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\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)  

-x^2 + 4x -5 = 0          a = -1   b = 4   c = -5     plug in to the formula above to find the two values of x       

Given the following functions perform the following operatons :f(x) o. g(x)

Hello Guest!

\(f(x)=5x-4 \) and  \(g(x)=-2x+3\)

\(f(x)=g(x)\\ 5x-4=-2x+3\\ 7x=7\)

\(x=1\)

1.)      \(10x-11=\color{blue} -1\)

2.)   \(-10x-14=\color{blue}-24\)

3.)      \(10x+11\color{blue}=21\)

4.)        \(10x+4\color{blue}=14 \)

  !

what is the answer???

I will asume the double headed horizontal lineas are parallel

  then    x+8     +     6x-58      + 90^o     = 180^o     (straight line)

     now you can solve for 'x'

Let center ( r,3) radius:r

(x-r)^2+(y-3)^2=r^2
plug in (12,0)

(12-r)^2+(-3)^2=r^2
r=45/8

F(1)=10,f(6)=?,f(n)=f(n-1)+3

This is an arithmetic sequence written with recursive form.

d=3, a1=10
an= 10+(n-1)(3)

  =3n+7

f(6)=3(6)+7=25

Angle up by Y    180 - 115 = 65

Angles of triangle = 180           180 = 65 +     4k+5      +      6k+10     Now you should be able to easily solve for k

Imaginary roots come in + -  p airs           the other root is  2 - 3 sqrt5 i

(x - 2 - i 3 sqrt5)(x-2+i 3 sqrt 5 )    Multiply this all out to get:

=  x^2 -4x+49  

You are welcome !

add 2x      and add  1 to both sides of the equation to get

6 < 5x

x> 6/5                      (6/5, + inf)

  23x + 10     -  110    =  5x+8

   solve for 'x'   then   ZJK  =  5x+8

Thanks very much!

x = x_o  + v_o t  + 1/2 a t²         x = 0 ( the ground level)    x_o = original height of the ball 

                                            v_o = original velocity = 0      a = -10 m/s²          t = 5

0 = x_o - 1/2 (10) (5²)

 x_o = 125 m

We have two graphs, one for f(x)=Cos2x and another for g(x)=3Sin2x

for both of them being between 0 - 180 deg.

The question is: Calculate the values for x where f(x) = g(x) if x \(\in \) (0;180)

Hello juriemagic!            Answer 1 # is wrong!

\(f(x)=g(x)\\ cos\ 2x=3sin\ 2x\)

\(u=2x\)

\(cos\ u=3sin\ u\\ cos^2\ u =9(1-cos^2\ u)\\ cos^2\ u=9-9cos^2\\ 10cos^2\ u=9\\ cos\ u=\pm\sqrt{\frac{9}{10}}=\pm \frac{3}{\sqrt{10}}\)

\(u_1=18.435^{\circ}\\ u_2=161.565^{\circ}\)

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

\(x_1=9.217^{\circ}\\ x_2=80.783^{\circ}\)

  !

 b - c = 22.

1. The slope of the bisecting line is 8/7.

2. k = 44.

The answer is vectors d and f.

(4+6)  is to 6     as    HJ  is to 9

10 / 6 = HJ/9

90 = 6 * HJ

HJ = 15

red    20    40   60  80  100  120   140   160  min

blue  35               70          105      140           min

140 min is  2 hr 20 min   

Assuming 12 pm is noon,  tablets will be taken together at  2:20 PM     or    14:20

x+y=2400                           y = 2400-x

3x + 5y = 9000

Substitute the blue equation into the second eqution , solve for x      then you can solve for y by substituting

   this value of x into one of the equations

This will be \(f(x) = (x-2-\sqrt2)(x-2+\sqrt2)(x-3-\sqrt6)(x-3+\sqrt6)\)

I'll leave you to multiply it out to confirm that it does indeed have rational coefficients.

Edit:  corrected signs.  Thanks to EP for making me aware of this.

If I understand your question, then there are:

108  117  126  135  144  153  162  171  180  189  198  207  216  225  234  243  252  261  270  279  288  297  306  315  324  333  342  351  360  369  378  387  396  405  414  423  432  441  450  459  468  477  486  495  504  513  522  531  540  549  558  567  576  585  594  603  612  621  630  639  648  657  666  675  684  693  702  711  720  729  738  747  756  765  774  783  792  801  810  819  828  837  846  855  864  873  882  891  900  909  918  927  936  945  954  963  972  981  990  999  Total =  100 such numbers.

You simply start with a 3-digit number that is divisible by 9. Take the first one of 108. This is divisible by 9 because: 1 + 0 + 8 =9. Then you add this sum of 9 to 108: 108 +9 =117. Then add up the digits of 117 = 1 + 1+ 7 =9. Finally, you add this last 9 to 117: 9 + 117 =126 which is divisible by 9. Or 126 mod 9 =0.

Note: All the  100 numbers above meet your conditions. However, by the time you add their digit up 3 times, many of them will exceed 3 digits: Take 999. 9 + 9 + 9 =27. 27 + 999 =1026: and 1+0+2+6=9: 9 + 1026 =1035.........and so on. Whether, this is acceptable to your Math Teacher, that I don't know.

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....  also ml is a measure of  (liquid) volume

25g / 29.5 ml  =  .8475  g / ml

I THINK:

49 c 5   * 22 =   49! / ( 44! 5!)    * 22 = 41 951 448      so  1 out of 41 951 448