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3 years ago

Which table shows input and output values that represent a linear function?

Mathematics

1 answer:

shepuryov [24]3 years ago

4 0

Answer:

Table A

Step-by-step explanation:

In order for it to be a linear relationship, the change in the x values and y values (f(x)) needs to be consistent.

In every table, the x values change the same, so we can focus on the y values.

Notice in table A, the f(x) values go down consistently by 10 for every change in x.

All of the other tables are not consistent.

Therefore, table A is the only linear function.

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Find the perimeter of a rhombus the length of whose diagonals are 10 cm and 24 m.

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4 years ago

Can anyone help me about question 2

madreJ [45]

9514 1404 393

Answer:

3(4/3)^2543

Step-by-step explanation:

Using logarithms base 2, we have ...

$(a_n)^{\log{a_n}}=(a_{n+1})^{\log{a_{n-1}}}\\\\(\log{a_n})(\log{a_n}) = (\log{a_{n-1}})(\log{a_{n+1}}) \\\\ \dfrac{\log{a_{n+1}}}{\log{a_{n}}}=\dfrac{\log{a_n}}{\log{a_{n-1}}}=\dots\dfrac{\log_2{16}}{\log_2{8}}=\dfrac{4}{3}$

That is, the ratio of each term to the previous is a constant equal to 4/3. This is the definition of a geometric sequence. This sequence has first term 3 and common ratio 4/3, so the general term is ...

$\log_2 a_n=3\left(\dfrac{4}{3}\right)^{n-1}$

and the 2544th term is ...

$\boxed{\log_2{a_{2544}}=3\left(\dfrac{4}{3}\right)^{2543}}$

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3 years ago