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Step 1)  Find the slope of the given equation ... I'm having trouble reading your question, is it 2/3rds?

Step 2)  Find the negative reciprocal of the answer to step 1) ... -3/2  ... because perpendicular lines

              have slopes that are negative reciprocals.

Step 3)  Use the point intercept form for a line to find the needed equation.

               y - y1  =  m(x - x1)     --->     y - 8  =  -3/2(x - -1)

Step 4)  Simplify the equation from step 3) and solve for y.

there are  4 J + 4 Q + 4 K + 4 A   = 16 out of 52       16/52 = 4/13

Equation of the line passing through \(P_1(8,9)\ and\ P_2(-2,-7)\).

Hello Guest!

\(m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-7-9}{-2-8}\\ \color{blue}m=1.6\)

\(f(x)=m(x-x_1)+y_1\)

\(f(x)=1.6(x-8)+9\\ \color{blue}f(x)=1.6x-3.8\)

  !

\( \)

thanks for showing me what you have done.

Your graph looks interesting but I can't say more.

My memory of complex numbers is rudimentary at best. 

thanks melody! this problem was pretty hard

Yes that is right.

You have, or can have   (x+y+z) four times.  Put them altogether.   

example

if I have   6(x+3)+m(x+3)

then I have 6 lots of x+3 and I add m lots of x+3   I end up with  6+m lots of x+3

so

6(x+3)+m(x+3) = (6+m) (x+3)

LCM(123450, 987650)=2438507850

GCD(123450, 987650)==50

four

There are 10080 possible seatings.

There are 236 ways to arrange the books.

if you want to square 

     sqrt ( 160 - 64 sqrt 3)     you will get        160 - 64 sqrt 3       

n==5 , 12 , 19 , 26 , 33 , 40 , 47 , 54 

The probability of being within one unit of the origin is the area within a circle centered at the origin with

a radius of 1 divided by the area of a square with side lengths of 2.

The area of the circle is:  pi · r²  =  pi · 1²  =  pi.

The area of the square is  2 · 2  =  4

The probability is  pi / 4

3^ (2^ (1000)) mod 10^10 ==[1565649921] + 1==1565649922 - the last digit is 2

58^100 mod 10^10==6,358,757,376

Sum==3 + 7 + 6 ==16

3^a = 2          3^b = 5          --->     3^a · 3^b  =  2 · 5         --->     3^{a + b}  =  10

3^x  =  150  =  15 · 10          --->     3^x  =  15 · 3^{a + b}

Since  15  =  3^{log(15) / log(3)}          --->     3^x  =  3^{log(15) / log(3)} · 3^{a + b}

--->     x  =  [ log(15) / log(3) ] + a + b

 One of the dimensions is too large    35 cm is bigger than   32.5 cm    so you have to use the larger shipping size (26 x 38.5) price   5.20

Melody I tried graphing it on desmos, if you would like to play around with it

(2x + 1/2 - 1/3)⁶  =  (2x + 1/6)⁶

The expansion is:  1·(2x)⁶·(1/6)⁰  +  6·(2x)⁵·(1/6)¹  +  15·(2x)⁴·(1/6)²  + ...

The term of interest is:  15·(2x)⁴·(1/6)² 

Simplify this term to get the answer.

why is it 5.20 for the 3rd?
dont we get the average since it starts from 26?
i mean ----> (3.40+5.20)/2

SO would that simplify to \(p(x+y+z)+q(x+y+z)+r(x+y+z)=1+x+y+z\)

The first one costs       $1.90

The second one costs $2.90

The third one costs      $5.20

You need to solve this equation:  x + 6  =  x · 6

--->   x + 6  =  6x   --->   6  =  5x   --->   x  =  1.2

In the right triangle ABC, angle B is 90 degrees. If tan C = 2. Find cos A. No calculator.

tanC = 2/1 = 2

cosA = 2 / √5 = 0.894427191

Since  tan(C) = 2     --->     AB = 2  and  BC = 1     (or multiples of these numbers)

Using  AB = 2  and  BC = 1  and the Pythagorean Theorem,  AC  =  sqrt(5).

Therefore,  cos(A)  =  2 / sqrt(5)