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The question is...

What are the coordinates of the point on the graph of  f(x)  where the slope of f(x)  =  -3  ?

the slope of f(x) at any  x  value  =  f'(x)  =  -2x + 3

What  x  value makes the slope of f(x) be  -3  ?

What  x  value makes  f'(x)  be  -3 ?

f'(x)  =  -3

-2x + 3  =  -3

-2x  =  -6

x  =  3

When  x = 3 ,  the slope of f(x)  =  -3

When  x = 3 ,  f(x)  =   f(3)  =  2

So at the point  (3, 2) , the slope of  f(x)  is  -3 .

Thank you!!

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YOU GOT IT!.

The imaginary part is the one with the ' i '  in it   (as in i maginary)

Not quite right !!

y =1,200 x (1 + 2%)^x

y =1,200 x  1.02^x - this is the correct way of writing it.

\(h=\sqrt{\frac{g^2}{d}-5t}-1\)

                                          Add  1  to both sides of the equation.

\(h+1=\sqrt{\frac{g^2}{d}-5t}\)

                                          Square both sides of the equation.

\((h+1)^2=\frac{g^2}{d}-5t\)

                                          Add  5t  to both sides.

\((h+1)^2+5t=\frac{g^2}{d}\)

                                                Multiply both sides by  d .

\(d[(h+1)^2+5t]=g^2\)

                                                Take the ± square root of both sides.

\(±\sqrt{d[(h+1)^2+5t]}=g \\~\\ g=±\sqrt{d[(h+1)^2+5t]}\)

Power Property of Logs

Product Property of Logs

Equality  Property of Logs

2log(x) =log(x^2)

-log(y) = The minus sign means that you can divide it by first log(x^2)

-2log(z) =log(z^2), and the minus sign again means you can divide it by the first log(x^2)

So, the whole thing can be written like this:

Log(x^2) / [log(y)*log(z^2)], OR:

Log [x^2 / yz^2] - Or the first one on your list.

1403 IS rounded to the nearest foot...it was something like 1402.83

P(x)  is the population of rabits at any point in any year. To get the population after  3  years, calculate  P(3). To get the population halfway through the third year, calculate  P(3.5) .

P'(x)  is the instantaneous rate of change in population per change in year. For example...

P'(11) = -4  means that after  11  years, the population was increasing by  -4  per  1 year....in other words....the population was decreasing by  4  per year.

These are alwas a little difficult

-4y^2 + 3xy - 12y + 9x            factor by grouping

y ( -4y + 3x)  + 3 (-4x + 3x)

Take out the commmon factor and then write the rest in parentheses

(-4y + 3x) ( y + 3)   =

(3x - 4y) ( y + 3)

We have a 30-60-90  right triangle

The side across from the 30° angle  = 5   cm  =  the base of the triangle

The side across from the 60° angle  is   √3   times this  =  5 √3  cm = height of the triangle

So.....the area is    (base) (height)  / 2  =

(5) * (5 √3)  /  2  =

(25/2) √3    cm^2    .....  this is exact  !!!

100 - 4 = 96

Since 6 = 2 x 3 and 96/6 = 16, therefore:

96 - 16 = 80 numbers that should have prime factors of 5 and greater.

Remember that the bisected apex angle  sets up the following relationship

x / 4   =  2.25 / 3       cross-multiply

3x  =  4 * 2.25

3x  =  9     divide both sides by 3

x  =  3

The second one is similar

x + 8           2x - 5 

____     =   _____           cross-multiply

  10               14

14 ( x + 8)  =  10 (2x - 5)      simplify

14x + 112  =  20x  - 50     add/subtract  50, 14x  to/from  both sides

6x  =  162        divide both sides by 6

x  =  27

so do I put the answer as 1400 or 1403 when its rounded to the nearest foot?

2x^2   + 8x  + 14   =  0        divide through by 2

x^2  + 4x  +  7   =  0        subtract 7 ffrom both sides

x^2  +  4x  =  -  7         complete the square on x

x^2  + 4x  + 4  =  - 7  + 4

(x + 2)^2  =  - 3       take the root of both sides

x + 2  =   ±√-3

x + 2  =  ±√3 i

x  =  -2  ±√3 i  ⇒  First answer

x^2 + x  - 12    factors  as   (x + 4) ( x - 3)

3x^2 + 11x  - 4 factors as  ( 3x - 1) (x + 4)

x^2 - 4  =  (x + 2) (x - 2)

So we have

   (x + 4) ( x - 3)

  ___________

     (x - 2)

_______________         =

   (3x - 1) ( x + 4)

  ____________

   (x + 2) ( x - 2)   

(x + 4) ( x - 3)           (x + 2) ( x - 2)

____________    *   ____________       =

      (x - 2)                 (3x - 1) (  x + 4)

(x + 4) ( x - 3) ( x + 2) ( x - 2)

______________________    =

   (x - 2) ( 3x - 1) ( x + 4)

(x - 3) ( x + 2)

___________     =

     3x - 1

x^2 - x - 6

________

    3x - 1

Find the short side by  tan 53 = opp/ adj = 400/x = 1.327   x= short side = 301.42

TWO short sides  + TWO long sides = perimeter = 1403 ft

First book can be any of 3

next book can only be 1 of 2    (so as not to match

next book can only be 1 of 2

......

3 * 2^7 =  384        my guess   !   

We have 9   ways to fill the first position  (1-9), 9 ways to fill the second position (every number 0-9 except the first one we chose) and 8 ways to fill the third position (every number 0-9 except the first two we chose)  =  9 * 9 * 8    =  648

5, 7

10, 11, 13, 14, 15, 17, 19

20, 21, 22, 23, 25, 26, 28, 29

30, 31, 33, 34, 35, 37, 38, 39

40, 41, 42, 43, 44, 45, 46, 47, 49

50, 51, 52, 53, 55, 56, 57, 58, 59

60, 61, 62, 63, 65, 66, 67, 68, 69

70, 71, 73, 74, 75, 76, 77, 78, 78

80, 82, 83, 84, 85, 86, 87, 88, 89

90, 91, 92, 93, 94, 95, 97, 98, 99, 100

I'll let you count them

I haven't done this yet :| 

However, symbolab.com will solve something like this for you and show its steps. It's very useful. 

rectangular solid area =2[LW + LH + WH]

=2[6*4 + 6*2 + 4*2]

=2[24 + 12 + 8 ]

=2 x [ 44 ]

= 88  Square Units.

No EP!!. The computer did!!.