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? 3

Answers

Answer 1

Given:

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

A number is added to x, y, and z yields consecutive terms of a geometric sequence.

To find:

The number which is added to  x, y, and z, then find the first three terms in the geometric sequence.

Solution:

Let the unknown number be k.

After adding k to x, y, and z, we get

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

These are the consecutive terms of a geometric sequence. So,

[tex](7+k)^2=(1+k)(15+k)[/tex]

[tex]49+14k+k^2=15+k+15k+k^2[/tex]

[tex]49+14k=15+16k[/tex]

Isolate the variable terms.

[tex]49-15=16k-14k[/tex]

[tex]34=2k[/tex]

[tex]\dfrac{34}{2}=k[/tex]

[tex]17=k[/tex]

The unknown number is 17.

Now,

[tex]x=1+k[/tex]

[tex]x=1+17[/tex]

[tex]x=18[/tex]

Similarly,

[tex]y=7+k[/tex]

[tex]y=7+17[/tex]

[tex]y=24[/tex]

And

[tex]z=15+k[/tex]

[tex]z=15+17[/tex]

[tex]z=32[/tex]

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


Related Questions

Carlo borrows 4180 add a rate of 4.1% Per year compounded annually he does not start payments until after 2.8 years which of the following is closest to the total amount he owes after 2.8 years

Answers

Answer:497.76

Step-by-step explanation:

Grade low in math help if you can :) Geometry

Lauren wants to build a model airplane using a scale where 2 inches represents 15 feet. If the airplane is 75 feet long, how long should the model be?
A.
5 inches
B.
7.5 inches
C.
10 inches
D.
15 inches

Answers

Answer:

C) 10 inches

Step-by-step explanation:

I think the simplest way to do this is as follows:

divide 75 by 15 to get how many times you need to multiply 2in by

75/15=5

since 15(5)=75 or the actual size of the airplane,

2(5)=10 which is the size of the model airplane

please help me and I have more too​

Answers

Answer:

b. x=3

Step-by-step explanation:

i hope this helps :)

Answer:

4x+20=6x+14

Step-by-step explanation:

20=2x+14

6=2x

3=x

Mahi has 31 rolls of string. Each roll holds 12 yards of string. How many feet of string does she have?

Answers

Answer:

1116ft of string, hope this helps !!

Step-by-step explanation:

(31 x 12) x 3 =

372 x 3 =

1,116

6. A plumber charges $45 for travel and $60 per hour. The cost for h hours can be found using this
expression.
60h + 45
What is the total cost of a repair that takes 3 hours?
OA. $648
OB. $225
OC. $165
OD. $108

Answers

Hope This Helps You!!!

Have a great day!!!

PLEASE HELP ME!! I NEED HELP FAST!

Question 3 (10 points) (08.03/08.05 MC) A pair of equations is shown below:

y = 7x - 8
y = 5x – 2

Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points)

Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points)​

Answers

Answer:

part A) rearrange the equations to form simultaneous equations:

y-7x=8

y-5x=-2

now eliminate the y values by minusing the two equations:

(y-7x=8)-(y-5x=-2)

to get:

-2x=-6

x=3

now substitute x into one of the equations to get y:

y=5x-2

y=15-2

y=13

[tex]x = 3 \\ y = 13[/tex]

part B) the lines will intercept at (3, 13)

Step-by-step explanation:

hope this helps!


You are on a road trip and have driven 24 miles, which is 3/4 of the total distance.
What is the total distance of this trip?

Answers

32 miles. ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

The perimeter of the triangle is 30 cm.
The perimeter of the rectangle is also 30 cm.
b
a
a
a
a
RE
b
Use this information to find the area of the square below.
b
Eਦੇ ਸਾਊ ਜ0
+
b
b
b
ਬਰੀ ਹੈ। ਅਜੋਕੇ ਸੰਤ
CHE

Answers

Answer:

25

Step-by-step explanation:

3a=30... equation 1

2a+2b=30... equation2

equation 2 => a+b=15 ... equation 3

equation 1 => a = 10 ... equation 4

equation 4 & equation 3 => b = 5

5^2 = 25

Answer:

20 cm

Step-by-step explanation:

triangle

30/3=10=a

rectangle

30-20=10/2=5=b

square

4 times 5=20

1 2 3 4 5 6 7 8 9 10 The variety of organisms within an ecosystem is characteristic of which type of diversity? a. Genetic diversity b. Ecosystem diversity c. Species diversity d. Regional diversity Please select the best answer from the choices provided A B C D Mark this and return

Answers

Answer:

its C  (Species diversity)

Step-by-step explanation:

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HELP I NEED HELP ASAP

Answers

Answer:

I think D

Step-by-step explanation:

I am not sure sorry

Rule: y is 1/3 times as large as x. If x=0 y=? x=6 y=? x=12 y=?

Answers

Answer:

So for 0

0*1/3 = 0

6*1/3= 2

12*1/3= 4

Step-by-step explanation:

An equation is formed of two equal expressions. The value of y when the value of x is 0, 6 and 12 is 0, 2, and 4, respectively.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the statement that "y is 1/3 times as large as x", therefore, the rule can be written as,

y=(1/3)x

Now, the value of y for different value of x can be written as,

1.) When x=0

    y = (1/3)x

    y = (1/3)(0)

    y = 0

2.) When x=6

     y = (1/3)x

     y = (1/3)(6)

     y = 2

3.) When x=12

    y = (1/3)x

    y = (1/3)(12)

    y = 4

Hence, the value of y when the value of x is 0, 6 and 12 is 0, 2, and 4, respectively.

Learn more about Equation here:

https://brainly.com/question/14686792

#SPJ2

Look at the photo to answer

Answers

answer is two .....

Do 2b+b and 3b have the same value for all values of b

Answers

Answer:

Expression 2b+b and 3b have same values for all values of b.

Step-by-step explanation:

Given the two expression 2b+b2b+b and 3b3b and values of b as 1, 2 and 3.

Consider first expression that is, 2b+b2b+b .

Substituting the value of b=1b=1 ,

2\left(1\right)+\left(1\right)=2+1=32(1)+(1)=2+1=3 ....1

Substituting the value of b=2b=2 ,

2\left(2\right)+\left(2\right)=4+2=62(2)+(2)=4+2=6 ....2

Substituting the value of b=3b=3 ,

2\left(3\right)+\left(3\right)=6+3=92(3)+(3)=6+3=9 ....3

Consider second expression that is, 3b3b .

Substituting the value of b=1b=1 ,

3\left(1\right)=33(1)=3 ....4

Substituting the value of b=2b=2 ,

3\left(2\right)=63(2)=6 ....5

Substituting the value of b=3b=3 ,

3\left(3\right)=93(3)=9 ....6

For value of b=1, equation 1 and equation 4 are same, for value of b=2, equation 2 and equation 5 are same and for value of b=3 equation 3 and equation 6 are same.

Therefore both expression are same for all values of b.

Step-by-step explanation:

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PLEASE HELP DUE SOON! Find the area of the shaded region. Write your answer in exact form.

Answers

Can you repost the picture I can’these it

Can u find the value of the x.

Answers

Answer:x=8

Step-by-step explanation:

x²-3x=-3x+64

- Add 3x to both sides

x²-3x+3x=-3x+3x+64

= x²=64

- Square both sides

√x²=√64

x=±8

- Since the question is asking for the positive value of x, the answer is 8.

Determine whether the three side lengths form a triangle. 3,5,7

Answers

Yes. Because the sum of the two small numbers are bigger than the longest side.

3+5 >7

A factory produces 90 packages of mixed nuts in 1 min. A quality control manager selected 10 of these 90 packages at random and then counted the number of nuts in each package. The manager recorded the results.

30, 31, 36, 32, 35, 35, 35, 33, 31, 36

What is the estimated median number of nuts in all 90 packages?

Enter your answer in the box.

nuts =

Answers

answer:

34

explanation:

First of all, put the numbers in order

30, 31, 31, 32, 33, 35, 35, 35, 36, 36

Then, find the middle number.
In this case, there is an even amount of numbers so, we have to pick the 2 middle numbers which is 33 and 35.

Now all you have to do is add these two numbers together then divide by 2 which will give you 34.

or, in simpler questions like this one, you can just say 34 as you know it is between 33 and 35.


In other questions, it might have and odd amount of numbers, for example:

3, 3, 5, 8, 10

so all you would do here is pick the middle number which would be 5. (it has 2 numbers on each side of it)

Answer:

34

Step-by-step explanation:

just because its 34  add my

Plssss help with this ty

Answers

Answer:

132 units squared

Step-by-step explanation:

To start we can find the area of the rectangle, to do that we need to do

12*6=72

then we can find the area of the triangle, the formula to find a triangle's area of (b*h)/2, so we can do that

(10*12)/2=60

then we can add them together

72+60=132

Answer: 90

Step-by-step explanation:

Triangle=60

square=36

Now add them!

60+36=96

help plsssss need help will give brainliest

Answers

Answer:

[tex]\boxed {\boxed {\sf 22a-14b}}[/tex]

Step-by-step explanation:

We are given this expression:

[tex]17a-10b+5a-4b[/tex]

We are asked to simplify. For this expression, we will need to combine like terms. Like terms are terms with the same variable. In this expression, there are 2 variables: a and b. Use the commutative property of addition to move the like terms together.

[tex](17a+5a)+(-10b+ -4b)[/tex]

Add inside the parentheses.

[tex]22a+ (-10b+-4b)[/tex]

A positive next to a negative, like +- becomes a negative.

[tex]22a+ (-10b-4b)[/tex]

[tex]22a+ -14b \\22a-14b[/tex]

The expression 17a-10b+5a-4b is equal to 22a-14b.

A triangle has two sides of length 17 and 19. What is the smallest possible whole-number length for the third side?

Answers

Answer:

3

Step-by-step explanation:

A triangle has two sides of length 17 and 19. What is the smallest possible whole-number length for the third side?

To solve for the above question, a rule applies.

The rule states that:

The sum of any 2 sides must be greater than than the third side.

The possible values for the third side are

19 - 17 < x < 19 + 17( x is the third side )

2 < x < 36

Thus the smallest possible whole number is 3

If the perimeter of a rectangle is 28 inches, what could be the two dimensions of the rectangle?
11 inches
4 inches
9 inches
3 inches
7 inches

Answers

Answer:

11 and 3

Step-by-step explanation:

11x2 = 22

3x2 = 6

6+22=28

Desmond really like Legos. Last Saturday Desmond counted his Legos and realized that

he has 65 altogether! Desmond has 7 less green Legos than red Legos, and the amount of

blue Legos he has is two more than three times his red Legos. How many of each color

Lego does Desmond have?
Answer Quick.
Only reply if you have the answer please

Answers

Answer: 14 red, 7 green, 44 blue

Step-by-step explanation:

First, use the letter r as a variable to represent the number of red Legos. The number of green Legos (g) is 7 less than the number of red Legos, or g = r-7. The number of blue Legos (b) is 2 more than 3 times the number of red Legos, or b = 3r+2. The total number of Legos is the number of red + green + blue Legos, which can be represented as 65 = r+g+b.

Substitute the equations for g and b in. This should give you a final equation of 65 = r+(r-7)+(3r+2). To solve for the number of red Legos, first add up all of the terms to get 65 = 5r-5. Now add 5 to each side (70 = 5r). Finally, divide each side by 5 (r = 14).

To find the number of green Legos, substitute the number of red Legos (14) into the equation for the green Legos (g = r-7). This should get you the equation g = 14-7 which simplifies to g = 7.

To find the number of blue Legos, substitute the number of red Legos (14) into the equation for the blue Legos (b = 3r+2). This gives you the equation b = (3*14)+2. First, multiply 3 and 14 to get b = 42+2. Finally, add them together to get b = 44.

Isaac walks 8 km north and then 12 km east. How far is Isaac from his starting point?

Answers

Answer:

Step-by-step explanation:

Distance from starting point = 8 + 12 = 20km

ok screw it i need to sneep i can't even do simple addition its too late

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Simplify: [tex](8^{\frac{2}{3}) ^{4} }[/tex]

Answers

[tex]{ \large{ \sf{ \implies{(8 {}^{ \frac{2}{3} }) {}^{4} }}}}[/tex]

[tex]{ \large{ \sf{ \implies( \sqrt[3]{8} {}^{2} ) {}^{4} }}}[/tex]

[tex]{ \large{ \sf{ \implies{{(2 {}^{2} ) {}^{4} }}}}}[/tex]

[tex]{ \large{ \implies{ \sf{4 {}^{4} }}}}[/tex]

[tex]{ \large{ \therefore{ \sf{256} \: \: ans.}}}[/tex]

can someone help me

Answers

Answer:

z equals 13 yeeeeeeeeetttttttttttttt I hopppppeeeee thhhhhaaaaatttttt heeeeelllllllpppppppsssssss

what is the perimeter of this polygon?

Answers

Answer:

Step-by-step explanation:

Did you try adding it all up and combine the like terms to get your answer

HELPP!! PLEASE ITS DUE SOON

Zoe throws a dart at a target 9 times. She hits the bullseye all 9 times.
What is the relative frequency of Zoe hitting the bullseye?

Answers

Answer:

100%

Step-by-step explanation:

Assuming Zoe throws a dart at a target 9 times. The relative frequency of Zoe hitting the bullseye is 100%.

Relative frequency

Relative frequency=Number of times a dart is throwed/Number of times the bullseye is hits×100


Where:

Number of times a dart is throwed=9 times

Number of times the bullseye is hits=9 times

Let plug in the formula

Relative frequency=9/9×100

Relative frequency=100%

Inconclusion the relative frequency of Zoe hitting the bullseye is 100%.

Learn more about relative frequency here:https://brainly.com/question/3857836

While grocery shopping, you notice your favorite brand of soda has a big sticker, "Now 50% more than our 12oz!" How much soda is in the new bottle? Show all work.

Answers

Answer:

18 ounces

Step-by-step explanation:

Answer:

im not sure but maybe it should be 18 ounces

please help me ahhh im doing 8th grade math with pythagorean theorem i really need help please 15 points!!

Answers

184^2+b^2= 545^2

33856+ b^2= 297,025

b^2= 263169

b= 513

The length is 513 ft

Which represents the inverse of the function
f(x) = 4x?

Answers

Answer:

Step-by-step explanation:

that options given seem wrong but what do i know thats just difficult dude im just in the 4th grade

Answer:

4th option

Step-by-step explanation:

let y = f(x) , then rearrange making x the subject, that is

y = 4x ( divide both sides by 4 )

[tex]\frac{1}{4}[/tex] y = x

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then

[tex]f^{-1}[/tex] (x) = h(x) = [tex]\frac{1}{4}[/tex] x

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