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2 years ago

Use the functions f (x)= –x^2 + 8x – 11, g(x) = 14 - 2/3x,and h(x) = -x – 7 to find each function value.

Mathematics

1 answer:

Sonja [21]2 years ago

8 0

-2f-3g it the right answer

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Which quantity is proportional to 16⁄4?

Aleks [24]

4.

This is because 4 goes into 16 4 times, hence 4 x 4 being 16.

Therefore, the answer would be four.

Hope this helps!

6 0

3 years ago

Read 2 more answers

Write the equation -4x^2+9y^2+32x+36y-64=0 in standard form. Please show me each step of the process!

IgorC [24]

Hey there, hope I can help!

$-4x^2+9y^2+32x+36y-64=0$

$\mathrm{Add\:}64\mathrm{\:to\:both\:sides} \ \textgreater \ 9y^2+32x+36y-4x^2=64$

$\mathrm{Factor\:out\:coefficient\:of\:square\:terms} \ \textgreater \ -4\left(x^2-8x\right)+9\left(y^2+4y\right)=64$

$\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}4$
$-\left(x^2-8x\right)+\frac{9}{4}\left(y^2+4y\right)=16$

$\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}9$
$-\frac{1}{9}\left(x^2-8x\right)+\frac{1}{4}\left(y^2+4y\right)=\frac{16}{9}$

$\mathrm{Convert}\:x\:\mathrm{to\:square\:form}$
$-\frac{1}{9}\left(x^2-8x+16\right)+\frac{1}{4}\left(y^2+4y\right)=\frac{16}{9}-\frac{1}{9}\left(16\right)$

$\mathrm{Convert\:to\:square\:form}$
$-\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y^2+4y\right)=\frac{16}{9}-\frac{1}{9}\left(16\right)$

$\mathrm{Convert}\:y\:\mathrm{to\:square\:form}$
$-\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y^2+4y+4\right)=\frac{16}{9}-\frac{1}{9}\left(16\right)+\frac{1}{4}\left(4\right)$

$\mathrm{Convert\:to\:square\:form}$
$-\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y+2\right)^2=\frac{16}{9}-\frac{1}{9}\left(16\right)+\frac{1}{4}\left(4\right)$

$\mathrm{Refine\:}\frac{16}{9}-\frac{1}{9}\left(16\right)+\frac{1}{4}\left(4\right) \ \textgreater \ -\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y+2\right)^2=1$

$Refine\;once\;more\;-\frac{\left(x-4\right)^2}{9}+\frac{\left(y+2\right)^2}{4}=1$

For me I used
$\frac{\left(y-k\right)^2}{a^2}-\frac{\left(x-h\right)^2}{b^2}= 1$
$As\;\mathrm{it\;\:is\:the\:standard\:equation\:for\:an\:up-down\:facing\:hyperbola}$

I know yours is an equation which is why I did not go any further because this is the standard form you are looking for. I would rewrite mine to get my hyperbola standard form. However the one I have provided is the form you need where mine would be.
$\frac{\left(y-\left(-2\right)\right)^2}{2^2}-\frac{\left(x-4\right)^2}{3^2}=1$

Hope this helps!

4 0

3 years ago

You buy a new video game for $59.99

vivado [14]

$64.79 would be the cost after tax is added

3 0

3 years ago

Jared made 4 bird houses in 3 days. How many days will it take him to make 28 bird houses.

pogonyaev

4 times 7 = 28

3 times 7 = 21

It will take him 21 days to make 28 bird houses.

6 0

3 years ago

Marty was renting a boat and wanted to get the best plan. Rental plan A charges a fee of

harina [27]

The system of equations that represent the situation are as follows;

C = $50 + $25h

C = $10 + $35h.

According to the question;

Mary was trying to rent a boat and wanted to get the best plan.

Let C = Charged fees

and h = hours of rental

For Plan A:

Rental plan A charges a fee of
$50 plus $25 per hour.

C = $50 + $25h

For Plan B:

Plan B charges a fee of $10 plus $35 per hour.

C = $10 + $35h.