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thanks you

Earnings(hours) = $(50 + 4.25*hours)

Earnings(6) = $(50 + 4.25*6) = $75.5

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Use the calculator here:

$${\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{13}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{205}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}\right)}{{\mathtt{6}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{205}}}}{\mathtt{\,-\,}}{\mathtt{7}}\right)}{{\mathtt{6}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{3.552\: \!970\: \!177\: \!212\: \!725\: \!5}}\\
{\mathtt{x}} = {\mathtt{1.219\: \!636\: \!843\: \!879\: \!392\: \!2}}\\
\end{array} \right\}$$

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I'm afraid this question doesn't mean a thing to me!

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Is the following what you are looking for?

Collect the ab terms and the constant terms:

5ab² -5ab -3a²b+3

ab is common to the first three terms above, so

ab(5b - 5 - 3a) + 3

ab(5(b-1) - 3a) + 3

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Do g(2) first:  g(2) = -2*2 - 3 = -7

Put this into f:  f(g(2)) = -(-7) + 4 = 7 + 4 = 11

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Here's a way of doing a) without using L'Hopital's rule:

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Undefined.....To see why, note that the sin^-1 (5/4) is asking us to find an angle where the sine is equal to 5/4...but the sine is never greater than 1. So.....we're really being asked to find the sine of an angle that doesn't exist !!!!

If believe you're asking to find the value of the inverse when 21 is substitued into it.... we can do so thusly.....

6(x + 2) - 3= 21      add 3 to both sides

6x + 12 = 24           subtract 12 from both sides

6x = 12                   divide by 6 on both sides

x = 2

Thus (2, 21) is a point on the graph of the original function and (21, 2) is a point on the graph of the inverse.

I can't see any functions......???

Given that f(x) = x2 + 3x + 6 and g(x) = the quantity of x minus three, over two, solve for f(g(x)) when x = 1.

We want to evaluate f(g(1))

So g(x) = (x - 3)/2   and when x =1, g(1) = (1 - 3) /2 = -2/2 = -1

So f(g(1)) = f(-1) = (-1)^2 + 3(-1) + 6 =  1 - 3 + 6 = 4

well with the game host question then for starters i belive they are rigged of all technicallities then they wouldnt keep the money in the box plus you said decided to play a trck so theres no money in the box you picked so thats out of the question so then if youve watched the show alot go for the mllion if not still go for the million if you have nothing to lose so yeah thers my answer

We want to multiply here.......remember......sin(14) is just a number.......and we're just multiplying this number by 10.

no try counting it on your hands 10 finger then 9 so there you go

An equation for the line that passes through the point (4, 5) with a slope of 6 can be found using the point-slope formula:  y - y1  =  m(x - x1).

In this problem, m = 6, x1 = 4, and y1 = 5:

      y - 5  =  6(x - 4)

     y - 5  =  6x - 24

     y  =  6x - 19

If x = 24:

     y  =  6(24) - 19

     y  =  125

We know the adjacent side (1.5) and the hypoteneuse(5)....we can use the cosne inverse to find the angle

So we have

cos-1(1.5 / 5) = about 72.54°      ...... it is safe......

To  make this easier to type, I'm going to replace f(x) with y, to give the equation:

    y  =  x² - 9

To find the inverse, use this two-step process:

Step 1:  interchange x and y:

    x  =  y² - 9

Step 2:  solve for y:

   x + 9  =  y²

    y²  =  x + 9

    y  =  ±√(x + 9)

In theis case, the inverse is not a function.

(1.1*10^3)*(8.6*10^42) = 9.46 x 10⁴⁵

Just type .....6.022 x 10^23

f(x) = [3x + 5]/ 7    first, write f(x) as y...so we have

y = [3x + 5] / 7       we want to get x by itself.....multiply both sides by 7

7y = 3x + 5             subtract 5 from both sides

7y - 5 = 3x              divide both sides by 3

[7y - 5]/ 3  = x        "exchange" x and y  

[7x - 5] /3 = y          for "y,' write f^-1(x)....

[7x - 5] / 3 = f^-1(x)   and that's it !!

Nice answer, Stormegetton......good humor, too !!!

We are solving for x

first off we add 4 to -18 giving us -14 

(If you are confused of how I got this there will be an explanation below*)

now we have -14+X=19

X will be whatever makes that -14 into 19

So we know we can knock out that -14 by adding 14 so far this makes X=14 

making the total on that side 0

but 0 does not equal 19

now all we have to do is add 19 to X (which is 14) to get our final answer:

33

so X=33

lets plug this in

-14+33=19

if we add a negative number to a positive number it's the same as just subtracting

so 33-14=19

Now that we know our answer is correct we can Use that big ol #2 pencil and add that answer in and do the rest! 

May the odds be ever in your favor

also if you were wondering about the -18+4=-14 here is the explanation

If I borrowed 18 bucks from Benedict cumberbatch I would be -18 dollars in debt

if I payed him 4 dollars I would only be 14 dollars in debt 

get it?

if not then just pm me

-18+4+x=9-12    simplify

-14 + x = -3        add14 to both sides

x = 11

(1 + cx) (1 + x)^4

Expanding (1+ x)^4 we have

(1 + 4x + 6x^2 + 4x^3 + x^4)

So  (1 + cx)(1 + 4x + 6x^2 + 4x^3 + x^4) produces two x^3 terms, i.e. 4x^3 and 6cx^3

So

4 + 6c = 22     subtract 4 from both sides

6c = 18           divide both sides by 6

c = 3

Melody, I only know how to do (a) using L'Hospital's   

Taking the derivative of the top and the bottom =

(1/2)(2)/√(2x + 4) = 1/√(2x + 4)

So

lim x → 0   1/√(2x + 4)  = 1/2

For (c)....note that     -1 ≤ sin x^2 ≤ 1    ....and I believe we can do this one like (e) using the Squeeze Theorem