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Thanks, it seems I took the derivative wrong.

1)   \(\frac{x}{6}=6\)

\(6\times\frac{x}{6}=6\times6\)

\(\frac{6x}{6}=6\times6\)

\(1x=6\times6\)

\(x=6\times6\)

\(x=36\)

2)  \(\frac{x}{-3}=1\)

\(-3\times\frac{x}{-3}=1\times-3\)

\(\frac{-3x}{-3}=1\times-3\)

\(1x=1\times-3\)

\(x=1\times-3\)

\(x=-3\)

3)  \(2x+6=28\)

\(2x+6-6=28-6\)

\(2x+0=28-6\)

\(2x=28-6\)

\(2x=22\)

\(\frac{2x}{2}=\frac{22}{2}\)

\(1x=\frac{22}{2}\)

\(x=\frac{22}{2}\)

\(x=11\)

4)  \(-6x-5=-59\)

\(-6x-5+5=-59+5\)

\(-6x-0=-59+5\)

\(-6x=-59+5\)

\(-6x=-54\)

\(\frac{-6x}{-6}=\frac{-54}{-6}\)

\(1x=\frac{-54}{-6}\)

\(x=\frac{-54}{-6}\)

\(x=9\)

5)  \(7=6x-4x-1\)

\(7=2x-1\)

\(7+1=2x-1+1\)

\(7+1=2x-0\)

\(7+1=2x\)

\(8=2x\)

\(\frac{8}{2}=\frac{2x}{2}\)

\(\frac{8}{2}=1x\)

\(\frac{8}{2}=x\)

\(4=x\)

\(x=4\)

6)  \(-5-7x-5x=-113\)

\(-5-12x=-113\)

\(-5-12x+5=-113+5\)

\(0-12x=-113+5\)

\(-12x=-113+5\)

\(-12x=-108\)

\(\frac{-12x}{-12}=\frac{-108}{-12}\)

\(1x=\frac{-108}{-12}\)

\(x=\frac{-108}{-12}\)

\(x=9\)

7)  \(6+4x=5x=14\)

Not an Equation

8)  \(-7+x=-9\)

\(-7+x+7=-9\)

\(0+x=-9\)

\(x=-9\)

9)  \(6+x=-6\)

\(6+x-6=-6-6\)

\(0+x=-6-6\)

\(x=-6-6\)

\(x=-12\)

10)  \(3x+6=-18\)

\(3x+6-6=-18-6\)

\(3x+0=-18-6\)

\(3x=-18-6\)

\(3x=-24\)

\(\frac{3x}{3}=\frac{-24}{3}\)

\(1x=\frac{-24}{3}\)

\(x=\frac{-24}{3}\)

\(x=-8\)

11)  \(6x+5=53\)

\(6x+5-5=53-5\)

\(6x+0=53-5\)

\(6x=53-5\)

\(6x=48\)

\(\frac{6x}{6}=\frac{48}{6}\)

\(1x=\frac{48}{6}\)

\(x=\frac{48}{6}\)

\(x=8\)

12)  \(4+x+4x=54\)

\(4+5x=54\)

\(4+5x-4=54-4\)

\(0+5x=54-4\)

\(5x=54-4\)

\(5x=50\)

\(\frac{5x}{5}=\frac{50}{5}\)

\(1x=\frac{50}{5}\)

\(x=\frac{50}{5}\)

\(x=10\)

13)  \(4x+7-5x=-1\)

\(-1x+7=-1\)

\(-x+7=-1\)

\(-x+7-7=-1-7\)

\(-x+0=-1-7\)

\(-x=-1-7\)

\(-x=-8\)

\(-x\times-1=-8\times-1\)  or \(\frac{-x}{-1}=\frac{-8}{-1}\)

\(x=8\)

14)  \(5+3x=2x+18\)

\(5+3x-2x=2x-2x+18\)

\(5+x=2x-2x+18\)

\(5+x=0+18\)

\(5+x=18\)

\(5+x-5=18-5\)

\(0+x=18-5\)

\(x=18-5\)

\(x=13\)

Evaluate the following limit: lim h→0 ((3+h)^3−27)/h

\(\displaystyle\lim_{h \rightarrow 0}\;\frac{(3+h)^3-27}{h}\\~\\ =\displaystyle\lim_{h \rightarrow 0}\;\frac{(3+h)^3-3^3}{h}\qquad note:\;a^3-b^3=(a-b)(a^2+ab+b^2)\\~\\ =\displaystyle\lim_{h \rightarrow 0}\;\frac{((3+h)-3)((3+h)^2+(3+h)*3+3^2)}{h}\\~\\ =\displaystyle\lim_{h \rightarrow 0}\;\frac{h[(3+h)^2+3(3+h)+9]}{h}\\~\\ =\displaystyle\lim_{h \rightarrow 0}\;\:(3+h)^2+3(3+h)+9\\~\\ =9+9+9\\~\\ =27 \)

Find the following limit:
lim_(h->0) ((h+3)^3-27)/h

((h+3)^3-27)/h = h^2+9 h+27:
lim_(h->0) (h^2+9 h+27)

lim_(h->0) (h^2+9 h+27) = 27+9 0+0^2 = 27:
Answer: |27

I'm not sure how the proper way to do it in school is, but for unfamiliar decimals like 0.108 you can turn it into fraction actually pretty easily. Since the decimals go out to the thousandths place, that means that your denominator is 1000 and the 3 digits are your numerator.

So 108/1000 is the fraction form. This can then by reduced to 27/250

When we learned how to convert fractions to decimals in school, we used long division, but I don't know what you guys use now.

The position of a particle is given by x(t) = (t2 - 4)3 where x(t) is measured in centimeters and t is measured in seconds.

\(x(t)=(t^2-4)^3\)

Find where the particle is moving to the left.

velocity is negtive

\(x(t)=(t^2-4)^3\\ x'(t)=3(t^2-4)^2*2t\\ x'(t)=6t(t^2-4)^2\\ \)

Since t cannot be negative, velocity can never be negative.  

Nothing was here, stop stalking my profile.

3 x 4 = 12

Well im just going to guess that you need to plug it in, if thats the case heres the work:

y-(-5)= 1/2(x-4)+ 3

y-(-5)= 1/2(-5-4)+ 3

y-(-5)= 1/2(-9)+ 3

y-(-5)= -4.5+ 3

y-(-5)= -1.5

then your point would be (-5,-1.5) 

or 1 $10 bill, 2 $1 bill, 1 $.25, and 1 $.05

(1/3)(2x - 7)  =  4

Get rid of the  1/3  by multiplying both sides by 3:

     3 · (1/3)(2x - 7)  =  3 · 4

                     2x - 7  =  12

Add 7 to both sides:

                           2x  =  19

Divide both sides by 2:

                             x  =  9.5

What do you need to do with that equation?

18 from -20:

     -20 - 18  =  -38

Using the formula:  d  =  r · t:

Let the rate of the slower car be  x

Then the rate of the faster car is  1.5x

Since each car travels for  4.5  hours:

the distance that the slower car travelled is  4.5 · x

the distance that the faster car travelled is  4.5 · 1.5 x  =  6.75x

The total distance that they travelled was  405  miles:

   4.5x + 6.75x  =  405

              11.25x  =  405

                       x  =  405 / 11.25  =  36

Therefore, the slower car travelled at the rate of  36  miles per hour

and the faster car travelled at the rate of  1.5 · 36  =  54  miles per hour.

you want to change it to 1/2 times 2/1 which is 2/2 = 1

So to express that numerically would be:

-4/5 / 4

The easiest way to divide fractions is to multiply by the recipricol of the number which is being divided.

The recipricol is simply the fraction flipped upside down.

So for 4 (= 4/1), the recipricol is simply 1/4:

-4/5 * 1/4

Then the top and bottom of both fractions can be performed:

(-4*1) / (5*4)

The fours on the top and bottom can cancel out, leaving us with:

-1/5.

9 1/2% = 9.5%

To do this problem, turn the percentage into a decimal. This is done by dividing the percentage by 100 (since 100% is 1 in decimal notation).

So:

9.5% = 0.095

0.095 * 50 = 4.75

I'm not quite sure what you're referring to.
 

The only possible multiplication in the midpoint formula is perhaps multiplication of the two x's and two y's respectively by 1/2.

If that's what you're referring to, it's important because it averages the two numbers.

15?! Geez, you'll be up there with the dino's soon Rose! Nice to see you again, and happy birthday!

No, the cashier gave him back too much money in change....she gave him 12.30

12.30 + 38.70 = 51   not 50 dollars     she should have given him a 10 dollar bill ONE one dollar bill and 3 dimes for 11.30

"Rate of change" is really only relevant when looking at change over a period of time.

You can find the amount of change given those values: it's just the difference between them.

First, convert  88.2 km/hr to m/s

88.2 km/hr x 1 hr/3600 s  x 1000m/1km = 24.5 m/s

Then vf = vo + at     vf= 0 (car comes to a stop)  vo = 24.5     a = -300m/s^2

0 = 24.5 + (-300)t    yields t = .081667 s

xf=xo + vot + 1/2 at^2

xf =  24.5 (.081667) + 1/2(-300)(.081667)^2      yields  xf = 1.00 m    (minumum barrier thickness)

0.5 / -5 * 50

0.5 / -5 is the same thing as -5/50 (multiplying by -5/50)

-5/50 * 50

-5*50/50

50's on the top and bottom cancel out, leaving us with -5.

-5*50/50 = -5