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3 years ago

The set of ordered pairs represents a function. Write a rule that represents the function.

Mathematics

1 answer:

Furkat [3]3 years ago

7 0

Answer:

y = 3x^3 is the rule representing the function.

Step-by-step explanation:

There are 4 points given.

(0,0), (1,3), (2,24), (3,81), (4,192)

We are asked to find the function or rule connecting x and y

On seeing the pair, first let us find y/x

We observe that y is a multiple of 3. Let us find the values of y/3

y/3 = 0, 1, 4, 9, 16

= 0^2,1^2,3^2,4^2,....

i.e. y/3 is the square of x.

Hence relation is y = 3x^2

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Find an explicit rule for the nth term of the sequence.The second and fifth terms of a geometric sequence are 18 and 144, respec

vova2212 [387]

Given:

second term = 18

fifth term = 144

The nth term of a geometric sequence is:

$\begin{gathered} a_n\text{ = ar}^{n-1} \\ Where\text{ a is the first term} \\ r\text{ is the common ratio} \end{gathered}$

Hence, we have:

$\begin{gathered} \text{ar}^{2-1}\text{ = 18} \\ ar\text{ = 18} \\ \\ ar^{5-1}=\text{ 144} \\ ar^4\text{ =144} \end{gathered}$

Divide the expression for the fifth term by the expression for the second term:

$\begin{gathered} \frac{ar^4}{ar}\text{ = }\frac{144}{18} \\ r^3\text{ = }\frac{144}{18} \\ r\text{ = 2} \end{gathered}$

Substituting the value of r into any of the expression:

$\begin{gathered} ar\text{ = 18} \\ a\text{ }\times\text{ 2 = 18} \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}\text{ =}\frac{18}{2} \\ a\text{ = 9} \end{gathered}$

Hence, the explicit rule for the sequence is:

$a_n\text{ = 9\lparen2\rparen}^{n-1}$

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1 year ago

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Alona [7]

Answer:

Step-by-step explanation:

You can add the numbers to get the perimeter

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26 + 42 1/2= 68 1/2

That is answer choice A

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