OK    ax^2 + bx + c = 0      the max is when x = 1  (the midpoint between the two given points)

  When x = 1   f(x) = 54     a(1^2) + b + c = 54      a + b + c = 54    c = 54-a-b

Sub in the values given

a (-2^2) + b(-2) + c = 0      4a-2b+c=0           4a-2b + 54-a-b = 0        3a-3b+54 = 0

a(4^2) + b(4) + c = 0       16a+4b+c = 0         16a+4b + 54 -a-b=0       15a+3b+54=0         Multiply green equation by -5 and add to this

-15a+15b-270

15a+3b+54

18b -216 = 0    b= 12     a =  -6     c =48

-6x^2 +12x + 48 = 0

y asymptote  ⇒   CORRECT   !!!

x asymptotes 

x^2  + 2x  - 3                  ( x + 3) ( x - 1)               (x + 3)

___________  =            ______________ =   ________

2x^2  - x   - 1                  (2x + 1) ( x - 1)             (2x + 1)

x = 1/2   is also CORRECT!!!!!

GOOD JOB!!!

[We have a "hole"  at   x = 1    ]

1. No function shown 

2.  3x^2 - 7   =  0

Factors of p  = ±1, ±7

Factors of q =  ±1, ±3

Possible zeroes  =   ±1/3 , ±1, ±7/3, ±7

3.  No expression shown

There are 90 four-digit palindromes

would this be correct 

https://prnt.sc/qd7oxk

Ok, I see what it means and it's also incorrect, but I notice the problem asks for "at least" 2 girls next to each other, not JUST two girls.

Thanks, guys.....I really appreciate all the  nice comments!!!!

C(n,k) stands for the binomial coefficient: https://en.wikipedia.org/wiki/Binomial_coefficient

Actually, there are two ways to arrange the girls, so the number of arrangements is 2*403,200 = 806,400.

Also, your answer is incorrect

Hello! I'm just wondering, what does the "C" mean when you say C(5,2)? I know this but I forgot it already.

There are 8 ways to choose the two positions where the girls are standing, and C(5,2) ways to choose the two girls in those positions.  There are then 7! ways to arrange all the other team members, so there are 8*C(5,2)*7! = 403,200 possible arrangements.

a=(11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43); i=0; j=2; c=a[0]*a[1]; cycle: m=a[i]*a[j]; if(m<500, c=sort(c,m), goto next);j++; if(j next: i++; j=i+1; if(j

OUTPUT: (143, 187, 209, 221, 247, 253, 299, 319, 323, 341, 377, 391, 403, 407, 437, 451, 473, 481, 493)>>Total = 19 such numbers.

Got it. Thanks

You can take q(x) = -15/2*(x - 1)^2.

Using a little bit of case work, we find that P can have 19 different values.

This can be found by using a right triangle formed using the radius of the smaller circle, which is 5 cm, and half of one of the chords of the larger circle, which equals 12. The radius of the larger circle is 13 cm.

A rhombus is a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and four equal sides.  A rhombus inscribed in a rectangle touches the sides of the rectangle so by this we can infer that the diagonals of the largest inscribed rhombus are equal to the length and breadth of the rectangle. If we have the length(l) and breadth(b) of the rectangle, the length of the diagonal of the largest rhombus inscribed inside it is d1 = l and d2 = b. The area of a rhombus is given by the formula,

Area = (d1*d2)/2

Putting in the values of d1 = 9 and d2 = 3, we get:

Area = (9*3)\2 = 27/2 = 13.5

The equation of this hyperbola in standard form is ((x+8)^2)/16 - ((y-4)^2)/144 = 1.

The point scavenger is this guitar-h u m p i n g rat.

Check your  3rd and 4th answers.....   the rest look OK..... 

a=3; c= (a!)^2 *(a^2 - 2)! ; d=5/6*(a^2)!*(((a - 2)!)^2;if(c==d, goto4, goto5);printc,d, a; a++;if(a<100, goto1, 0)

OUTPUT:  n = 11

Happy Birthday!   Math (and you) have come a long way since your abacus-using high school days !

   Time for a brewski !

Braden is ordering a flower arrangement with roses and carnations. He doesn't want to spend more than $30 on the arrangement. Roses cost $5 each and carnations cost $2 each.

I will assume the students are distinguishable and 'a' and 'b' will not stand next to each other...

a - - b

b - - a

a - b -

b - a  -

- a - b

- b - a         are six ways for  a  and b  NOT to be next to each other. 

    There are tow ways EACH for  c   and  d to fill in the blanks for each of these six ways

         6 x 2 = 12 ways

Solve for x:
sqrt(sqrt(sqrt(4 - x) + 4) + 4) = x

sqrt(sqrt(4 - x) + 4) = x^2 - 4

Using Newton-Raphson iteration method, it readily gives the value of x as:
x = 2.50701864409