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You have 2 integers that work:

CAT = 135 = [1+ 3+ 5]* 1 * 3 * 5 =135

CAT = 144 = [1 + 4+ 4]*1 * 4* 4 = 144

Nothing wrong with your method, EP......just shows another way to solve it

This is always good   !!!!

3.     (x^(4)+4x^(2)-6x-24)-(x+4)

Simplify  and we have     x^4 -4x^2  -7x - 28

WolframAlpha  shows that we have no rational roots for this  : 

https://www.wolframalpha.com/input/?i=%28x%5E4%2B4x%5E2-+6x+-+24%29+-+%28x%2B4%29

Are you sure that you have the correct function  ????

And now I'm at 29 ¯\_(ツ)_/¯

im honestly so confused

Ugh.... this easier method escaped my thought !  Thanx !   ~EP

We can break into cases:

111 - 1 number
11* - 10 numbers
1*1 - 10 numbers
*11 - 10 numbers
*1* - 100 numbers

This gives us a total of 131 memorable numbers.

Yah, I saw that in the previous post, but I thoght I would post reasoning for the answer.....maybe soemone will show us the correct way to get the correct answer (if indeed this answer is incorrect ! )

-12(x - 5)  =  (y + 2)^2

Vertex  =  ( 5, -2)

Opens to the left

4p = -12

p = -3

The   focus  is   l p l  =   l -3 l  =   3 units from the vertex

The directrix  is   2 l p l  =  2 l - 3 l  =  2(3)   =   6 units from the focus

Focus  =  (5 + 3 , - 2)  =  (5 - 3, 2)   =   (2, -2)

The equation of the directrix  is    x  = (5 + 3)   ⇒     x  =   8

Can you do number three again, forgot to put the equation for it in.

somehow posted as a guest and in my account, glitch i guess?

No equation is shown in 1    and no expression is shown in 3.....

You already posted this... https://web2.0calc.com/questions/algebra_11688

You already posted this... https://web2.0calc.com/questions/algebra_11688

Yeah, that's what I thought too, but it's incorect.

(-2,0)    and  ( 4,0)

These must be the roots of the quadratic...so we have that

y  = a ( x + 2) ( x - 4)      simplify

y  = a (x^2 - 2x - 8)

And since  54 is a max, then using symmetry, the point  ( [-2 + 4]/2, 54)  = (1,54)  must be on the graph

So

54   =  a ( 1^2 - 2(1) - 8)

54 = a (-9)

a = -54/9  = -6

So.....the function is

y = (-6) ( x^2 -2x  - 8)

y = -6x^2 + 12x  + 48

Here's a graph  :  https://www.desmos.com/calculator/s8dqi0vdcn

Here is my try at this Q:

There are 8 positions where the two girls can stand side by side     and you can reverse their order to have 16 possibilities of positioning 2 girls next to each other....

  Now haow many ways can you choose 2 girls from the 5 on the team?     5 c 2 = 10 ways

10 x 16 = 160 ways of girl placement

there are 7 other positions to fill....how many ways can you fill them ?  

7 x 6 x 5 x 4 x 3 x 2 x1 = 7!  = 5040

5040 x 160 = 806400   possibilities    

Dude I joined like 10 days ago and have less than 50 points, not to mention this is the first post by OP that I've seen, I'm not downvoting anybody

The highlighted box AND the one before it are incorrect....

    read the question....both of those boxes should be UNITS   ..... in other words, they should be numbers (not points or equations)....     Now try it!

I count 10 quadrilaterals

y = mx + b       m is the slope    b is the y-intercept (this happens when x = 0)

Put in the point given

2 = -3/2 (-6) + b       solve for 'b'   for your answer    ...you CAN do it ! 

I count 12 triangles

Here is a confirmation graph:

https://www.desmos.com/calculator/120umkmcim