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3 ( x^2- 8/3x)         + 7          complet the square on 'x'

3 (x - 8/6)^2           + 7 - 3* 64/36

3 ( x- 4/3)^2         +  1 2/3                          Now you can add   a  d  e 

Wow that was much simplier than I thought! 

Thank you so much!!!

Multiply the magnitudes and add the angles

z1z2   will still be in Q1 when you add the angles

z1z3    will be in Q2

z1z4                    Q3

You try the rest....

Hi there! I have figured out the answer but dont really know how to put it into words... 

lets try though!

So we know that \(|x-3|\) will have to be positive because of the absolute value. 

and if we expand out the radical \(\sqrt{x^2-9}\) we get\(\sqrt{(x-3)(x+3)}\)

Now that we have this we can subtract \(|x-3| \) from the left side. This means that our new equation is

\(\sqrt{(x-3)(x+3)}=-|x-3|\)

note: because of the absloute value we can get rid of the negitive

Because there is a radical we can square both sides to get

\((x-3)(x+3)=|x-3|^2\)

We have to disbtrube the left side so

\(x^2+3^2=(x-3)^2\)

simpify \(3^2=9\) you can solve from there!

also this might not be the best way to solve a question like this because it is my personal way aswell the way I learned it.

Hope this helps

~Wolf :D

For simplicity,  assume the triangles are side length of 1

  Line AD is TWO of the equilateral triangles heights    BC is just one of the side lengths = 1

Formula for height of equlateral triangle:  sqrt 3/2  * side length = sqrt3/2 *1 = sqrt3/2

    but you  have two of these  so 2 * sqrt3/2 = sqrt 3

Now ratio oa AD to BC  is    sqrt 3 / 1 = sqrt 3

Maximum value will occur at x = - b/2a           b = -8    a = -1

    use this value of 'x' in the equation to calculate the maximum value (y)

This graph should help you answer the question:

I am sorry it was incorect..

You wallet contains 39 coins , consisting entirely of nickels and dimes , worth a total of $2.55. How many nickels are in the jar 

Is this a gotcha trick question?  You say 39 coins in my wallet, then ask how many nickels in a jar.  This is impossible to tell from the facts that are provided.  It reminds me of the question:  if an airplane crashes exactly on the border between Texas and Oklahoma, in which state would the survivors be buried?  Well, of course you don't bury survivors.  And I don't know how many nickels are in the jar.   

_.

romb - a = 6 , corners = 30 , 150 , diagonals - ?           t.me/Javohir_06  

I'm having a bit of a problem understanding the problem.  Are you trying to say something like: 

How long are the diagonals of a rhombus that has sides 6 units long and angles 30^o and 150^o ? 

_.

Sorry, but it says that its wrong.

Probability of selecting all males: pm = (8/16)*(7/15)*(6/14)*(5/13) = 1/26

Similarly, probability of choosing all females: pf = 1/26

Hence probability of not having all males or all females (i.e. at least one male/female pair): p = 1 - pm - pf = 12/13

I did not notice the word distinct.    (So I accept my answer was wrong)

My answer assumed that the trucks were all the same. 

B makes a 60 out of 360^o   cicular area of radius 6

60/360  x   pi  6^2    add to this the shaded semicirle area  then subtract the unshaded semi circle area and you are left with

60/360  x  pi   x  6^2   units^2 

Using the quadratic equation, the two solutions to 4x^2+7x-1=0 are \(\frac{-7+\sqrt{65}}{8}\ \text{and} \frac{-7-\sqrt{65}}{8}\). I think you can solve the rest from there.

n = nickels                 value      5n

d = dimes = 39 - n      value    10(39-n)              summed = 255

5n + 10(39-n) = 255

-5n  = -135

n=27  

1.2n-4.4<5.2      add 4.4 to both sides

1.2n < 9.6     divide both sides by 1.2

n < 8             

       7+6 + 5 +4 +3 + 2+1 = .........

rate x time = d

rates    x   and x+1       time     t1   and  t1-1/2        (1/2 hr = 30 minutes)

x(t1) = 45   or    t1 = 45/x

and

  (x+1)(t1-1/2) = 45

   (x+1)(45/x-1/2) = 45

    45 -1/2x + 45/x-1/2 = 45

     -1/2x + 45/x -1/2 = 0

-1/2x^2 -1/2x +45 = 0                 x = 9 km/hr from Quadratic formula    then t1 = 45/9 =5 hr     x+1 = 10 km/hr

PV = sqrt(6).

There are 354 ways to divide the group.

Pete = x

Alan rate = x-5

together  rate   x -5 -4 = x-9

1/x  + 1/(x-5) = 1/(x-9)                      solve for x  pete's rate

x-5 + x   = (x-5)(x)/(x-9)

(2x-5)(x-9) = x^2-5x

2x^2 -18x- 5x+45-x^2+5x = 0

x^2 -18x +45 = 0                                        x = 15 days       alan  10 days     together  6 days 

look for perfect squares less than 54     49   36   25   16  9   4   1  0

   subtract them from 54 to see if any results in a perfect square

54-49 = 5     so if sqrt x = 5     would be one  x = 25

54-36=18             sqrtx=18                              x = 324

            29                                                               841

            38                                                               1444

            45                                                              2025

            50                                                              2500    

            53                                                              2809      

            54                                                               2916         eight values of x

Because she will get 1.5 points for each question left unanswered and she leaves 3 questions unanswered,

she will receive 3 x 1.5 points  =  4.5 points.

To get at least 100 points, she will need 100 - 4.5 points  =  95.5 points on the first 22 questions.

Since she gets 6 points for each correct answer, she will need 95.5 / 6  =  15.92 correct answers --->

she will need 16 correct answers.

16 x 6  =  96 points + 4.5 points  =  100.5 points.

f(x)  =  ln(2x + 5)

                                       y  =  ln(2x + 5)

Interchange x and y:       x  =  ln(2y + 5)

solve for y:                     e^x  =  2y + 5

                                  e^x - 5  =  2y

                           (e^x - 5) / 2  =  y

                                    g(x)  =  (e^x - 5) / 2

                                    g(4)  =  (e⁴ - 5) / 2

Now, it's calculator time!

Solve for x over the real numbers:

1-3 x==-2 (x+3):
1-3 x==2 (x+3) or 1-3 x==-2 (x+3)

Expand out terms of the right hand side:
1-3 x==2 x+6 or 1-3 x==-2 (x+3)

Subtract 2 x+1 from both sides:
-5 x==5 or 1-3 x==-2 (x+3)

Divide both sides by -5:
x==-1 or 1-3 x==-2 (x+3)

Expand out terms of the right hand side:
x==-1 or 1-3 x==-2 x-6

Subtract 1-2 x from both sides:
x==-1 or -x==-7

Multiply both sides by -1:
x==-1     or     x==7