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yea, and my name is Abi!

Trick question

15x + 3y   =  6     divide through by  3

5x  + y   =  2

And

2y  = -10x  + 4   rearrange as

10x + 2y   = 4    divide  through  by 2

5x + y   = 2

The lines are the same !!!.....the number of "intersection" points is  infinite

True! it's rlly nice and cool your like a friend, my name is katrina . 

Yea CPhill thats really impressive that you know all this!

Lol well how do you know these? are you like a secret FBI agent?

When the system shown below is solved graphically, how many ordered pairs will be in the solution set?          15x + 3y = 6    and     2y = -10x + 4 

I'm TOO old  !!!!

Wow CPhill your really smart. How old r u to be knowing all of these? I'm only 11

Rearrange  as

-8x + 5y  =  8

8x + 7y =  16

This works out  nice and neat....add the two equations

12y = 24     divide  both sides by 12

y  =24/12    = 2

And using  either equation

8x + 7(2)  =16

8x  + 14   = 16

8x  =  16 - 14

8x  =  2

x =  2/8    =  1/4

The intersection is   ( 1/4, 2 )

Let's see...we need  two integers that  multiply to 2   =  1, 2

And  2 two integers that multiply to 6  =  1, 6  or  3,2

Every term is positive...so no negatives  will apply

So....let's try

(2x + 3) ( x + 2)       hey ....got  it  on the  first try  !!!

Proof

2x*x + 2x*2  + 3*x  + 3*2  =

2x^2 + 4x + 3x + 6  =

2x^2  + 7x + 6  =     just what we started with  !!!

No man....you pointed my stupid  "addition" error out to me.....the thx is to  you  !!!!

We  have  a problem here

f(3)   =  0      and f (3)  = 28

This is impossible......this would not  be   function because it  does not  pass the vertical line test......but a polynomial is always a  function

Yea sorry, I just saw that you corrected your answer,LOL!

We have a triangle ABC where AB = 17, BC = 18, and AB = 8.  Let M be the midpoint of AB.  What is the length of CM?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

a = 18        b = 8         c = 17

CM = [sqrt(2a² + 2b² - c²)] / 2

CM = 11.034

The roots of the second equation are  5/6 +- sqrt (109)/6    via Quadratic Formula

    add 2 to each of these roots to get

         17/6 +- sqrt(109) /6

multiply them together to get c    289/36 - 109/36 = 180/36 = 5

I'm pretty sure that it's correct....LOL!!!!

Wow, well CPhill even if its wrong that's still really cool that you know how to do that!

Thank you !

Duh!!!!   on me.......just a sign error....

Should be

(-7/3) + 10/3  + 4  =

1  +  4   = 

5

Now we agree  !!!....thx for the  correction  !!!

Area ABC  = (1/2) BC * AD

200  = (1/2) 15 * AD

400  = 15 * AD

400 / 15  = AD

80/3  = AD

See the following  image :

Since  AB is parallel to DE.....triangle  EDC   is  similar to triangle ABC

And  DC  and   BC   are corresponding  sides

Sinc AB = AC....then AD  bisects BC...so

DC =(1/2) BC

So the scale factor  of  EDC to ABC  = 1/2

So the area  of  EDC to ABC =  (scale factor)^2  (area of ABC ) =  (1/4) (200)   = 50 = [EDC ]

So   [ ABDE  ]  =  [ ABC ] - [EDC ] =   200  - 50   =   150

We have triangle ABC where AB = AC and AD is an altitude.  Meanwhile, E is a point on AC such that AB is parallel to  DE.  If BC = 15 and the area of triangle ABC is 200, what is the area of ABDE?

[ABDE] = 3/4[ABC]  

https://web2.0calc.com/questions/in-triangle-abc-ab-5-ac-6-and-bc-7-circles-are-drawn

Oh my gosh, CPhill! I'm a huge fan! I hate to say this, but that answer was wrong, the correct answer is 5. When I put it in it said (-7/3)+2(5/3)+4=5.