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algol [13]
3 years ago
7

Which function forms a geometric sequence when x = 1, 2, 3, . . . ?

Mathematics
1 answer:
irinina [24]3 years ago
6 0

Answer:

a) f(x)=3(4)^{x}

Step-by-step explanation:

The correct options are:

a) f(x)=3(4)^{x}

b) f(x)=3(x)^{2}

c) f(x)=2x+4

d) f(x)=x+(2)^{4}

We have to identify which of these options will form a geometric sequence. A geometric sequence is defined as the sequence in which the ratio of two consecutive terms remain the same. This ratio is known as common ratio of the sequence. General term of a geometric sequence is defined as:

a_{n}=a_{1}(r)^{n-1}

Here,

a_{n} is the nth term of the sequence. Replacing n by different values will give us the term of the sequence at that values.

The option resembling the general term of the geometric sequence is option a, with only difference that in place on "n", the variable x is used in the option. So option a should be our answer. Lets verify this.

f(x)=3(4)^{x}

For x = 1, the value will be:

f(1) = 12

For x = 2, the value will be:

f(2) = 48

For x =3, the value will be:

f(3) = 192

The ratio of these terms is:

Ratio of f(2) and f(1) = 4

Ratio of f(3) and f(2) = 4

Therefore, the function given in option a represents a geometric sequence.

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jolli1 [7]

Answer:

Length: 20

Width:15

Step-by-step explanation:

Hope this Helps!

3 0
2 years ago
The linear function f(x) = 0.9x + 79 represents the average test score in your math class, where x is the number of the test tak
Levart [38]

Given:

The linear function for average test score in your math class is

f(x)=0.9x+79

where x is the number of the test taken.

The linear function g(x) in the given table represents the average test score in your science class, where x is the number of the test taken.

To find:

Part A: The test average for your math class after completing test 2.

Part B: The test average for your science class after completing test 2.

Part C: Which class had a higher average after completing test 4?

Solution:

Part A:

We have,

f(x)=0.9x+79

Put x=2 in the above function, to find the test average for your math class after completing test 2.

f(2)=0.9(2)+79

f(2)=1.8+79

f(2)=80.8

Therefore, the test average for your math class after completing test 2 is 80.8.

Part B:

From the given table it is clear that g(x) =79 at x=2.

Therefore, the test average for your science class after completing test 2 is 79.

Part C:

Put x=4 in f(x), to find the test average for your math class after completing test 4.

f(4)=0.9(4)+79

f(4)=3.6+79

f(4)=82.6

From the table it is clear that the value of g(x) is increased by 1 as x is increased by 1. So, the value of function g(x) at x=4 must be 1 more than 80.

g(4)=81

It is clear that,

82.6>81

Therefore, math class had a higher average after completing test 4.

3 0
3 years ago
Parallelogram P was dilated to form parallelogram P prime.
Nimfa-mama [501]

Answer:

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3 years ago
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y varies jointly as x and z, and y = 32 m, x = 6 m, and z = 8 m. What is the value of y when x = 5 m and z = 12 m
Fantom [35]
We are given y = kxz
We also know 32 = k×6×8, so k = 32/48 = 2/3.
We are then asked to solve:

y =  \frac{2}{3}  \times 5 \times 12 = 40
3 0
3 years ago
Read 2 more answers
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Katena32 [7]

Answer:

15) x = 112

18) x = 120

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Step-by-step explanation:

I hope that is useful for you :)

5 0
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