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spin [16.1K]
3 years ago
5

Write a recursive definition for the sequence 14, 10, 6, 2...

Mathematics
2 answers:
Anastasy [175]3 years ago
8 0

The answer is:

<h3>d. a_{1}=14, a_{n}=a_{n-1}-4</h3>

VladimirAG [237]3 years ago
7 0
The general form of recursive definition for arithmetic sequence:
a_{n}=a_{1}+d(n-1)

So, what we need to do is to find a_{1} and d.
a_{1}=14
d=a_{2}-a_{1}=10-14=-4
Having found these two values we can now define our recursive sequence:
a_{n}=14-4(n-1)
a_{n}=14-4n+4
a_{n}=18-4n
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What is the equation for a line that passes through the points (-4,-3) and (8,12)?
kherson [118]

Step-by-step explanation:

vv

6 0
3 years ago
What are the x-intercepts of a parabola with a vertex of (-1,-16) and a y-intercept of (0,-15)?
Svetlanka [38]
The vertex-form equation is
  y = a(x+1)² -16
Putting in the y-intercept values, we have
  -15 = a(0+1)² -16
  1 = a . . . . . . . . . . . add 16

Then the x-intercepts can be found where y=0.
  0 = (x+1)² -16
  16 = (x+1)²
  ±4 = x+1
  x = -1 ± 4 = {-5, 3}

8 0
3 years ago
Solve and show your work for each question a). B). C).
Andreyy89

Answer:

Step-by-step explanation:

a) Here, the first term is .48 and the common ratio is 1/100 (since each new 48 is 1/100 th of the previous 48).                                   a

Use the formula s = sum of geometric series = -----------

                                                                                  1 - r

                                           0.48              48

which in this case is s = --------------- = ------------ = 48/99 = 16/33

                                          1 - 1/100        100 - 1

Check this result by finding 16/33 on a calculator.  Is the result equal to 0.484848484848.... ?  Yes

b) Here we have the bar over the 8 only.  0.48 with the bar over the 8 is equivalent to 0.4888888888 ...

                                                              0.08

or 0.4 + 0.0888888888 ...      or 0.4 + ------------

                                                                1 - 1/10

                                             

                                              0.08                       8

and this simplifies to 0.4 + ------------  =  0.4 + ---------

                                                9/10                      90

Evaluating this last result on a calculator results in 0.488888888 ...

c)  0.48 expressed as a fraction is  48/100 = 12/25

6 0
3 years ago
Are these functions?
OlgaM077 [116]

Answer:

Relation 1 : Not a function

R2 : Function

R3: Function

R4: Not a function

7 0
3 years ago
Read 2 more answers
We want to find the zeros of this polynomial p(x)= ( x^2-1)(x^2-5x+6)
Scrat [10]

Answer:

see explanation

Step-by-step explanation:

To find the zeros let p(x) = 0 , that is

(x² - 1)(x² - 5x + 6) = 0

Factorise each factor

x² - 1 ← is a difference of squares and factors as (x - 1)(x + 1)

x² - 5x + 6 = (x - 2)(x - 3), thus

(x - 1)(x + 1)(x - 2)(x - 3) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x + 1 = 0 ⇒ x = - 1

x - 2 = 0 ⇒ x = 2

x - 3 = 0 ⇒ x = 3

The zeros are x = ± 1, x = 2, x = 3

4 0
3 years ago
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