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KengaRu [80]
3 years ago
15

Create three geometric sequences of your own (including one that is decreasing). Extend your sequences to include five terms. Th

en, identify the order of each term and the common ratio. Type your work in the text box below.
Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
4 0

Answer:

a)  a_n=5\,\,(2)^{n-1}

b)  b_n=100\,\,(\frac{1}{2} )^{n-1}

c)  c_n=160\,\,(-\frac{1}{2} )^{n-1}

Step-by-step explanation:

a)  Geometric sequence with first term 5 and common ratio 2, where the nth term can be calculated via:

a_n=5\,\,(2)^{n-1}

The first five terms are: a_1=5;\,\,\,a_2=10;\,\,\,a_3=20; \,\,\,a_4=40;\,\,\,a_5=80

b) Geometric sequence with first term 100 and common ratio 1/2, where the nth term can be calculated via:

b_n=100\,\,(\frac{1}{2} )^{n-1}

The first five terms are: a_1=100;\,\,\,a_2=50;\,\,\,a_3=25; \,\,\,a_4=12.5;\,\,\,a_5=6.25

c)  Geometric sequence with first term 160 and common ratio -1/2, where the nth term can be calculated via:

c_n=160\,\,(-\frac{1}{2} )^{n-1}

The first five terms are: a_1=160;\,\,\,a_2=-80;\,\,\,a_3=40; \,\,\,a_4=-20;\,\,\,a_5=10

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Does the following table shows a proportional relationship between the variables g & h​
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*the table being referred to is attached below

Answer:

The table does not show a proportional relationship between variable g and h.

Step-by-step explanation:

For a proportional relationship to exist between two variables, there must be a constant, of which serves like a unit rate, when comparing two variables.

Thus, in the table attached below, there is no obvious constant of proportionality between variable g and variable h.

Thus, \frac{9}{3} ≠ \frac{36}{6} ≠ \frac{81}{9}

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3 years ago
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What is the value of u and v?
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Answer and Explanation:

Since this is an isosceles right triangle, you can use the ratio of side lengths specific to this type of triangle where both legs are the hypotenuse over root 2:

u = v = 164√2 / √2 = 164

so:

u = 164

v = 164

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Np buddy its B. Hope u get a good grade

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2 years ago
20 points!!! Please Help<br><br> Does the equation x2 - 4x + y2 = -3 intersect the x-axis?
OverLord2011 [107]

Answer:

Yes, twice

Step-by-step explanation:

The equation will intersect the x-axis when y = 0, so we have

x² - 4x = -3    now solve this quadratic for x...

  x² - 4x + 3 = 0    

factor...

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

so at x = 1 and x = 3, the function crosses the x-axis

See the graph below

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3 years ago
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Cindi is planting a rectangular flower bed with 40 orange flower and 28 yellow flowers. She wants to plant them so that each row
Vilka [71]

Answer: 17 rows, 7 of yellow flowers and 10 of orange flowers.

Step-by-step explanation:

We have 40 orange flowers

we have 28 yellow flowers.

The total number of flowers is 40 + 28= 68

Now, we want to find the maximal comon factor between 28 and 40 (that will be the number of flowers in each row)

for this, we took the smallest number and find its factors, and then we see if those factors are also of the greater number.

28/1 = 28 ----> 40/28 is not integer, so 28 is not a factor of 40.

28/2 = 14 ----> 40/14 is not integer, so 14 is not a factor of 40.

28/3 is not integer.

28/4 = 7 ----> 40/7 is not integer, so 7 is not a factor of 40.

28/5 is not integer.

28/6 is not integer.

28/7 = 4, 40/4 = 10, so 4 is a factor of both 28 and 40.

Then the maximum number of flowers that we can put in each row is 4.

this means that we have:

28/4 = 7 rows of yellow flowers (with 4 flowers each)

40/4 = 10 rows of orange flowers (with 4 flowers each)

a total of 17 rows.

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3 years ago
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