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Fill in the blank with a constant, so that the resulting quadratic is the square of a binomial.  x^2 + 4x + 5x +  ___     

20.25  

The binomial is (x + 4.5)  

(x + 4.5)²  =  x² + 9x + 20.25   

There are four points that are 5 units from the line y=13 and 18 units from the point (7,15). What is the sum of the x and y and coordinates of all four of these points?

Hello Guest!

\(\sqrt{18^2-(x-7)^2}+15=13+5\ |-18\\ \sqrt{18^2-(x-7)^2}-3=0\)

\(x_1=7-3\sqrt{35}\\ \color{blue}x_1=-10.748\\ \color{blue}y_1=18\\ x_2=7+3\sqrt{35}\\ \color{blue}x_2=24.748\\ \color{blue}y_2=18\)

\(-\sqrt{18^2-(x-7)^2}+15=13-5\ |-8\\ -\sqrt{18^2-(x-7)^2}+7=0\)

\(\color{blue}y_3=8\\ x_3=7-5\sqrt{11}\\ \color{blue}x_3=-9.583\\ \color{blue}y_4=8\\ x_4=7+5\sqrt{11}\\ \color{blue}x_4=23.583\\ \)

\(P1\ [-10.748, 18]\)        \(P2\ [24.748, 18]\)

\(P3\ [-9.583, 8]\)            \(P4\ [23.583,8]\)

  !

$8 = 2^3$

$2^4, 2^6, 2^8$

$2^4 \cdot {3^2, 5^2, 7^2}$

$2^6 \cdot {3^2}$

$3+3+1=\boxed{7}$

$k=3$

1     4      9     16     25     36     49     64     81     100     121      144     169      196    225     256    289    324    361     400   441   484   529   576    625

676     729     784      841     900    961       every 4th one.....  count 'em    

x = 10% amount        90-x  = 100% (pure) amount

acid in ingredients     =     acid in final product

.10x    + 1.0(90-x)      = .58(90)            solve for 'x'   the 10% amount   

                                                                       then pure amount to use = 90-x

Put t= 0 into the first equation to caculate  a1      1 + sin 0  = 1

       t =0 into the second equation to calculate a2   3 sin0   = 0

t=7/6   in the first equation to calculate  b1

  t = 7/6 in the second equation to calculate b2      make sure your calculator is in radian mode !

It's a square , so find the perpindicular distance between the two lines

6x-8y + 5 = 0

3x-4y+15 = 0    

Here is a graph with  perpindicular line between the two lines given in the Q  ....calculate the distance between the two shown points to get the side length of the square, s

       then area = s * s

Never mind this equation seems exceedingly obvious unless there's some trick I'm missing. 

$\begin{align*} \sum^{2020}_{n=1} [\frac{1}{n^2} - \frac{1}{(n+1)^2}] = \frac{1}{1} - \frac{1}{4} + \frac{1}{4} - \frac{1}{9} + \frac{1}{9} ... -\frac{1}{2020^2} + \frac{1}{2020^2} - \frac{1}{2021^2} \end{align*} $

Thus, terms cancel and..

$$\begin{align*} 1 - \frac{1}{2021^2} \end{align*} $$

3 * 2ⁿ >100    n is the day number

2^n > 33.33

n = 6      day 6          day1=  6   ,  12 ,   24 ,   48 ,  96  ,   day 5 = 192

But here is a guess

  5000 (1 + .05/2)^6    is the amount in the first account at the end of three years    add this to 5000 to get the "new amount"

      then         "new amount" * (1 +.045/n)^(16n)        is the final amount        

                                                                     where 'n' is the amount of compounding periods per year in the second account

Can you edit your question ?....do not put in dollar signs in the text....it gets latex (or something) converted and unintelligable.....

dx/ dt is the speed of the particle in the x direction = 2

dy/dt is the y direction speed = 3

Use pythagorean theorem to calculate the  resultant  speed     =    sqrt (2^2 + 3^2 ) = sqrt 13

The speed of the particle is 5.

96/5

oh wait i think i explained this wrong ill link you the oringinal post on this.

5xy              -10yz                     - 6xz                   since   x = -4  y = 1   z = -1.5   then

5 (-4)(1)       -10 ( 1)(-1.5)         -6 (-4)(-1.5)

i dont understand how you got that

SInce we know what x y and z supposedly are, we just sub them into the equations to see if true:

Here is the second equation

5 (-4)(1)     -10 ( 1)(-1.5)   -6 (-4)(-1.5)       does this equal -41 ????      do the same for the other two equations to check your answer....

so you just interchange x, y, and z and get the 3 answers?

IF this is true

i figured out that (a,b,c) is (-12,5,9)     then   x = -4   y =1    z = -1.5      sub those into the equations to see if it makes all three of them true...

Thank you for the answer! However, how did you get π/4 for (b)?

Expand and simplify to get

2x^2 + 20x+38 = f(x)

roots ....via quadratic formula are   -5 +-sqrt6         axis if symmetry is x =  -5

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Wait, I got 3 Ep, this is since everyone takes a language. there is 6 more in chinese then spanish. so you do 47+6 to get 53 you then add 53 an 47 to get 100. Then you do 100-97 to get 3