Three numbers form an arithmetic sequence whose
common difference is 3. If the first number is
increased by 1, the second increased by 6, and
the third increased by 19, the resulting three
numbers form a geometric sequence. Determine
the original three numbers.

Answers

Answer 1

Let x be the first number in the sequence. Then the first three numbers are

{x, x + 3, x + 6}

The next sentence says that the sequence

{x + 1, x + 9, x + 25}

is geometric, which means there is some fixed number r for which

x + 9 = r (x + 1)

x + 25 = r (x + 9)

Solve for r :

r = (x + 9)/(x + 1) = (x + 25)/(x + 9)

Solve for x :

(x + 9)² = (x + 25) (x + 1)

x ² + 18x + 81 = x ² + 26x + 25

8x = 56

x = 7

Then the three numbers are

{7, 10, 13}


Related Questions

a 40 foot ladder is leaning against a building and forms a 29.32° angle with the ground. How far away from the building is the base of the latter? Round your answer to the nearest hundred

Answers

9514 1404 393

Answer:

  34.88 feet

Step-by-step explanation:

The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

We want to find the length of the side adjacent to the measured angle. The hypotenuse is the ladder length.

  cos(29.32°) = distance/(40 ft)

  distance = (40 ft)cos(29.32°) ≈ 34.876°

The base of the ladder is about 34.88 feet from the building.

_____

Additional comment

It extends about 19.59 feet up the side of the building.

find the value of n . 80×π×n=1100000​

Answers

Answer:

110000/8π

Step-by-step explanation:

Divide 1100000 by 80 and cancel 0. Then divide pi

Find the volume of the figure. If necessary, round the answer to the nearest whole number.

Answers

Answer:

V = 108 ft³

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Geometry

Volume of a Rectangular Prism Formula: V = lwh

l is lengthw is widthh is height

Step-by-step explanation:

Step 1: Define

Identify variables

l = 4 ft

w = 3 ft

h = 9 ft

Step 2: Find Volume

Substitute in variables [Volume of a Rectangular Prism Formula]:               V = (4 ft)(3 ft)(9 ft)Evaluate [Order of Operations]:                                                                      V = 108 ft³

A medical researcher is using rats to do an experimental test to determine the appropriate dosage for a new cancer drug. Each rat will be given a different dosage of the drug. The oncologist will then measure the growth rate of the cancerous tumor. What best describes the input and output variables that will be used in this experiment?

Answers

The input of the experiment is the amount of dose of the drug and the output is the growth rate of the cancerous tumor.

Given information:

A medical researcher is using rats to do an experimental test to determine the appropriate dosage for a new cancer drug.

Each rat will be given a different dosage of the drug.

The oncologist will then measure the growth rate of the cancerous tumor.

Now, in the experiment, the oncologist tries to study or calculate the growth rate of a cancerous tumor. So, the output that he/she will get will be the growth rate of the cancerous tumor.

The experiment is done on the rate by giving them a dosage of the drug. The dosage can vary based on the study criterion. So, the amount of dosage of the drug should be the input of the experiment.

Therefore, the input of the experiment is the amount of dose of the drug and the output is the growth rate of the cancerous tumor.

For more details, refer to the link:

https://brainly.com/question/5527886

Kayla parks her car at the corner of Ogilvie and Montreal Rd. She walks 80m East and then turns 30° to the left towards her office building and continues walking for another 100m until she reaches her building. She then takes the elevator to her office 60m above ground level and looks out the window. She can see her car from here. How far is it from where she is to her car in a direct line?

Answers

9514 1404 393

Answer:

  184 m

Step-by-step explanation:

The direct distance from Kayla's car (C) to the door of her office building (B) can be found using the Law of Cosines. The interior angle of the triangle at the turning point is 180° -30° = 150°, so the distance is ...

  t² = b² +c² -2bc·cos(T)

  t² = 80² +100² -2·80·100·cos(150°) = 30256.406

The direct distance from her window to the car can be found from the Pythagorean theorem. The legs of the right triangle are the distance from the car to the building (CB) and the height from the building entrance to the window (BW).

  CW = √(t² +60²) ≈ 184.001

The direct line distance from Kayla to her car is 184 meters.

_____

For the first computation, we used the usual notation for a triangle, where capital letters (CTB) are the vertices and angles, and corresponding lower-case letters are their opposite sides.

Twenty students randomly assigned to an experimental group receive an instructional program; 30 in a control group do not. After 6 months, both groups are tested on their knowledge. The experimental group has a mean of 38 on the test (with an estimated population standard deviation of 3); the control group has a mean of 35 (with an estimated population standard deviation of 5). Using the .05 level, evaluate the researcher's hypothesis that the instructional program affects students' knowledge. What is the correct cutoff score(s)

Answers

Answer:

The solution according to the problem given is provided below in the explanation segment.

Step-by-step explanation:

According to the question,

[tex]H_o: \mu_1=\mu_2[/tex]

[tex]H_a: \mu_1 \neq \mu_2[/tex]

Level of significance,

[tex]\alpha = .05[/tex]

The test statistics will be:

⇒ [tex]Z = \frac{(\bar x_1 - \bar x_2)}{\sqrt{\frac{\sigma_1^2}{n_1} +\frac{\sigma_2^2}{n_2} } }[/tex]

       [tex]=\frac{(38-35)}{\sqrt{\frac{(3)^2}{30} +\frac{(5)^2}{30} } }[/tex]

       [tex]=2.82[/tex]

The p-value will be:

= [tex]0.0024[/tex]

What is the remainder for the synthetic division problem below?
2/ 3 1 2 -7
A. 25
B. 17
C. -29
D. -39

Answers

Answer:

B.17

Step-by-step explanation:

B.17

B.17

B.17

B.17

Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. let x represent the length of each of the equal pieces of yarn that julie decides to cut. what is the equation that can be used to determine the total length of all the yarn that she ends up cutting, y? is the graph of the equation continuous or discrete?

Answers

Answer:

The answer is below

Step-by-step explanation:

Let x represent the length of each of the equal piece of yarn. Since they are 4 equal pieces of yarn, then the total length of the equal pieces of yarn = 4x.

Also, besides cutting the 4 equal pieces of yarn Julie further cuts a yarn 7.75 inches long, therefore if y represent the total length of all the yarn that she ends up cutting, hence:

y = 4x + 7.75

Since the graph produced by this equation have all points connected to each other, hence this is a continuous graph.


Which equation represents a line that passes through (4,1/3) and has a slope of 3/4?
Oy- 3/4= 1/3(x-4)
Oy-1/3= 3/4(x-4)
Oy- 1/3= 4(x-3/4)
Oy-4 = 3/4(x-1/3)

Answers

Step-by-step explanation:

With this kind of problem, we're looking at an equation in the form

y - y1 = m(x - x1)

(m = slope)

so we can substitute m, y1, and x1 with the values we're given.

y - y1 = m(x - x1)

y - 1/3 = 3/4(x - 4)

Answer:

y - 1/3 = 3/4(x - 4)

Find the length of the third side?

Answers

By using pythagoras theorem you can find the answer
Your answer is 3 root 6

Answer:

2

Step-by-step explanation:

let x be the third side

Using Pythagoras' identity in the right triangle

x² + 5² = ([tex]\sqrt{29}[/tex] )²

x² + 25 = 29 ( subtract 25 from both sides )

x² = 4 ( take the square root of both sides )

x = [tex]\sqrt{4}[/tex] = 2

find the value of the trigonometric ratio​

Answers

Answer:

ur box cannot be opend  repain the window

Step-by-step explanation:

sin A=opposite / hypotenusesin A=32/40 orsin A=32/40 (divide a number by 2)sin A=9/5

please mark this answer as brainlist

Find f′ in terms of g′

f(x)=x2g(x)

Select one:

f′(x)=2xf′(x)+2xg′(x)


f′(x)=2xg′(x)


f′(x)=2x+g′(x)


f′(x)=x2g(x)+2x2g′(x)


f′(x)=2xg(x)+x2g′(x)

Answers

f(x)g(x) if you find the derivative of two products, you get f(x)g’(x)+f’(x)g(x). Let’s say x^2 = f(x).

(x^2)(g’(x))+2x(g(x)) so it would be your last option, 2x(g(x))+x^2(g’(x))

PLSS HELPPPP WILL GIVE BRAINLESSS A 22-foot ladder is resting against the side of a building. The bottom of the ladder is 3 feet from the building. Find the measure of the angle the ladder makes with the ground. Round your answer to the nearest tenth of a degree.

Answers

Answer:

The answer is 82.2  

Step-by-step explanation

hope this helps

A sample of 375 college students were asked whether they prefer chocolate or vanilla ice cream. 210 of those surveyed said that they prefer vanilla ice cream. Calculate the sample proportion of students who prefer vanilla ice cream.

Answers

Answer:

The sample proportion of students who prefer vanilla ice cream is 0.56.

Step-by-step explanation:

Sample proportion of students who prefer vanilla ice cream:

Sample of 375 students.

Of those, 210 said they prefer vanilla ice cream.

The proportion is:

[tex]p = \frac{210}{375} = 0.56[/tex]

The sample proportion of students who prefer vanilla ice cream is 0.56.

Hey guys if you could help ASAP thank you

Answers

Answer:

Step-by-step explanation:

The answer is B

if you have 2^3 * 2*4 to find out what that equals, leave the base (2) alone and add the powers. You get 2^(3 + 4) = 2^7

Let's see if that works.

2^3 = 8

2^4 = 16

8 * 16 = 128

Now what is 2^7?

2^7 = 128 just as it should

Now returning to your question

3^7.869 = answer B You leave the base alone (7) and add the powers. The 8 is 8/10

The 6 is 6/100

The 9 is 9 / 1000 Just add the fractions and keep the 7 and the 3.

In 20P4 how many choices are
there for vice-president from a
state of four officers?
Note: The vice president is the second officer
to be elected.
Acellus

Answers

Answer:  B) 19

Explanation:

There are 20 choices for president, and 20-1 = 19 choices for vice president. You count down by 1 each time you fill a seat. So that means you'll have 19-1 = 18 choices for the third seat, and 18-1 = 17 choices for the fourth seat.

for 0 degrees ≤ x < 360 degrees , what are the solutions to sin (x/2) + cos(x) - 1 =0

Answers

Recall the double angle identity for cosine:

cos(x) = cos(2×x/2) = 1 - 2 sin²(x/2)

Then the equation can be rewritten as

sin(x/2) + (1 - 2 sin²(x/2)) - 1 = 0

sin(x/2) - 2 sin²(x/2) = 0

sin(x/2) (1 - 2 sin(x/2)) = 0

sin(x/2) = 0   or   1 - 2 sin(x/2) = 0

sin(x/2) = 0   or   sin(x/2) = 1/2

[x/2 = arcsin(0) + 360n °   or   x/2 = 180° - arcsin(0) + 360n °]

… …   or   [x/2 = arcsin(1/2) + 360n °   or   x/2 = 180° - arcsin(1/2) + 360n °]

x/2 = 360n °   or   x/2 = 180° + 360n °

… …   or   x/2 = 30° + 360n °   or   x/2 = 150° + 360n °

x = 720n °   or   x = 360° + 720n °

… …   or   x = 60° + 720n °   or   x = 300° + 720n °

(where n is any integer)

We get only three solutions in 0° ≤ x < 360° :

720×0° =

60° + 720×0° = 60°

300° + 720×0° = 300°

Answer:

B: (0, 60, 300)

Step-by-step explanation:

right on edge

(ii). nth term of: 10+4-2...​

Answers

9514 1404 393

Answer:

  an = 10 -6(n -1)

Step-by-step explanation:

The series is an arithmetic series with a first term of 10, and a common difference of 4-10 = -6. The n-th term of an arithmetic series is given by ...

  an = a1 +d(n -1) . . . . . for first term a1 and common difference d

__

For the parameters this series has, the n-th term is ...

  an = 10 -6(n -1)

The sume of the reciprocals of two consecutive integers is 3/2. Find the two integers

Answers

Answer:

1 and 2

Step-by-step explanation:

Let's say our first number is x. Our second number is the number after that, or x+1. A reciprocal of a number is 1/that number. Therefore, the reciprocal of x is 1/x and the reciprocal of x+1 is 1/(x+1). The question states the sum of the reciprocals of the two numbers is equal to 3/2. Therefore,

1/x + 1/(x+1) = 3/2

multiply both sides by 2 to remove a denominator

2/x + 2/(x+1) = 3

multiply both sides by x to remove a denominator

2 + (2*x)/(x+1) = 3x

multiply both sides by (x+1) to remove the other denominator

2*(x+1) + 2*x = 3x*(x+1)

expand

2*x+2 + 2*x = 3x²+3

combine like terms

4x + 2 = 3x²+3

subtract (4x+2) from both sides to make everything equal to 0 and to form a quadratic

3x² - 4x + 1 = 0

To factor this, we need to find two numbers that add up to b and multiply to a*c in an equation of form ax²+bx + c. Here, a=3, c=1, and b = -4

Two numbers that add to -4 and multiply to 3*1=3 are -3 and -1. We can thus factor this out to get

3x²-3x-x+1 = 0

3x(x-1) -1 ( x-1) = 0

(3x-1)(x-1) = 0

Therefore, solving for 0, we get

3x-1=0

x = 1/3

x-1 = 0

x=1

The only integer solution possible is x=1

To confirm, 1/1 + 1/(1+1) = 3/2, so x=1 is correct, with 1+1=2 being the second integer

Expand and simplify the following expressions. a. (2 − 3)( − 6)

Answers

Answer:

your answer should be six I hope this help

Answer:

the should be 6

Step-by-step explanation:

(2-3)(-6)

-12+18

=6

Please help me please please help ASAP

Answers

Step-by-step explanation:

70 + 45 = 115

180 - 115 = 65

angle c = 65

use sohcahtoa

cos angle = adjacent

hypotenuse

cos 65 = 2.5

b

b cos 65 = 2.5

use the calc for further answers

hope that helped

An advertising firm wanting to target people with strong desires for success conducted a study to see if such people differed in the types of television shows they watched. Randomly selected participants recorded the shows they watched for a week, then their desire for success was assessed, and finally they were divided into two groups. Low Success seekers watched 8 comedies, 15 romances, 6 documentaries, 13 dramas, and 3 news shows. High Success seekers watched 3 comedies, 3 romances, 9 documentaries, 7 dramas, and 8 news shows.
1. Use the five steps of hypothesis testing.
2. Sketch the chi-square distribution. Be sure your sketch gives a rough indication of its shape and shows the cutoff score and the sample's score.
3. Explain the logic of what you have done to a person who is familiar with the logic and steps of hypothesis testing for the t test and analysis of variance, but who knows nothing about chi-square tests.
4. Figure a measure of effect size and indicate whether it is small, medium, or large.

Answers

Answer:

Blablabla

Step-by-step explanation:

Bababa

In a scatter plot, each ____. Group of answer choices individual is represented by a single point group mean is represented by a single point individual is represented by two data points group mean is represented by two data points

Answers

Answer:

Individual is represented by a single point

Step-by-step explanation:

A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 0 1 2 x 0 0.10 0.03 0.02 1 0.06 0.20 0.07 2 0.05 0.14 0.33 (a) What is P(X

Answers

Answer:

[tex]P(x = 1) = 0.33[/tex]

[tex]P(y = 2) = 0.42[/tex]

Step-by-step explanation:

Given

                    y

x [tex]\begin{array}{cccc}P(x,y) & {0} & {1} & {2} & {0} & {0.10} & {0.03} & {0.02} & {1} & {0.06} & {0.20} & {0.07} & {2} & {0.05} & {0.14} & {0.33}\ \end{array}[/tex]

Solving (a)

[tex]P(x = 1)[/tex]

To do this, we simply add all data where x = 1

So, we have:

[tex]P(x = 1) = P(x=1|y=0) + P(x=1|y=1) + P(x=1|y=2)[/tex]

[tex]P(x = 1) = 0.06 + 0.20 + 0.07[/tex]

[tex]P(x = 1) = 0.33[/tex]

Solving (b)

[tex]P(y = 2)[/tex]

To do this, we simply add all data where y = 2

So, we have:

[tex]P(y = 2) = P(x=0|y=2) + P(x=1|y=2) + P(x=2|y=2)[/tex]

[tex]P(y = 2) = 0.02 + 0.07 + 0.33[/tex]

[tex]P(y = 2) = 0.42[/tex]

Find the inequality represented by the graph

I'm using khan academy btw

Answers

Answer:

Step-by-step explanation:

slope of line through (0,0) and (4,3) =(3-0)/(4-0)=3/4

eq. of line is y-0=3/4(x-0)

y=3/4 x

put x=4

y=2

2=3/4×4

2=3

which is true if 2<3

2<3

so y<3/4 x

Which description does NOT guarantee that a quadrilateral is a square?
A. A quadrilateral has all sides congruent and all angles congruent.
B. A quadrilateral is a parallelogram with perpendicular diagonals.
C. A quadrilateral is both a rectangle and a rhombus.
D. A quadrilateral has all right angles and has all sides congruent.

Answers

Answer:

C A quadrilateral is both a rectangle and a rhombus

which equation is equivalent to 8+2(x-1)=5

Answers

Answer:

8+2x-2 = 5

2x+6 =5

2x = -1

Step-by-step explanation:

8+2(x-1)=5

Distribute

8+2x-2 = 5

Combine like terms

2x+6 =5

Subtract 6

2x+6-6=5-6

2x = -1

A note card company has found that the marginal cost per card of producing x note cards is given by the function below, where C'(x) is the
marginal cost, in cents, per card. Find the total cost of producing 900 cards, disregarding any fixed costs.
C'(x) = -0.05x + 77, for x S 1000
The total cost is
cents

Answers

Answer:

49,050cents

Step-by-step explanation:

Given the expression for calculating the marginal cost per card of producing x note cards expressed as

C'(x) = -0.05x + 77

On intergrating the marginal cost, we will get the total cost

C(x) =  -0.05x²/2 + 77x

Substitute x = 900 into the resulting expression

C(900) =  -0.05(900)²/2 + 77(900)

C(900) = -20,250+69,300

C(900) = 49,050

Hence the total costs in cents is 49,050cents

The following three shapes are based only on squares, semi circles, and quarter circles. Find the perimeter in the area of each shaded part

Answers

Answer: 46.26

Step-by-step explanation:

Since it is a square the sides are all the same, and since it’s a half circle, the dashed line is the diameter of the circle. To find the circumference on a circle, the equation is diameter times pi. 3.14 is commonly used for pi which is what I’m using 3.14, but of you are told to use a different number use that. 9*3.14 is 28.26. Since ther are exactly two half circles in the diameter, here’s no point in dividing by 2. The rest of the perimeter are just 2 sides of the square. So 9+9+28.26 is 46.26.

Lily wants to put a ribbon border around two round clocks. Each clock has a diameter of 24 centimeters. Using 3.14 for π, approximately how many meters of ribbon does Lily need?

Answers

Answer:

1.5 meters

Step-by-step explanation:

You need to use circumference for this problem and the formula is dπ.

Plug in:

24π

Solve with pi:

24×3.14 = 75.36

Since there is two clocks, multiply:

75.36 × 2 = 150.72

In 1 meter there is 100 centimeters so divide

150.75 ÷ 100 = 1.5

So you will need 1.5 meters of ribbon.

Other Questions
Simplify |3 11| (15 3 + 2) 2 Nuclear energy can provide electricity for the world needs, but it is___A. cheap B. unlimited 0 C. dangerous D. safe According to Newton's law of universal gravitation, the force F between two bodies of constant mass m and M is given by the formula F = G m M d 2 , where G is the gravitational constant and d is the distance between the bodies. a. Suppose that are constants. Find the rate of change of force F with respect to distance d . Which expression is equivalent to 24x+72?24(x72)negative 24 times open paren x minus 72 close paren24(x3)negative 24 times open paren x minus 3 close paren24(x+3)24 times open paren x plus 3 close paren24(x+72) When looking at the home page, where do you think you will find information about different kinds of bridges?a. Resourcesc. Build a bridgeb. Teacher's guided. None of the above the radius of a circle is 17m. find its area in terms of pi PLEASEEEE HELP!!Read the excerpt from act 3, scene 2, of The Tragedy of Julius Caesar and the information in the paragraph below it.Excerpt:ANTONY. Friends, Romans, countrymen, lend me your ears.I come to bury Caesar, not to praise him.The evil that men do lives after them;The good is oft interrd with their bones.So let it be with Caesar.Background information:"The Evil That Men Do is the title of a song by the English heavy metal band Iron Maiden. The lyrics of the chorus say that peoples evil deeds live on.Iron Maidens reference to the line from Shakespeares play is an example ofA.) cultural allusion.B.) literary allusion.C.) historical allusion.D.) religious allusion. 1) What is the function of the plasma membrane? (5pts)2) How does high and low temperature affect a plasma membrane's fluidity? (5pts)3) How does passive transport differ from active transport? (5pts)4) What are the three main types of passive transport? Describe each of them. (5pts)5) List the three types of tonic solutions and describe which way water moves in each one. (5pts) A 117 kg horizontal platform is a uniform disk of radius 1.61 m and can rotate about the vertical axis through its center. A 62.5 kg person stands on the platform at a distance of 1.05 m from the center, and a 28.3 kg dog sits on the platform near the person 1.43 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis. Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Spinning an American roulette wheel 8282 times and recording the number the ball lands on. Give Jeason: si System is accepted by all nations in the world. what is the product of 7/9 and 1/4 in fraction form? precautive measures taken when using pooter The structure of the cell membrane was discovered in 1895 by _________. Finding a similarity to Olive Oil, he discovers membranes are made of __________.A. Charles Overton, amino acidsB. Gorter and Grendel, amino acidsC. Charles Overton, lipidsD. Irving Langmuir, lipids Find the missing length indicated What should be the FIRST step when making an outline?Decide on the details to include as evidence in your outline.Decide what information you will not include in your outline.Decide what information to include in each paragraph of your report.Decide on the main points to address in your outline. Case law comes from court rulings.True or false The central thesis of the passage is that class-size reductions:A.can improve academic achievement under some conditions but may not be the most effective way to do so.B.improve academic achievement when teachers use techniques well suited to small classes.C.improve academic achievement only in the early elementary grades.D.are less efficient than other means of improving academic achievement. 16. Research on the relationship between personality and job performance indicates a. people who are extraverted perform slightly less well than those who are intraverted. b. dependable people are better performers than those less dependable. c. there is little relationship between reliability and job performance. d. achievement-oriented people are so goal-oriented that they often fall short in their performance. Russell Inc. had sales of $2,210,000for the first quarter of 2017. In making the sales, the company incurred the following costs and expenses. Variable FixedCost of goods sold $921,000 $441,000Selling expenses 71,000 46,000Administrative expenses 87,000 99,000Prepare a CVP income statement for the quarter ended March 31, 2017.