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2 years ago

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:

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 x-coordinate of the vertex. In this case, a = -8, b = 32, and c = 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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Which relationship would most likely have a positive correlation?

tiny-mole [99]

Answer:

Step-by-step explanation:

The only thing to do here is just check all of the answers.

A makes no sense, as the number of keys on a keyboard doesn't affect the amount of memory in a computer at all (no correlation).

B makes a bit more sense, but it's still wrong. If a train travels faster, it gets places quicker, or the time goes down. If (If one goes up, the other goes down) is true, then you have negative correlation.

C makes the most sense, as if there's more people at a game, then those more people will probably buy more hot dogs. If (If one goes up, so does the other) is true, then you have positive correlation, which is what we want.

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3 years ago

I’m stuck on this I need the correct answer ASAP !

Reil [10]

Answer:

S is the center of the circle shown below. The correct answer choice is A.

Step-by-step explanation:

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4 years ago

Draw the graphs of the equations x – y = 1 and 2x + y = 8. Shade the area bounded by these two lines and y-axis. Also, determine

NikAS [45]

Answer:

Using Geometry to answer the question would be the simplest:

Step-by-step explanation:

Remembering the formula for the area of a triangle which is $A=\frac12bh$ . One can then tackle the question by doing the following:

Step 1 Find the y-intercepts

The y-intercepts are found by substituting in $x=0$ .

Which gives you this when you plug it into both equations:

$-y=1\\y=-1\\y=8$

So the y-intercepts for the graphs are $(0,-1)\\$ , and $(0,8)$ respectively.

Now one has to use elimination to solve the problems by adding up the equations we get:

$x-y=1\\2x+y=8\\3x=9\\x=3$

Now to solve for the y component substitute:

$2(3)+y=8\\y=2$

Therefore, the graphs intersect at the following:

$(3,2)$

Now we have our triangle which is accompanied by the graph.

now to solve it we must figure out how long the base is:

$b=8-(-1)\\b=9$

The height must also be accounted for which is the following:

$h=3$

Now the formula can be used:

$A=\frac12bh=\frac12(9)(3)=\frac{27}2\ \text{units}^2$

7 0

3 years ago

Read 2 more answers

Let f(x) = x2 − 3x − 7. Find f(−3)

uranmaximum [27]

Substituting -3 for x, we have: (-3)^2-3*-3-7. This simplifies to 9+9-7, or 11.

3 0

3 years ago

PLEASE HELP!

erica [24]

The correct next step that Cynthia should do is to:

D. use the arc markings to determine the radius to construct the circle

The arc markings are actually used as the baseline in determining the center and the radius of the circle. The arc markings are created with the use of a compass. All other choices are completely irrelevant because what we need is the arc and not the angles. The angles do not create the circle. Letter C is also wrong because what we are trying to form is the circle and not the triangle. The triangle is already created.

4 0

3 years ago