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Veseljchak [2.6K]
2 years ago
13

Which function describes the arithmetic sequence shown -1, 1, 3, 5, 7, 9, 11, 13, ...

Mathematics
1 answer:
riadik2000 [5.3K]2 years ago
7 0

Answer:

f(n) = 2n - 3 describes the arithmetic sequence,

-1, 1, 3, 5, 7, 9, 11, 13,.......

Step-by-step explanation:

Function:

A function is like a machine that gives an output for a given input.

A function has an independent variable which is called the input of the function.

The output for a given input is called the dependent variable.

Here. 'n' is the independent variable

f(n) is the function dependent variable i.e function of n as an output.

For Arithmetic sequence

a_{n}= a_{1} + (n-1)d

Where

a_{n} = nth number of the sequence.

a₁ = First term

d = common difference = a₂ - a₁ = a₃ - a₂ = so on

For a function which describes Arithmetic sequence,

a₁ = -1

d = 1 - -1 =2

∴ f(n) = a₁ + (n -1 )d

substituting the values we get

∴ f(n) = -1 +(n-1)2

using distributive property

∴ f(n) = - 1 +  2n - 2

∴ f(n) = 2n - 3  ..........is the required function

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Reverse the two digits of my age, divide by three, add 20, and the result is my age. How many years old am I
lapo4ka [179]

Answer:

  • 48 years old.

Step-by-step explanation:

Let the age be xy or 10x + y.

Reverse the two digits of my age, divide by three, add 20, and the result is my age, convert this to equation:

  • (10y + x)/3 + 20 = 10x + y
  • (10y + x)/3 = 10x + y - 20
  • 10y + x = 3(10x + y - 20)
  • 10y + x = 30x + 3y - 60
  • 30x - x + 3y - 10y = 60
  • 29x - 7y = 60

We should consider both x and y are between 1 and 9 since both the age and its reverse are 2-digit numbers.

Possible options for x are:

  • 29x ≥ 7*1 + 60 = 67 ⇒ x > 2, at minimum value of y,

and

  • 29x ≤ 7*9 + 60 = 123 ⇒ x < 5, at maximum value of y.

So x can be 3 or 4.

<h3>If x = 3</h3>

  • 29*3 - 7y = 60
  • 87 - 7y = 60
  • 7y = 27
  • y = 27/7, discarded as fraction.

<h3>If x = 4</h3>

  • 29*4 - 7y = 60
  • 116 - 7y = 60
  • 7y = 56
  • y = 8

So the age is 48.

6 0
1 year ago
What is the cost of the bill if a drink costs $3, a meal costs $20, an appetizer costs $5.50 and a slice of cake cost $3. 75?​
skelet666 [1.2K]
32.25 is the cost of the bill
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3 years ago
Kim wants to draw a triangle with a 20 degrees angle and a 70 degrees angle so that the side between them is 4 inches long. How
Nikitich [7]

Answer:

2

Step-by-step explanation:

The side has to be between the angles.

So, Angle1 - Side - Angle2

So, we can only swap the angles. So no other permutation is possible with the given conditions.

[If there's any problem with the solution, please inform me]

3 0
2 years ago
Factor the following expression <br> 10x^5+5x^3-14x^2-7-
Tatiana [17]

Answer:

C. (5x^3-7)(2x^2+1)

Step-by-step explanation:

Given expression is,

10x^5+5x^3-14x^2-7

=10x^5-14x^2 + 5x^3 - 7  (By the commutative property)

=2x^2(5x^3-7)+5x^3-7     (Taking 2x^3 common from first two terms )

=(5x^3-7)(2x^2+1)      (Taking 5x^3-7 common from both terms)

\implies 10x^5+5x^3-14x^2-7=(5x^3-7)(2x^2+1)

Hence, Option C is correct

5 0
2 years ago
Is 3/4 a rational number
Verizon [17]

Hello,

<em>3/4 is a rational number because it can be written as a fraction.</em>

Thanks,

<em>Deku ❤</em>

6 0
3 years ago
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