If x = 1, y = 7, and z = 15, determine a number that when added to x, y, and z yields
consecutive terms of a geometric sequence. What are the first three terms in the
geometric sequence?

Answers

Answer 1

Answer:

The first three terms in the geometric sequence are 18, 24, 32.

Step-by-step explanation:

A number when added to [tex]x,y,z[/tex] that yields consecutive terms of a geometric sequence is an unknown number [tex]t\in \mathbb{Z}[/tex]

Given

[tex]x = 1, y = 7, z = 15[/tex]

We know

[tex]\alpha _1 = 1+t[/tex]

[tex]\alpha _2 = 7+t[/tex]

[tex]\alpha _3 = 15+t[/tex]

Recall that a geometric sequence is in the form

[tex]\boxed{a_n = a_1 \cdot r^{n-1}}[/tex]

Therefore, once  [tex]\alpha_1, \alpha_2, \alpha_1[/tex] are consecutive terms,

[tex]15+t = (1+t) r^{3-1} \implies 15+t = (1+t) r^2[/tex]

To find the ratio, for

[tex]\dots a_{k-1}, a_k, a_{k+1} \dots[/tex]

we know

[tex]\dfrac{a_k}{a_{k-1}} =\dfrac{a_k}{a_{k-1}} =r[/tex]

Therefore,

[tex]\dfrac{(7+t)}{(1+t)} =\dfrac{(15+t)}{(7+t)} \implies (7+t)^2 = (15+t)(1+t)[/tex]

[tex]\implies 49+14t+t^2=15+16t+t^2 \implies -2t=-34 \implies t=17[/tex]

The ratio is therefore

[tex]r=\dfrac{4}{3}[/tex]

Therefore, the first three terms in the geometric sequence are 18, 24, 32.


Related Questions

Draw the image of the rotation of quadrilateral SORT by 270° about the origin.

I need visual help, not a number answer please :)

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

A rotation 270° CCW is the same as a rotation 90° CW. To see what the figure looks like in its new location, make a copy on a semi-transparent medium, then align the +x axis on the copy with the -y axis on the original graph, keeping the origin in the same place.*

Algebraically, the transformation is ...

  (x, y) ⇒ (y, -x)

For example, ...

  S(7, -6) ⇒ S'(-6, -7)

In the attachment, the rotated figure is in red.

_____

* The exercise of physically doing this on paper or with transparencies can give you the insight you need to learn to do it mentally.

⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆

THAT IS THE RIGHT ANSWER

A baseball is projected upward at 64 feet per second. It can be approximated by the equation -16t^2+64t. The baseball reaches it maximum height at the vertex. That can be gotten from x= −/2a . How long until the baseball reaches its full height? Note a quadratic equation can be written as ax^2+bx+c

Answers

Answer:

f(t) = -16t²+64t

t = number of secondsf(t) = height (in feet)

The x-coordinate(t) of the vertex can be found using formula [tex]\frac{-b}{2a}[/tex], where:

a = -16b = 64

Therefore the t-value of the vertex is:

[tex]\frac{-64}{2(-16)} =\frac{-64}{-32} =2[/tex]

The baseball will reach its maximum height after two seconds.

8 and 1/3divided by 3 and 4/7

Answers

Answer:

7/3

Step-by-step explanation:

8 1/3 divided by 3 4/7

Let’s start by 8 1/3

Multiply 3 x 8 and then add 1

3 x 8 = 24 + 1 = 25

Add the denominator back

25/3

3 4/7

Multiply 7 x 3 and then add 4

7 x 3 = 21 + 4 = 25

Add the denominator back

25/7

Final Results: 25/3 & 25/7

Now we’re ready to divide!

Multiply 7 by 25

7 x 25 = 175

Multiply 3 by 25

3 x 25 = 75

Answer: 175/75

Finally Simplify

175/75 = 7/3

Final Answer: 7/3

simplify 4x + 3y - 2x

Answers

Answer:

2x+3y

Step-by-step explanation:

4x + 3y - 2x

Combine like terms

4x-2x    +3y

2x     +3y

4x+3y-2x

Like terms

4x-2x which equals 2x

So

2x+3y

The price of a car was decreased from $13,000 to $11,830. The price is decreased by what percentage?

Answers

Answer:

It is decreased by 9%

Step-by-step explanation:

First, find out how much money is decreased. To do this, subtract 13,000-11,830=1170. Finally, figure out how much percent 1170 is of the original price of $13,000.

The answer is 7%.

Hope this helps :)

Hello can anyone answer this question please I need help

Answers

9514 1404 393

Answer:

maximum: 40(8/3, 8/3)

Step-by-step explanation:

The graph shows the relevant vertex of the feasible region is ...

  (x, y) = (8/3, 8/3).

The value of z there is ...

  z = 11(8/3) +4(8/3) = (88 +32)/3

  z = 40

Write the equation of the line for the graph shown below.

Answers

Answer:

The answer is C

Step-by-step explanation:

y=-5x-3

Hope this helped

Answer:

I believe the answer is y = -5x -3  

Step-by-step explanation:

The formula is y=mx+b

m= rise over run

b= starting point

and seeing how the dot is on -3 I assume that the answer is y= -5x -3

also m should be in fraction form and if it isn't, you automatically put a 1 as the denominator.

Ravi bought 50kg rice at the rate of tk.40 per kg and sold it at the rate of tk.44 per kg. What is the percentage of profit

Answers

He paid 0.40 x 50 = 20

He sold it for 0.44 x 50 = 22

His profit was 22-20 = 2

Percentage was 2/20 = 0.10 = 10 %

Answer 10 %

Look at the numbers below. −9.8 −5.4 1.0 14.8 Which shows the best way to add these numbers using the Commutative and Associative Properties? A. (–9.8 + 1.0) + (–5.4 + 14.8) B. (–9.8 + 14.8) + (–5.4 + 1.0) C. (1.0 + 14.8) + (–9.8 + (–5.4)) D. (1.0 + (–9.8)) + (14.8 + (–5.4)

Answers

Answer:

B

Step-by-step explanation:

i did the test and it was correct, ur welcome

PLEASE HELP! much appreciated :D

Find the value of x.

Answers

Answer:

a

Step-by-step explanation:

What is the least possible degree of a polynomial that has the root -3 + 2i, and repeated root -2 that occurs twice?

4
3
2
5

Answers

Answer:

4

Step-by-step explanation:

complex roots always occur in pairs.

so roots are -3+2i,-3-2i ,-2,-2

number of roots=4

What is the different of (5-3x) and (5x-10)

a. 8x-5

b. 15-8x

c. 8x + 15

d. none of the above

Answers

Answer:

15 - 8x

Step-by-step explanation:

Remark

This all depends on how you read the question. In other words, which comes first 5 - 3x or 5x - 10. It's not clear.

If you do the first one first, you get

5 - 3x - (5x - 10)         Remove the brackets.

5 - 3x - 5x + 10          Collect like terms

15 - 8x                       So that makes the middle one correct.

Now do it the other way.

5x - 10 - (5 - 3x)

5x - 10 - 5 + 3x

8x - 15

That answer isn't available here. So ..

The answer is 15 - 8x

solve for "X" where x±4=12​

Answers

Answer:

x = 8, 16

Step-by-step explanation:

x + 4 = 12

x = 12- 4

x = 8

x - 4 = 12

x = 12 + 4

x = 16

I hope this can help you

in a class, 64 offers mathematics while 94 offers chemistry , How many will offer the both course?

Answers

Answer:

30

Step-by-step explanation:

94-64=30 will offer the same course because the chemistry offers ocerride the mathematics offers

Singh's house the weekly consumption of milk is 6.5 liters what is their daily consumption of milk if they consume same quantity of milk every day

Answers

Answer:

Their daily consumption of milk is of 0.93 liters.

Step-by-step explanation:

Weekly consumption:

6.5 liters.

Daily consumption:

A week has 7 days.

Each day the amount consumed is the same, so the daily consumption is:

6.5/7 = 0.93

Their daily consumption of milk is of 0.93 liters.

Find the value of x on this triangle

Answers

Answer:

33

a2+b2 =c2

a2+ 33 squared = 55 squared

a + 1936 = 3025

3025-1936=1089

square root of 1089 is 33

pleeeaaasssseeee mark as brainliest

What is the remainder of 119 divided by 4

Answers

The remainder is three. 4 can go into 119 29 times with a remainder of three.

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

The remainder when dividing 119 by 4 is 3.

We have,

To find the remainder when dividing 119 by 4, we perform the division and observe the remainder.

When we divide 119 by 4, we get:

119 ÷ 4 = 29 remainder 3

The quotient is 29, which means that 4 goes into 119 twenty-nine times without any remainder.

However, there is a remainder of 3.

Therefore,

The remainder when dividing 119 by 4 is 3.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ6

Proving the Single Opposite Side Pair Theorem
Given: AD = BC and AD || BC
Prove: ABCD is a parallelogram.
Angles Segments Triangles Statements Reasons
ZBCA
ZDAC
А
Statements
Reasons
B
D
с
Assemble the proof by dragging tiles to
the Statements and Reasons columns.

Answers

9514 1404 393

Explanation:

1. AD ≅ BC, AD ║ BC . . . . given

2. ∠DAC ≅ ∠BCA . . . . alternate interior angles theorem

3. AC ≅AC . . . . reflexive property

4. ΔDAC ≅ ΔBCA . . . . SAS postulate

5. AB ≅ CD, ∠BAC ≅ ∠DCA . . . . CPCTC

6. AB ║ CD . . . . converse of alternate interior angles theorem

7. ABCD is a parallelogram . . . . definition of a parallelogram (has 2 pairs of parallel & congruent sides)

_____

We don't know what your tiles/choices are for statements or reasons. We have shown the triangles are congruent, so their corresponding parts (sides/angles) are congruent. That lets us claim opposite sides are congruent and  parallel. YMMV

Answer:

Picture Down Below

Step-by-step explanation:

in a small town in New York, we initiated a cohort study and followed 5,900 people for a mean follow-up of 2 years. At the end of the 2nd year, none of the participants was lost to follow-up. During this follow-up, we identified 600 cases of malaria. What was the cumulative incidence?
a. 10.1%
b. 10.1 per 1,000
c. 50.8%
d. 10 cases

Answers

Answer:

Option A

Step-by-step explanation:

From the question we are told that:

Sample size n=5900

Number of newly developed cases No.C=600

Generally the equation for Cumulative Incidence is mathematically given by

[tex]CI=\frac{No.C}{n}[/tex]

[tex]CI=\frac{600}{5900}[/tex]

[tex]CI=0.101[/tex]

[tex]CI= 10.1%[/tex]

Option A

Which sets of ordered pairs show equivalent ratios? Use the grid to help you.

Check all that apply.

A: (1, 2), (2, 3), (4, 7)

B: (2, 2), (4, 4), (6, 6)

C: (3, 1), (4, 1), (5, 1)

D: (4, 1), (8, 2), (12, 3)

E: (2, 1), (4, 3), (5, 4)

Answers

Answer:

B and D

Step-by-step explanation:

in B the ratio of x/y = 1 for all pairs.

in D the ratio of x/y = 4 for all pairs.

in all other sets there are different ratios inside the set.

Answer:

The pairs (2, 2), (4, 4), and (6, 6) have ratios of 1 and the pairs (4, 1), (4, 1),      (8, 2), and (12, 3) have ratios of 4. The other pairs do not have similar ratios.

Step-by-step explanation:

Step 1; In order to pair up the pairs with equivalent rations, we first need to calculate the ratios for all the pairs by dividing the first value with the second value. The same procedure must be followed throughout to be able to pair them up.

Step 2; By dividing the values, the ratios are;

For (1, 2), the ratio is  = 0.5,

For (2, 3), the ratio is  = 0.6666,

For (4, 7), the ratio is  = 0.5714,

For (2, 2), the ratio is  = 1,

For (4, 4), the ratio is  = 1,

For (6, 6), the ratio is  = 1,

For (3, 1), the ratio is  = 3,

For (4, 1), the ratio is  = 4,

For (5, 1), the ratio is  = 5,

For (4, 1), the ratio is  = 4,

For (8, 2), the ratio is  = 4,

For (12, 3), the ratio is  = 4,

For (2, 1), the ratio is  = 2,

For (4, 3), the ratio is  = 1.333,

For (5, 4), the ratio is  = 1.25.

Step 3; Now we pair up the sets with the same ratios, out of these 15 pairs. The pairs (2, 2), (4, 4), and (6, 6) have ratios of 1 and the pairs (4, 1), (4, 1),      (8, 2), and (12, 3) have ratios of 4. The other pairs do not have similar ratios.

I hope this is right and it helps you !!!!!!!!!!

A tennis coach divides her 9-player squad into three 3-player groups with each player in only one group. How many different sets of three groups can be made?

Answers

Answer:

84

9 choose 3

Step-by-step explanation:

Is the relationship shown by the data linear? If so, model the data with an equation.

Answers

Yes it is linear, you go up my fours in the y side and go down by two on the x side. The equation is y=2x+19

give me examples of equivalent expressions of square root 54 with a radican of 3

Answers

Try this answer 3√54

An investor puts $800 into an account that pays 7.5% interest compounded annually. The total amount A in the account after t years is given by which function below?
A = 800(1.75) ^t
A = 800(1.075) t
A = 800(1.075)^ t
A = 800 + (1.075)^ t

Answers

Answer:

A = 800( 1.075)^(t)

Step-by-step explanation:

The equation for interest is

A = p (1+r/n) ^ nt   where p is the principle, r is the interest rate, n is the number of times per year  and t is the years

A = 800( 1+ .075/1)^(1*t)

A = 800( 1.075)^(t)

Let's see

[tex]\\ \tt\leadsto A=P(1+r/n)^{nt}[/tex]

n is 1

[tex]\\ \tt\leadsto A=P(1+r)^t[/tex]

[tex]\\ \tt\leadsto A=800(1+0.075)^t[/tex]

[tex]\\ \tt\leadsto A=800(1.075)^t[/tex]

Option C

Zane wants to enlarge two of his photos to frame on his bedroom wall. He has 184 photos from rock concerts he's been to and 88 photos of city
skylines
How many possible combinations of 1 rock concert photo and 1 city skyline photo could Zane choose from?

Answers

Answer:

B

Step-by-step explanation:

184*88=16,192

Which expression is equivalent to 7x , if b > 0?

Answers

Answer:  Choice C

Work Shown:

[tex]7x^2*\sqrt{2x^4}*6\sqrt{2x^{12}}\\\\7*6x^2*\sqrt{2x^4*2x^{12}}\\\\42x^2*\sqrt{4x^{4+12}}\\\\42x^2*\sqrt{4x^{16}}\\\\42x^2*\sqrt{(2x^8)^2}\\\\42x^2*(2x^8)\\\\42*2x^{2+8}\\\\84x^{10}\\\\[/tex]

So that's why the answer is choice C

The requirement that x is nonzero isn't technically necessary. The original expression simplifies to choice C even when x = 0 is the case. Also, we don't have issues such as division by zero errors that could arise. It's a bit curious why your teacher put in that condition.

Answer:

C.

Step-by-step explanation:

7x²×sqrt(2x⁴)×6×sqrt(2x¹²)

we see right away that as constant multiplication factor we have 7×6 = 42.

and then we get from each sqrt expression a sqrt(2), which leads to sqrt²(2) = 2 and therefore 42×2=84.

the only answer option with 84 is C.

now, to be completely sure, and to get some practice, let's look at the other parts :

sqrt(2x⁴) = sqrt(2)×sqrt(x⁴) = sqrt(2)×x²

sqrt(2x¹²) = sqrt(2)×sqrt(x¹²) = sqrt(2)×x⁶

=>

7x²×sqrt(2)×x²×6×sqrt(2)×x⁶ =7×6×2×x²×x²×x⁶ = 84x¹⁰

perfect. C is confirmed.

Does the graph below represent a proportional relationship?

———————————————

A. Yes, because the graph is a straight line

B. No, because it crosses the y -axis

C. Yes, because it crosses the y -axis

D. No, because the line doesn't pass through the origin, point (0,0)

Answers

The answer is A.
The reason being straight lines mean equal proportions, while curved lines are exponential or quadratic.

Answer:  D. No, because the line doesn't pass through the origin, point (0,0)

Explanation:

A direct proportional graph is always a straight line through the origin.

Algebraically, the form of any direct proportion equation is y = kx, where k is some constant. It plays the role as the slope.

We can rewrite y = kx as y = kx+0 to see that the y intercept is always 0 for these types of equations.

Unfortunately, this line shown has a y intercept of 2 instead of 0. So it's not a direct proportion.

Which expression is equivalent to 7√x^2/5√y^3? Assume y≠0

Answers

Answer:

Step-by-step explanation:

If the √y³ term is in the denominator, then the expression needs to be written with parentheses:  7√x²/(5√y³)

find the product using suitable product 854×102 step by step explanation​

Answers

Answer:

87108

Step-by-step explanation:

854 x 102

= 854 x ( 100 + 2 )

= 854 ( 100 ) + 854 ( 2 )

= 85400 + 1708

= 87108

87108

854
102 x
——-

87108

Ophelia is making homemade spaghetti sauce by combining 48 oz of tomato paste with 6 cups of water.how many cups of water are needed for every ounces of tooth paste

Answers

1 cup per 8 oz

48/6 = 8

every 1 cup of water 8 oz of tomato paste.

1 cup per 8 oz
explained : there are 48 oz of tomato paste and 6 cups of water 48 over 6 is 8 therefore per every 1 cup of water there are 8 oz of tomato paste



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