The second term in a geometric sequence is 20. The fourth term in the same sequence is 11.25. What is the common ratio

Answers

Answer 1

let [tex]a_n[/tex] be the n'th term of the sequence.

so [tex]a_1[/tex] is the first term, [tex]a_2[/tex] the second term and so on...

In a geometric sequence with [tex]a_1=c[/tex], and common ratio r, the terms are as follows:

[tex]a_1=c[/tex]
[tex]a_2=cr[/tex]
[tex]a_3=c r^{2} [/tex]
[tex]a_4=c r^{3} [/tex]
.
.
that is, each term is its previous term times the common ratio r.

In our example

[tex]a_2=cr=20[/tex] and [tex]a_4=c r^{3}=11.25 [/tex]

[tex] \frac{a_2}{a_4}= \frac{cr}{c r^{3}}= \frac{1}{ r^{2}}= \frac{20}{11.25}= 1.778 [/tex]

so [tex]r^{2} =1/1.778=0.56[/tex]

[tex]r= \sqrt{0.56}= 0.75[/tex]

Answer: r=0.75

Related Questions

The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m.
The area of the base is __________
The volume is _________

Answers

Refer to the diagram shown below.

The square base has a base length of a = 230 m.
The area of the base is
A = a*a = 230*230 = 52,900 m²

The height is h = 150 m.
The volume is
V = (1/3)*A*h
= (1/3)*52900*150
= 2,645,000 m³

Answer:
The area of the base is 52,900 m²
The volume is 2,645,000 m³

Answer:

The area of the base is 52,900 m²

The volume is 2,645,000 m³

Step-by-step explanation:

Simplify 1 over quantity x minus 3 plus 4 over x all over 4 over x minus 1 over quantity x minus 3

Answers

We can begin this problem by creating a common denominator. our fraction is:

(1/(x-3)+4/x)/(x-1)/(x-3), giving us the common denominator of x(x-3). We then take each individual fraction in the complex fraction, making it so that each one has the denominator x(x-3). 1/(x-3) becomes x/x(x-3), 4/x becomes 4(x-3)/x(x-3), and (x-1)/(x-3) becomes x(x-1)/x(x-3).

Now, our fraction is (x/x(x-3)+ 4(x-3)/x(x-3))/x(x-1)/x(x-3), or simply ((x+4(x-3)/x(x-3))/x(x-1)/x(x-3)). If we multiply the numerator and denominator by x(x-3), we get the fraction (x+4(x+3))/(x(x-1)).

Distributing the 4, we get (x+4x+12)/(x(x-1)), or (3x+12)/(x(x-1)). (I don't know if you want the denominator factored or not, but if you want it expanded then it's (3x+12)/(x^2-x).)

I hope this was easy enough to follow! I haven't written anything like this before so I'm sorry if it wasn't very good.

Given expression: [tex]\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}}[/tex].

[tex]\mathrm{Least\:Common\:Multiplier\:of\:}x,\:x-3:\quad x\left(x-3\right)[/tex]

[tex]\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}[/tex]

[tex]\frac{4}{x}-\frac{1}{x-3}=\frac{4\left(x-3\right)}{x\left(x-3\right)}-\frac{x}{x\left(x-3\right)}[/tex]

[tex]=\frac{4\left(x-3\right)-x}{x\left(x-3\right)}[/tex]

[tex]=\frac{3x-12}{x\left(x-3\right)}[/tex]

[tex]\frac{4}{x}-\frac{1}{x-3}=\frac{x}{x\left(x-3\right)}+\frac{4\left(x-3\right)}{x\left(x-3\right)}[/tex]

[tex]=\frac{x+4\left(x-3\right)}{x\left(x-3\right)}[/tex]

[tex]=\frac{5x-12}{x\left(x-3\right)}[/tex]

[tex]\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}}=\frac{\frac{5x-12}{x\left(x-3\right)}}{\frac{3x-12}{x\left(x-3\right)}}[/tex]

[tex]\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]

[tex]=\frac{\left(5x-12\right)x\left(x-3\right)}{x\left(x-3\right)\left(3x-12\right)}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:x[/tex]

[tex]=\frac{\left(5x-12\right)\left(x-3\right)}{\left(x-3\right)\left(3x-12\right)}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:x-3[/tex]

[tex]=\frac{5x-12}{3x-12} \ \ \ : Final Answer.[/tex]

Alyssa is jogging near Central Park. She runs along 65th Street for about 0.19 miles, turns right and runs along Central Park West for about 0.28 miles. She then turns right again and runs along Broadway until she reaches her starting point. How long is her total run to the nearest hundredth of a mile? 0.68 miles 0.81 miles 1.15 miles 1.44 miles

Answers

The find the total distance, you must look for firs the missing side. To get use the formula that is derived from the Pythagorean theorem which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The formula for this is: a^2 + b^2 = c^2
So let the first side or a be .19
and the second side be .28
and now we are looking for c which is the missing side

.19^2 + .28^2 = c^20.0361 + 0.784 = .1145
get the square root of .1145
√.1145 = it is approximately 0.34

get the total distance by adding three sides
= .34 + .19 + .28
= 0.81

The total distance covered by her is 0.81 miles.

Given that

Alyssa is jogging near Central Park.

She runs along 65th Street for about 0.19 miles, turns right, and runs along Central Park West for about 0.28 miles.

She then turns right again and runs along Broadway until she reaches her starting point.

We have to determine

How long is her total run to the nearest hundredth of a mile?

According to the question

She runs along 65th Street for about 0.19 miles, turns right, and runs along Central Park West for about 0.28 miles.

Alyssa's route can be considered a right triangle with legs of length 0.19 and 0.28 (hundredths).

The total distance run is determined by using the Pythagoras theorem.

What is the Pythagorean theorem?

Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Therefore,

The distance run by her is,

[tex]\rm x^2 = (0.19)^2 +(0.28)^2\\\\ x^2=0.0361 + 0.784\\ \\ x^2 = .1145\\ \\ x= \sqrt{.1145} \\\\ x= 0.34[/tex]

Therefore,

The total distance covered by her is,

= .34 + .19 + .28

= 0.81 miles

Hence, the total distance covered by her is 0.81 miles.

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Given rectangle ABCD, segment AC is a diagonal, segment BE is perpendicular to segment AC at E. Segment AE = 8 inches and segment CE = 5 inches. What is the length of segment BE?

Answers

check the picture attached.

Let m(BAE)=m(ACD)=α

(BAE and ACD are congruent, since they are alternate interior angles, or Z angles)

Let m(ABE)=β.

So in triangle ABE, the measures of the angles are 90, α and β degrees.

This means that m(BCE)=β, since the 2 other angles of triangle BCE are 90 and α degrees.

thus, we have the similarity of triangles ABE and BCE,

so the following rations are equal:

[tex] \frac{AB}{BC} = \frac{BE}{CE} = \frac{AE}{BE} [/tex]

so

[tex] \frac{AB}{BC} = \frac{x}{5} = \frac{8}{x} [/tex]

so

[tex]\frac{x}{5} = \frac{8}{x}[/tex]

[tex] x^{2} =40[/tex]

[tex]x= \sqrt{40}= \sqrt{4*10}=2 \sqrt{10} [/tex] (inches)

Remark, we can also apply Euclid's theorem directly.

Find the measure of an angle whose measure is 20° less than the measure of its supplement.

Answers

Supplementary = angles add up to 180
Measure = 20 less

Labelled as x + (x - 20) = 180

Solve.

x + (x - 20) = 180
2x = 200
/2 /2
x = 100

Angle 1: Angle 2:
x - 20 x
100 - 20 100
80

Therefore the angle is 80 degrees.

Proof: 80 + 100 = 180 (supplementary)
100 - 80 = 20 (80 is less than supplement (100)

Hope I helped :))))

Convert 350 US dollars to British pound sterling .use 1 US dollar = 0.62 British pound sterling

Answers

If x=0.62y (x=dollar, y=sterling), then you can multiply both sides by 350 to get 350x=0.62*350y=217 sterlings

Philip buys the pizza shown below: A circular pizza is shown. The center is labeled as point A and a point on the circumference is marked B. What does AB represent?

Answers

Well because the line segment runs from the center of the circle to a point on the circumference, AB would represent the radius.

The ordered pair(1,0) is a solution to the inequality y true or false?

Answers

honestly id go with false but don't just take it from me

If Mercury's mass is 3 × 10^23 kilograms, and Saturn's mass is 6 × 10^26 kilograms, which statement is true?

Answers

[tex] \cfrac{6*10^{26}}{3*10^{23}}=2*10^3=2000 [/tex]

Saturn has about 2,000 times more mass.

Answer:

Saturn has about 2,000 times more mass.

Part A: If (7 to the power of 2)x = 1, what is the value of x?
Part B: If (7to the power of 0)x = 1, what are the possible values of x?

Answers

(7^2)x = 1
49x = 1
x = 1/49

Part B
7^0 = 1

so we have
1x = 1

x = 1

If y = f(x), and y = a f(x) is a vertical stretch or compression, a > 1 causes the graph to be stretched vertically by a factor of a.

Answers

A vertical stretch in the context of graphing functions occurs when the function is multiplied by a positive constant greater than 1, resulting in the graph being stretched vertically by that factor without affecting the y-intercept.

A vertical stretch occurs when we multiply the function by a positive constant greater than 1. For example, if we have y = a f(x) and a is greater than 1, this results in the graph being stretched vertically by a factor of a. This type of transformation doesn't affect the y-intercept since the behavior of the graph at x=0 remains unchanged. Multiplying the independent variable by a constant such as 1/2 would result in a horizontal stretching or compression, but this is different from the vertical stretching effect we are discussing here.

Additionally, suppose the vertical stretch factor is a natural number. In that case, we can think of the stretched function as being the sum of the original function added to itself repeatedly that number of times. This additive property also extends to the derivative, as the derivative of the vertically stretched function is the original derivative multiplied by the stretch factor. This is known as the vertical stretch property in the context of derivatives and calculus.

I need the blue one done! please help!!

Answers

An opposite is a person or thing that is totally different from or the reverse of someone or something else.
Examples: Night and Day, Black an White, Alive and Dead, Awake and Sleeping
Can i get branielst

PLEASE HELP

Natalie borrowed $1,800 from her mother to purchase a pre-owned car. She agrees to repay this amount by paying her mother $45 per week. This situation can be modeled by the function Which inequality represents the domain for this function?

Answers

Final answer:

The domain of the function is x ≤ 40, representing the maximum number of weeks Natalie can take to repay the loan.

Explanation:

The situation can be modeled by the function f(x) = 1800 - 45x, where x represents the number of weeks. The domain of this function represents the possible values for x. Since Natalie borrowed $1800 and agrees to repay $45 per week, the maximum number of weeks she can take to repay the loan is given by:

Step-by-step solution:

Set the function equal to zero: 1800 - 45x ≥ 0Solve the inequality for x by isolating x on one side: 45x ≤ 1800Divide both sides of the inequality by 45: x ≤ 40

Therefore, the inequality that represents the domain of the function is x ≤ 40. This means that Natalie can take up to 40 weeks to repay the loan without exceeding the borrowed amount.

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Help please.........,

Answers

y-6 = -4(x+1)

y-6 = -4x-4

add 6 to each side

y=-4x+2

A is the correct answer

triangle pqr is a right triangle. If PQ = 8, what is PR?

Answers

The answer for this is 4.

The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. The length of the side PR in ΔPQR is 4√3 units.

What is the 30-60-90 right triangle?

The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. Furthermore, the hypotenuse is twice the length of the shorter leg, and the larger leg is √3 times the length of the shorter leg.

For the given right-angled triangle, we can use the 30-60-90 rule. The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. Furthermore, the hypotenuse is twice the length of the shorter leg, and the larger leg is √3 times the length of the shorter leg.

Therefore, we can write,

PQ = 2(RQ)

8 = 2(RQ)

RQ = 4

PR = (RQ)√3

PR = 4√3

Hence, the length of the side PR in ΔPQR is 4√3 units.

The complete question is mentioned in the image below.

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What is the length of the hypotenuse in the triangle below ?

Answers

The answer is B. Since you know the lengths of both legs of the triangle, you can use the Pythagorean Theorem to solve. The Pythagorean Theorem says "a squared plus b squared equals c squared. The square root of c is the length of the hypotenuse." Since there is no answer that says 19.799 (This is the approximate answer), then the answer is B.

You have isosceles right triangle or 45-45-90 degree triangle.

In 45-45-90 triangles hypotenuse = x√2 [x=leg]

If leg = 14cm, then hypotenuse = 14√2 cm.

The function f(x) = is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?

Answers

What are your choices? It's going to be something with a negative x value.

Answer:

Step-by-step explanation:

N is between m and p. If MN=3x, NP=x, and MP= 6x-6, find the numerical value of MN

Answers

MN + NP = MP
3x + x = 6x - 6
4x = 6x - 6
4x - 6x = -6
-2x = - 6
x = -6/-2
x = 3

MN = 3x = 3(3) = 9 <==

Answer:

Step-by-step explanation:

What of the above terms indicates imaginary parallel lines that circle the earth?

Answers

The imaginary lines drawn all over the Earth's surface are called the latitudes and the longitudes. The purpose of these lines are mainly for navigation in aircrafts and satellite geographic locations. Each place in the Earth has a specific coordinates in terms of latitude and longitude. For example, Philippines is located 12.8797° North, 121.7740° East.

Between these two, the imaginary lines parallel to the equator of the Earth are the latitudes. Imagine a Cartesian plane that is revolved about either the x or y axis. You would form a sphere with x and y coordinates. The x-coordinates or the horizontal axis with respect to the equator of the Earth are the latitudes. The vertical axis are the longitudes.

2x – 4y = 12 3x – 6y = 21 solve

Answers

2x - 4y = 12.....= x - 2y = 6
3x - 6y = 21..= x - 2y = 7

these are parallel lines with no solution

What is the common difference of the following arithmetic sequence?
100, 102, 104, 106,…

Answers

The common difference in the arithmetic sequence 100, 102, 104, 106,... is 2.

Arithmetic Sequence: 100, 102, 104, 106,...

Common Difference: The common difference in an arithmetic sequence is the constant value by which each term is increased or decreased. In this sequence, the common difference is 2 because each term increases by 2.

Calculation: 102 - 100 = 2, 104 - 102 = 2, 106 - 104 = 2, so the common difference is 2.

Which of the following would best represent a cosine function with an amplitude of 3, a period of pi/2 , and a midline at y = –4? (1 point)

f(x) = –4 cos 4x + 3

f(x) = 3 cos(x – pi/2 ) – 4

f(x) = 4 cos(x – pi/2 ) + 3

f(x) = 3 cos 4x – 4

Answers

To transform the function [tex]f(x)= cos(x)[/tex] to have the amplitude of 3, we need to multiply the constant 3 to the function f(x), so we have [tex]y=3f(x)[/tex]

To transform the function [tex]f(x)=cos(x)[/tex] to have the midline [tex]y=-4[/tex] we need to subtract [tex]f(x)[/tex] by 4, so we have [tex]y=f(x)-4[/tex],

To transform the function [tex]f(x)=cos(x)[/tex] to have period of [tex] \frac{ \pi }{2} [/tex], we need to divide the original period [tex]2 \pi [/tex] by 4, so we have [tex]y=f(4x)[/tex]. Note that it is the [tex]4x[/tex] gives the effect of dividing the points on x-axes by 4 and the period is read on x-axes

Hence, the full transformation is given [tex]y=3f(4x)-4[/tex] which is the last option

Answer:

D) f(x) 3 cos 4x-4 (I just took it)

what type of number can be written as a fraction where p and q are intergers and q is not equal to zero

Answers

These are known as rational numbers.

Irrational numbers are the opposite.

Hope this helps!

If the tire is flat, then I will have to change it. Using the statement above, first state your variables in terms of p and q and which variable represents which statement. Then write this statement in symbolic form.

Answers

Correct Answer:

p: The tire is flat. q: I will have to change it. p -> q

The East Bay Deli, makes 6.85 pounds of pasta salad each day. West Bay Deli makes four times that amount each day. How many combined pounds of pasta salad is made per week between the two delis? Find a fourth of their combined weekly production of pasta salad.

Answers

The daily amounts of pasta made are
East Bay Deli: 6.85 lb
West Bay Deli: 4*6.85 = 27.4 lb

Total amount made per day is
6.85 + 27.4 = 34.25 lb

Total amount made per week is
34.25*7 = 239.75 lb
Answer: 239.8 lb (nearest tenth)

A fourth of the combined weekly production is
(1/4)*239.75 = 59.9375 lb
Answer: 59.9 lb (nearest tenth)

A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. what is the measure of the angle formed between the ramp and the freeway?

Answers

The ramp,the rise and the base, when illustrated, will form a right triangle. The hypotenuse is the ramp which measures 200 ft long. The rise is the vertical height which measures 37 feet. As you can see in the picture, the arc drawn below the ramp to the horizontal line directing to the freeways is the unknown angle that we have to find.

First, we find the angle made between the ramp and the rise (dashed line). Let's denote this is angle α. We make use trigonometric functions like cosine. Cosine of an angle is equal to the ratio of its adjacent side to the hypotenuse. In equation form:

cos α = 37/200, where α is the angle of inclination of the ramp
cos α = 0.185
α =cos^-1(0.185)
α = 79.34°

Next, let's denote the unknown angle as angle β. When you add the right angle and angle α, the sum would be angle β. Therefore,

β = 90° + 79.34°
β = 169.34°

A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. The measure of the angle formed between the ramp and the freeway is

[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]

From the information given:

The measure of the angle formed θ between the ramp and the freeway overpass can be determined by using the sine angle which is:

[tex]\mathbf{sin \theta = \dfrac{opposite}{hypotenuse}}[/tex]

[tex]\mathbf{sin \theta = \dfrac{37}{200}}[/tex]

[tex]\mathbf{ \theta = \dfrac{1}{sin} \Big( \dfrac{37}{200}\Big)}[/tex]

[tex]\mathbf{ \theta = sin ^{-1} \Big( \dfrac{37}{200}\Big)}[/tex]

Therefore, the measure of the angle formed between the ramp and the freeway is

[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]

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What does it mean for an equation to have no solution or infinitely many solutions?

PLEASE GIVE ME A DETAILED RESPONSE AS IM TAKING MODULE 7 ALGEBRA DBA TOMORROW AT 7PM

Answers

If an equation has no solution, no value of x will ever make the equation true. For example, x+1=x+2.
If an equation has infinitely many solutions, all equations of x will make the equation true. For example, x+1=1+x.

No-Solution implies an inconsistent equation, while infinitely many solutions indicate a condition that holds true for any value of variable.

When an equation has No-Solution, it means that there is no value of variable that satisfies equation. In other words, equation represents an inconsistent condition, and solution set is empty. For example, equation 2x + 5 = 2x + 7 has no solution because the variable x cancels out, leaving an inconsistency (5 ≠ 7),

When an equation has infinitely many solutions, it means that any value of variable will satisfy equation. The equation represents a condition that is always true, regardless of chosen value.

For example, the equation x + 5 = x + 5 has infinitely many solutions because any value of x will make the equation true (such as x = 1, x = 2, x = 3, and so on).

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Solve for x. A.x=7.5 B.x=16 C.x=17.5 D.x=27.5

Answers

You can't solve for x. There is nothing more you can do to the equation. Are you sure your solving for x?

Cloverville has a population of 25,000 people and is increasing at a rate of 0.2%. The population in 3 years will be
Approximately 25,500 people
Approximately 24,8500 people
Approximately 25,150 people

Answers

The formula is
A=pe^rt
A ?
P 25000
E constant
R 0.002
T 3years

A=25,000×e^(0.002×3)
A=25,150 ...Answer

No. Of roots in eq 8sec^x-6secx+1=0

Answers

Ok, let's assume it's "sec^2 x"

[tex] 8\sec^2x-6\sec x+1=0\\ 8\sec^2x-2\sec x-4\sec x+1=0\\ 2\sec x(4\sec x-1)-1(4\sec x-1)=0\\ (2\sec x-1)(4\sec x-1)=0\\ 2\sec x-1=0\\ 2\sec x=1\\ \sec x=\dfrac{1}{2}\\ x\in\emptyset\\\\ 4\sec -1=0\\ 4\sec =1\\ \sec x =\dfrac{1}{4}\\ x\in\emptyset [/tex]

So, the number of solutions (real ones) is 0.

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