex]h=1+t=1+5=6[/tex]

The number of hundreds is 6.

Hence, the number of blocks is 659.

b. Triangle DEF with coordinates D(-2, 2), E (1,5), and F (4, -1) is rotated 90° counterclockwise aboutthe origin

Answers

[tex]\begin{gathered} D^{}(-2,2) \\ E(1,5) \\ F(4,-1) \\ D´(-2,2) \\ E^{\prime}(-5,1) \\ F(1,4) \\ \text{The new coord}inates\text{ are }D´(-2,2),\text{ }E^{\prime}(-5,1)\text{ and }F(1,4) \end{gathered}[/tex]

cual es la raiz cuadrada de 4096 y 529

Answers

The square root of 4096 is 64 and the square root of 529 is 23.

The square root of a number x in mathematics is a number y whose square (the outcome of multiplying the number by itself, or y·y), is equal to x.

For instance, since 4² = (-4)² = 16, 4 and -4 are the square roots of 16.The square root of x is rational if and only if x is a rational integer that can be expressed as the ratio of two perfect squares. (The square root of 2 for proof that this number is illogical; the quadratic irrational for evidence against all non-square natural numbers.) The square root function changes rational numbers into algebraic numbers, which are a superset of rational numbers.

The given numbers are 4096 and 529.

Let us find the factors of 4096:

4096 = 2¹²

Therefore the square root of 4096 = √4096 = √(2¹²) = 2⁶ = 64 .

Let us find the factors of 529:

4096 = 23 × 23

Therefore the square root of 529 = √529 = √(23²) = 23 .

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Disclaimer : The question in English is :

What is the square root of 4096 and 529.?

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The bill at a restaurant came to $136.40. The patrons decided to leave a 15% tip. What was the total bill including tip?

Answers

Answer: 156.86

Step-by-step explanation:

Rudy has $90,000 in a savings account that earns 10% interest per year. The interest is not compounded. How much interest will he earn in 1 year?

Answers

The total interest earned by Rudy on the principal is $9000

Amount in Rudy's saving account = $90,000

Interest rate per year = 10%

The formula for simple interest is given:

A loan or deposit's principal amount serves as the foundation for simple interest. Compound interest, on the other hand, is calculated based on both the initial principal and the interest that is added to it each period.

Simple interest = P*R*T/100

where P = principal amount invested

R = rate of interest

T = time in years

Substituting the values in the formula we get:

Simple interest = 90000*10*1/100

= 9000

So, the interest amount is $9000

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Is the following a power function, a polynomial, both, or neither?f(x)=−17x^5

Answers

Answer:

Both

Explanation:

Given the function:

[tex]f(x)=-17x^5[/tex]

• A power function is a function with a whole number as its exponent.

,

• A monomial is a polynomial that has only one term.

The given funtion has 5 as its exponent, thus, it sis a power function. Furthermore, it is a monomial, thus it is also a polynomial.

f(x) is both a power function and a polynomial.

Hey there Ms or Mr could you please help me out with this problem? Just a heads up, this is my assignment not a quiz. My assignment is about distance and midpoint formula.

Answers

EXPLANATION

Let's see the facts:

Midpoint = (-2,5)

A=(4,7)

Let the point of B as B=(x,y)

Then,

[tex]\frac{x+4}{2}=-2,\frac{y+7}{2}=5[/tex]

Multiplying the frist equation by 2:

[tex]x+4=-2\cdot2[/tex]

Subtracting -4 to both sides:

[tex]x=-4-4[/tex]

Simplifying:

[tex]x=-8[/tex]

Multiplying the second equation by 2:

[tex]y+7=2\cdot5[/tex]

Subtracting -7 to both sides:

[tex]y=10-7=\text{ 3}[/tex]

The coordinates of the point B are:

B=(-8,3)

if a varies equal directly with b, and a=8 when b=20 what is the value of a when b= 14.5

Answers

[tex]\frac{8}{a}=\frac{20}{14.5}[/tex][tex]20a=8\cdot14.5[/tex][tex]a=\frac{116}{20}=5.8[/tex]

the supplement of an angle is 30 degrees more than the measure of the
what is the measure of
the angle?
angle,

Answers

Answer:

x = 75°

Step-by-step explanation:

supplementary angles sum to 180°

let x be the angle then x + 30 is the supplementary angle , so

x + x + 30 = 180

2x + 30 = 180 ( subtract 30 from both sides )

2x = 150 ( divide both sides by 2 )

x = 75

x + 30 = 75 + 30 = 105

the angle is 75° and the supplementary angle is 105°

Simplify 3^2 + 3(6 - 2^2) ÷ 6.

Answers

Fractions simplification

Apply PEMDAS method. Eliminate parenthesis first.

Then (3^2 + 3•6 - 3•2^2 )/ 6 = (3^2 + 3•6 - 3•2^2 )/ 6

now eliminate exponents

= [3• 3 + 3•6 + 3•4] / 6

= 3•5/6 now multiplicate

3•5= 15

Then

= 15/6 = 2 + 3/6 = 2 + 1/2 = 2.5

Angle JKL is an equilateral triangle jk=13x+5 KL=17x-19 and JL=8x+35

Answers

The value of x is 6, then the value of JK is 83, KL is 83 and JL is 83.

What is a triangle?

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

An equilateral triangle is a shape with three sides that have an equal measure of side length.

The 3 sides of triangle JKL are equal to each other, therefore we can equate any of the two sides together to find the unknown variable called x.

So, JK = KL

JK = 13x + 5

KL + 17x - 19

13x + 5 = 17x - 19

Collect like terms;

17x - 13x = 19 + 5

4x = 24

x = 24/4

x = 6

We can now proceed to find the sides;

JK = 13x + 5

13 x 6 + 5

= 78 + 5

= 83

JK = 83

KL = 17x - 19

= 17 x 6 - 19

= 102 - 19

= 83

KL = 83

JL= 8x + 35​

= 8 x 6 + 35

= 48 + 35

= 83

JL = 83

Hence, The value of x is 6, then the value of JK is 83, KL is 83 and JL is 83.

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what is probability that it is from the 70s is

Answers

Given :

the total number of collections = 60 vinyl

There are six from the 70s

So, the probability that is from 70s is :

[tex]\frac{6}{60}=\frac{1}{10}[/tex]

Given P250/75R18 tires, what would be the Circumference in inches of the tire?

Answers

Given data:

The given radius of the tire is r=18 in.

Th expression for the circumference is,

C=2πr

Substitute the given values in the above expression.

C=2(3.14)(18)

=113.04 in

Thus, the circumference of the tire is 113.04 inn.

ryan is buying pencil boxes. he wnats to buy the box that will fit the most markers. he can choose between the following 3 options

Answers

Answer:

what r the 3 following options??

Step-by-step explanation:

five friends are going to share 1/2 of a pizza. How much of a whole pizza will each friend eat?which equation can be used to solve the problem above?A.5÷1/2=nB.1\2÷5=nC.n÷5=1/2D.n÷1\2=5

Answers

In this case the answer is very simple .

Step 01:

Data

5 friends

1/2 pizza

Step 02:

We must distribute the pizza among 5 friends.

[tex]\frac{\frac{1}{2\text{ }}\text{ pizza}}{5\text{ friends}}\text{ = n}[/tex]

The answer is:

Option B.

1\2÷5=n


There are 151 people in the 6th
grade class. It costs $24 for each
person to go snorkeling. How
much did they pay altogether?

Answers

3624 is the correct answer because if you times 151 by 24 you will get 3624

Answer:

Step-by-step explanation:

it cost $3,624

What are the x intercept of the equation f(x)=3(x-7)(4x+2)

Answers

The x-intercepts are

x = 7

and

x = -1/2

SOLUTION:

we need to find the value of x where y or f(x) is 0

the expression x-7 will be zero if x=7

the expression 4x+2 will be zero if x = -1/2

2x – 1 over 5 - 3x +2 over 4

Answers

we have

(2x-1)/5-(3x+2)/4

{4(2x-1)-5(3x+2)}/20

{8x-4-15x-10}/20

{-7x-14}

5-(3x+2)/4

4(2x-1

How do I solve 5/9x+ 6=10?

Answers

Due to the inaccuracy of the provided information, we will suppose that the original expression is

[tex]\frac{5x}{9}+6=10[/tex]

Solve for x as shown below

[tex]\begin{gathered} \Rightarrow\frac{5x}{9}+6-6=10-6 \\ \Rightarrow\frac{5x}{9}=4 \\ \Rightarrow(9)\frac{5x}{9}=(9)4=36 \\ \Rightarrow5x=36 \\ \Rightarrow(\frac{1}{5})5x=\frac{1}{5}\cdot36 \\ \Rightarrow x=\frac{36}{5} \end{gathered}[/tex]

Therefore, the answer is x=36/5

Find each quotient. All final answers must be in simplest form.9x3y2 + 15x2y - 6x2/ 3x2 = X^2 + 8x - 163xy^2 + 5y + 2 3xy^2 + 5y - 2 3xy^2 - 5y - 2

Answers

ok

[tex]\begin{gathered} \frac{9x^3y^2+15x^2y-6x^2}{3x^2}\text{ = }\frac{9x^3y^2}{3x^2}\text{ + }\frac{15x^2y}{3x^2}\text{ - }\frac{6x^2}{3x^2} \\ \text{ = 3xy}^2\text{ + 5y - 2} \end{gathered}[/tex]

The answer is on the second row. 3xy^2 + 5y - 2

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