Which expressions are equivalent to 3(x + 3y + 2x − y )?

Mathematics

1 answer:

erma4kov [3.2K]3 years ago

4 0

Answer:

3(3x + 2y) and 9x + 6y

Step-by-step explanation:

3(x + 3y + 2x - y)

= 3 (x + 2x) + (3y - y)

= 3 (3x + 2y)

= (3 • 3x) + ( 3 • 2y)

= 9x + 6y

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Find the equation of an exponential function in the form y = ab^x, given the points (0, 3) and (2, 108/25). Please simplify your

lilavasa [31]

We have the equation:

$y=a\cdot b^x$

We know two points and we will use them to calculate the parameters a and b.

The point (0,3) will let us know a, as b^0=1.

$\begin{gathered} y=a\cdot b^x \\ 3=a\cdot b^0=a \\ a=3 \end{gathered}$

Now, we use the point (2, 108/25) to calcualte b:

$\begin{gathered} y=3\cdot b^x \\ \frac{108}{25}=3\cdot b^2 \\ 3\cdot b^2=\frac{108}{25} \\ b^2=\frac{108}{25\cdot3}=\frac{108}{3}\cdot\frac{1}{25}=\frac{36}{25} \\ b=\sqrt[]{\frac{36}{25}} \\ b=\frac{\sqrt[]{36}}{\sqrt[]{25}} \\ b=\frac{6}{5} \end{gathered}$

Then, we can write the equation as: