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Here's  my  guess

3 * 11    =   33

2 * 17  =     34

5 *  7   =     35

Anyone, else  ????

ABC,DEF = 142,857.

The  vertex  =    ( 2, 6)

The  x coordinate of  the  vertex =  -b  /  ( 2a)  =  2

-b  =  4a

b =  -4a

So....since   (2,6)   is  on the  graph we have

6 = a(2)^2   - 4a(2)  +  18

6  -18 =  4a  - 8a

-12  =  -4a

-12/-4 =  a    =  3

So  b =   -4(3)   =   -12

a +   b     =      3 -  12   =   - 9

We  can  solve  this graphically

See  here  :   https://www.desmos.com/calculator/zpcbhs2jhw

The  first two constraints form  a  1   x 1    square.....area  =   1

The  last  equation  forms  a triangle in this square  with  a  base of   (1/2)  and a height of  1

Its  area =  (1/2) (1/2) (1)  =  1/4

The  probability  is     ( 1/4 )   / 1    =  1/4    

a = 150.

9x^2   +  36x   +   a

Note   :

(3x  + 6)^2   =

(3x + 6) (3x + 6)  = 

9x^2  +  36x   +  36

a  = 36

This is equal  to  the number of  partitions  of   the integer 4

They are

4 = 4
3 + 1 = 4
2 + 2 = 4
2 + 1 + 1 = 4
1 + 1 + 1 + 1 = 4

5 ways

The  radius of  the  circle  must =  5  since  the  diagonal  is 1 unit from  the  center  and  4 units  from  the   circumference

Using  the Pythagorean Theorem.....the  length of  the  diagonal  =   sqrt ( 5^2  - 1)^2   =  sqrt (24)  

The  side of  the  square =   sqrt (24)   /sqrt (2)    = sqrt  12

The area of the  square =    (sqrt (12))^2   =   12

Missing important info     # of clams each borrowed and the interst rates each of them has to pay....

The  vertex   is  (3, 8)    and  the point  (0, -1)  is on the  graph

So we  have

-1   = a  (0  = 3)^2   +  8           solve  for  "a'"

-1  =  a ( 9 )  +  8

-1- 8 - a (9)

-9 =   9a

a  = -1

The  function is

y  = -1 ( x - 3)*2  +  8

y  = - 1 ( x^2  - 6x  +  9)  +  8

y =  -x^2  +  6x  - 9 + 8

y =  -x^2  + 6x  -  1

a = -1       b =  6        c  = -1

abc   =     6

(2x + 2)^6

The  x^4  term   is

C( 6, 2)  (2x)^4 (2)^2  =

15 (16x^4) (4)   =

15  *  16 *  4  x^4  =

960 x^4

There are 83 terms that are divisible by 4.

The slope   of   Ax + By  =  3   is      -A/B    

And  x + 3y  = - 5  ⇒  3y  =  -x  - 5     divide through by 3  ⇒  y = (-1/3) - 5/3

So....the slope of the second line =  (-1/3)   

And since this is parallel to the first line,  this implies that

-1/3  = -A/B

So  A = 1   and  B    = 3

Then B - A  =   3  -  1   =   2

The area of triangel OPQ is 14/5.

The probability of being admitted to at least one college is 1 - 1/7 - 1/8 - 1/9 - 1/10 = 1313/2520.

1. There are 360 ways to rearrange the letterrs of INFINITY.

2. There are 80*78*76 = 474,240 possible combinations.

AE = CE = ¹/₁₀(√50)

P = 33 + 42 + (33 + 42 - 1) 

The triple (x,y,z) is (1/4,1/4,1/2).

Right triangle with two equal legs   (because the other two angles are each 45 degrees)

   so   AE = CE

pythag theorem

   s^2 + s^2 = 1^2

     2 s^2 = 1

         s^2 = 1/2

 s = AE =CE =   sqrt (2) /2

The sum of all values of x such that f(x) = 0 is -3/2.

There are 64 possible palindromes.

oh thats wut u mean, lemme fix it

Thanks for the help but I don't think it's correct because you could place $1$ in every box which is different from placing all of them in one box so the answer should be greater than $1$