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3 years ago

Which answer describes the transformation of f(x )= x^2 − 1 to g(x) = ( x + 4 )^2 − 1?

Mathematics

1 answer:

OverLord2011 [107]3 years ago

5 0

The (x + 4) tells you that the function is moving 4 units to the left.
the answer would be letter C

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A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materi

blondinia [14]

Answer:

The required function is: $P(x)=-3x^2+78x-360$

The price for each feeder to maximize profit should be $13.

The maximum weekly profit is $147

Step-by-step explanation:

Consider the provided information.

Part (A)

The materials for each feeder cost $6, and the society sells an average of 30 per week at a price of $10 each.

Let x be the price per feeder.

Profit = Revenue - cost

So the profit per feeder is $x-6$

If we increase then for every dollar increase, it loses 3 sales per week.

This can be written as:

$30-3(x-10)$

$30-3x+30$

$-3x+60$

Where x-10 represents the increase in price and 3 represents the decrease in sales per week.

Thus the profit will be:

$P(x)=(x-6)(-3x+60)$

$P(x)=-3x^2+78x-360$

Hence, the required function is: $P(x)=-3x^2+78x-360$

Part (B) What price should the society charge for each feeder to maximize profits? What is the maximum weekly profit?

The above function is a downward parabola so the maximum will occur at vertex.

The x coordinate of the vertex of parabola is: $x=\frac{-b}{2a}$

Substitute a=-3, b=78 and c=-360 in above.

$x=\frac{-78}{2(-3)}=13$

Hence, the price for each feeder to maximize profit should be $13.

Now substitute the value of x in $P(x)=-3x^2+78x-360$

$P(x)=-3(13)^2+78(13)-360=$147$

Hence, the maximum weekly profit is $147

5 0

3 years ago

What is the slope of the function?

AfilCa [17]

Change in y divided by the change in x

4 0

3 years ago

What is the solution to the system of equations below?

Andre45 [30]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the equations

$y=-6x-10$

$y=-3x-21$

solving the system of the equations

Arrange the equation variables for elimination

$\begin{bmatrix}y+6x=-10\\ y+3x=-21\end{bmatrix}$

$y+3x=-21$

$-$

$\underline{y+6x=-10}$

$-3x=-11$

$\begin{bmatrix}y+6x=-10\\ -3x=-11\end{bmatrix}$

solve

$-3x=-11$

Divide both sides by -3

$\frac{-3x}{-3}=\frac{-11}{-3}$

$x=\frac{11}{3}$

$\mathrm{For\:}y+6x=-10\mathrm{\:plug\:in\:}x=\frac{11}{3}$

$y+6\cdot \frac{11}{3}=-10$

$y=-32$

Therefore, the solutions to the system of the equations are:

$y=-32,\:x=\frac{11}{3}$

But, it seems none of the options is true.

8 0

3 years ago

Read 2 more answers

PLS HALP!!!

andre [41]

Answer:

Step-by-step explanation:

The easiest way to arrange in order is by turning them in decimal form.

You can't work them out on paper, because you are not good with them? than use a calculator to find the decimal form, unless you don't have one.

7 0

3 years ago

Mary has a large sum of money to deposit, but since she has heard many stories from her grandmother about the Great Depression,

maks197457 [2]

Mary should make sure to choose a bank that is FDIC insured. Furthermore, if she has more than maximum deposit insurance amount to deposit, she should spread her deposits out among several separate banks. These should be totally different banks, not simply different branches of the same bank. The FDIC will insure up to the maximum deposit insurance amount at each bank, even if the bank fails.

3 0

3 years ago