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morpeh [17]
2 years ago
5

(4,7,12,19) How do you right this in recursive and explicit equations??????? pls help

Mathematics
1 answer:
Soloha48 [4]2 years ago
7 0

You can see how the difference between two consecutive terms is constantly increasing:

a_1 = 4

a_2 = 7 = 4+3

a_3 = 12 = 7+5

a_4 = 19 = 12+7

So, for the next terms we'll have to add +9, +11, +13 and so on.

Also, note that a_2 is obtained by adding the 2nd odd number to a_1, a_3 is obtained by adding the 3rd odd number to a_2, and so on.

So, the recursive formula is

a_n = a_{n-1}+(2n-1),\quad a_1=1

For the explicit formula, recall that the sum of the first n odd numbers is n squared. Taking into account the fact that we're not starting from 1, we have

a_n = n^2+3

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What is the value of the rational expression<br> 2x- 1<br> x+5<br> when x = 0?
nikitadnepr [17]

Answer:

5

Step-by-step explanation

becasue 2x0=0 and 1x0=0

and when you add 5 to 0 you get five

7 0
2 years ago
Y= 16t (squared) +120 what is t
Zina [86]

Answer:

Step-by-step explanation:

hello :

16t²+120 = y

16t² = y -120   so : t² = (y-120)/16

if  :  y-120 ≥ 0        t = ±√((y-120)/16)

5 0
3 years ago
A wood frame costs $1.50. Use a property to write an equivalent expression for the cost of a wood frame.
podryga [215]
Let the width of the frame = x
Let the cost of a linear foot of the frame = y
Let the inside dimension of the length of the frame = a
Let the inside dimension of the width of the frame = b.

The total length of the frame = 2*a + 4x
The total width of the frame = 2b

The total amount of the frame in feet is (2a + 4x + 2b)*y = Cost
If this is incorrect please leave a message on my home page.
6 0
3 years ago
The length of a swimming pool is 3 feet longer than it’s width. The swimming pool is surrounded by a deck that is 2 feet wide an
Firlakuza [10]

Answer:

The Length of swimming pool is 8.35 feet

The width of swimming pool is 5.35 feet

Step-by-step explanation:

Given as :

The length of swimming pool is 3 feet longer that its width

Let The width of swimming pool = w  feet

So, The Length of swimming pool = L = (w + 3) feet

Now, The swimming pool is surrounded by deck of 2 feet wide

The width of deck = w' = w + 2 + 2 = (w + 4) feet

The area of deck = 116 feet²

The length of deck = L' = L + 2 + 2 = (L + 4) feet

So, L' = (w + 3 + 4) feet

I.e L' = (w + 7) feet

∵ The area of deck = 116 feet²

So , L' × w' = 116 feet²

(w + 7)× (w + 4) = 116

Or, w² + 4 w + 7 w + 28 = 116

Or, w² + 11 w - 88 = 0

Solving the quadratic equation as

ax² + bx + c = 0

So, w = \dfrac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}

Or, w = \dfrac{-11\pm \sqrt{11^{2}-4\times 1\times (-88)}}{2\times 1}

Or, w = \dfrac{-11\pm \sqrt{473}}{2}

or, w = \dfrac{-11\pm 21.7}{2}

or, w = 5.35 , -16.35

The width of swimming pool = w = 5.35 feet

The Length of swimming pool = L = (5.35 + 3) feet = 8.35 feet

Hence, The Length of swimming pool is 8.35 feet

And The width of swimming pool is 5.35 feet

Answer

3 0
3 years ago
Polynomial of degree 4 has 1 positive real root that is bouncer and 1 negative real root that is a bouncer. How many imaginary r
Rainbow [258]

Answer:

<h3>The given polynomial of degree 4 has atleast one imaginary root</h3>

Step-by-step explanation:

Given that " Polynomial of degree 4 has 1 positive real root that is bouncer and 1 negative real root that is a bouncer:

<h3>To find how many imaginary roots does the polynomial have :</h3>
  • Since the degree of given polynomial is 4
  • Therefore it must have four roots.
  • Already given that the given polynomial has 1 positive real root and 1 negative real root .
  • Every polynomial with degree greater than 1  has atleast one imaginary root.
<h3>Hence the given polynomial of degree 4 has atleast one imaginary root</h3><h3> </h3>

8 0
3 years ago
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