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melomori [17]
2 years ago
9

The profit (in thousands of dollars) of a company is given by P(x) = -8x2 + 32x + 14.

Mathematics
1 answer:
andre [41]2 years ago
5 0

Answer:

C

Step-by-step explanation:

The profit (in thousands of dollars) of a company is given by the function:

\displaystyle P(x) = -8x^2+32x+14

And we want to find the maximum profit of the company.

Since the function is a quadratic with a negative leading coefficient, the maximum profit will occur at its vertex. Recall that the vertex of a quadratic is given by:

\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)

Find the <em>x-</em>coordinate of the vertex. In this case, <em>a</em> = -8, <em>b</em> = 32, and <em>c</em> = 14. Hence:

\displaystyle x=-\frac{(32)}{2(-8)}=\frac{32}{16}=2

To find the maximum profit, substitute this value back into the function. Hence:

\displaystyle P(2) = -8(2)^2+32(2) + 14 = 46

Therefore, the maximum profit of the company is 46 thousand dollars.

Our answer is C.

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For the given system of equations, considering different systems are split by ;, we have that:

  • No solutions: 3y = x + 2, 9y = 3x + 7; y = 2x + 3, y = 2x + 5
  • One solution: 2y = 3x, -5y = -10x,; x = 6, y = 9.
  • Infinitely many solutions: y = 5x + 2, 3y = 15x + 6.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

It's equations can be written in the format:

Ax = b

Using the above format, we have that:

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  • If both are zero, the system has infinite solutions.

At the first system, multiplying the first equation by -3 and adding with the second, we end up with:

0y = 0x + 2

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Which is a false statement, hence it has no solutions.

At the second system, the equations are multiples, hence it has infinite solutions.

At the third system, the coefficients are not zero and are not multiples, and it has one solution.

In the fourth system, the one solution is already given.

At the fifth system, we have that:

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Hence no solutions.

To learn more about system of equations, you can take a look at brainly.com/question/24342899

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