How many solutions exist for each system of equations? x + 2y = –1 2x + 3y = 0

Mathematics

1 answer:

Lelechka [254]2 years ago

8 0

Answer:

2 solutions x = 3 y = -2.

Step-by-step explanation:

x + 2y = –1

2x + 3y = 0

Multiply first equation by -2:

-2x - 4y = 2 Adding this to second equation:

- y = 2

y = -2.

Plug this into first equation:

x - 4 = -1

x = 3.

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The revenue equation (in hundreds of millions of dollars) for barley production in a certain country is approximated by R(x) = 0

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Answer:

The marginal-revenue equation is $R'(x)=0.1226x+1.1584$ .

The marginal revenue for the production of 200,000,000 bushels is $R'(x)=1.4036$ .

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Step-by-step explanation:

The derivative $R'(x)$ of the revenue function is called the marginal revenue function and is the rate of change of revenue with respect to the number of units sold.

We know the revenue function, $R(x) = 0.0613x^{2} +1.1584x+2.4813$ . Therefore, the marginal revenue function is

$R'(x)=\frac{d}{dx}R(x) = \frac{d}{dx}(0.0613x^{2} +1.1584x+2.4813)\\\\=\frac{d}{dx}\left(0.0613x^2\right)+\frac{d}{dx}\left(1.1584x\right)+\frac{d}{dx}\left(2.4813\right)\\\\R'(x)=0.1226x+1.1584$