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

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.

Kim wants to solve the equation 538+ 223= x. How should Kim rewrite the sum in order to solve for x?

If you think of the equation as an equation for a line.

=+
y
=
m
x
+
b

where

=5/9(−32)
C
=
5
/
9
(
F
−
32
)

or

=5/9−5/9(32)
C
=
5
/
9
F
−
5
/
9
(
32
)

you can see the slope of the graph is 5/9
5
/
9
, which means that for an increase of 1 degree Fahrenheit, the increase is 5/9
5
/
9
of 1 degree Celsius. Therefore, statement I is true.

This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of 9/5
9
/
5
degrees Fahrenheit. Since 95
9
5
= 1.8, statement II is true.

On the other hand, statement III is not true, since a temperature increase of 9/5
9
/
5
degrees Fahrenheit, not 5/9
5
/
9
degree Fahrenheit, is equal to a temperature increase of 1 degree Celsius.

The final answer is D.

Math question :) please help

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B.
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osmqbshxissjwvgxkoqjwvwnmddk​

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How many problems were answered correctly?
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32
18
20
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A company starts to track the number of phone calls received each month. Information about the number of phone calls the company received the first three months of tracking is listed below.


• During the first month, the company received 5,650 phone calls.

• During the second month, the company received 30% more phone calls than in the first month.

• During the third month, the company received 10,283 phone calls.


What was the percent increase in the number of phone calls from the second month to the third month?

español


Una empresa comienza a realizar un seguimiento del número de llamadas telefónicas recibidas cada mes. La información sobre la cantidad de llamadas telefónicas que recibió la empresa durante los primeros tres meses del seguimiento se enumera a continuación.


● . Durante el primer mes, la empresa recibió 5,650 llamadas telefónicas

● Durante el segundo mes, la empresa recibió un 30% más de llamadas que en el primer mes.

● Durante el tercer mes, la empresa recibió 10,283 llamadas telefónicas.


¿Cuál fue el porcentaje de aumento en la cantidad de llamadas telefónicas del segundo mes al tercer mes?

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If you get 9 = 0 as your final answer, how many solutions do you have in your set?


A) one solution
B) infinite solutions
C) no solution
D) two solutions

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