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ok i prove it below! 

\(AD=AB + BD \)

so  \(AB = 30 - 20 =10 \)

and \(AB = AC + CD \)

so \(CD = 30 - 16 = 14 \)

Finally \(AD = AB + BC + CD \)

so \(BC = 30 - 10 - 14 = 6 \)

so \(BC = 6\)

IM SORRY it is G  lol..

I think anwer is G. 6 units long

That's what I got, thanks ^-^

The directrix is  above the vertex, so this parabola turns downward

The form is

-4p [ y - k ] = [x - h]^2

(h, k)  is the vertex = (-4, -6 )     

And p is the distance between the vertex  and the directrix  given by 3 -  k  = 3 - (-6)  = 9

So we have

-4(9) [ y - (-6) ]  = [ x -  (-4) ] ^2

-36 [ y +  6]  = [ x + 4 ] ^2      divide both sides by -36

y  + 6  =  -(1/36) (x + 4)^2

y  = -(1/36) ( x + 4)^2  - 6

Was just a bit too slow before CPhill got the same answer!.

We have 9 "whole" cars and 2 "half "  cars....but 2 "halves" gives us another whole one

So...we have 10 whole cars

And Coupeville manufactures 2 + 1/2 0f them  = 2.5

So....the fraction  made in Coupeville   =  2.5  / 10    =  1/4    ⇒   B

thx sooooooo much

\(\forall -\dfrac 2 3 \leq x, ~\min\left(2x+2,~\dfrac 1 2 x + 1, ~\dfrac 3 4 x + 7\right) = \dfrac x 2 + 1 \\ \forall x < -\dfrac 2 3, ~\min\left(2x+2,~\dfrac 1 2 x + 1, ~\dfrac 3 4 x + 7\right) = 2x+2 \\ x \to \infty \Rightarrow \dfrac x 2 + 1 \to \infty \\ \text{and thus the Min of these three functions is unbounded.}\\ \text{One might say it's maximum values is }\infty \\ \text{but it's probably better to just say it has no maximum value}\)

I know I'm asking how you are but it wants a description so I just put my name 

Thank you! My teacher did not explain how to solve these types of questions so I've been having a difficult time. Appreciate the help!

These aren't that hard to identify......

We  have the form

a (b)^x

When   "b"  >  0   but  <  1.....we have decay

When "b"  > 1     ...we have  growth

[The "a"  doesn't  matter  ]

So.....in the first part

h(x)   = (0.2)^x     and    f(x)  = 4(0.3)^x      are decay functions

And...in the second part

h(x)  = (1.9)^x   and   d(x)  = 2(4.7)^x     are growth  functions

Thank you so much for your help! Have a wonderful day/night!

I believe the last answer is correct...if we remove the outliers  [ lowest and highest data values] the median is not affected

Example

16   20   22   23   24  27   55      median  is   23

20  22  23   24   27       median is still 23 

f(x)   = -x^2 -2x + 8

This is a parabola  that turns "downward"  because thw leading coefficient is negative

To find the x coordinate of the vertex...

In the form    ax^2  + bx  + c

The x coordinate of the vertex is    -b / [ 2a ]

So....in our function,  b = (-2)   and  a = (-1)

So...  -b / [ 2a]  = 2 / [ 2 * -1 ]   =  2 / -2   = -1

To find the associated y value for the function....put  -1  back into it and evaluate

- (-1)^2  -2(-1) + 8 =  -1 + 2 + 8  = 9

So...(-1,9)  is the "high point"  of the function

So....this function will increase  from  (-infinity, to -1)

To find out where it tis positive on this interval...we can  find the  root on this side  [ where it crosses the x axis]

So...we want to solve

-x^2 - 2x  + 8  =0   multiply through by -1

x^2 + 2x  - 8  =  0     factor

(x + 4) (x - 2)  =0

Set each factor to 0  and solve for x and we get   x = - 4   or  x  = 2

So....this tells us that the function is positive and increasing from  

-4 < x  <  -1    ⇒   B

Here is the graph :  https://www.desmos.com/calculator/lmmko24qwo

is it C???

78-78%=00%

So I have 00% Percentage Of Twitter Followers 

Is this what your questions means: 1/a + 1/(2*a) + 1/(3*a)=1/(b^2) - (2*b) ????

Mmm that should be a concern to you.

Substitute x=-3 and y=2 into the equation and see if the left side is equal to the right side.

If it is then (-3,2) satisfies the equation which means (-3,2) lies on the circle.

1) Now you can do that bit by yourself.

2) Now you need to know the centre of the circle. (look up the equation of a circle and see if you can work that out yourself)

3)Find the gradient of the line joining the centre to the point P

4)The tangent will be at right angles to this radius so what is its gradient?

5) Now you have a gradient and a point on the tangent so you can find the equation of this line.

Yes I do actually lol

I will assume that you mean

f(x) = sin3xcosx/(tan2x+1)    this has no global maximum   (ref: Wolframalpha)

so maybe you mean  

f(x) = (sin3xcosx/tan2x)+1       (yes I know this is how it should be interpreted bum a loy of people make mistakes here)

I spent ages working on the first interpretation,  I haven't got the energy to look at this second one at present but Wolfram Alpha says the maximum is  2.5

No 

Thank you Chris

Thank you again, Chris