CPhill

The roots are  x = -2  and x = 4  and the point (0,-8) is on the graph

So

-8 = a ( 0 + 2) ( 0 - 4)

-8 = -8a

a =1

So the function is

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

y = x^2  - 2x  - 8

The  integers 10 - 99  work

There are   99 - 10  + 1  =   90  of these

Could  you explain your reasoning, hot18594  ???

I know  that one  website  claims that there are 6 triangles (3 each)  formed from sides of ( 3,3,4)  and (4, 4, 2) but these triangles are isosceles so any orientation of them is the same

I agree with the guest  ⇒   1 /  18

( 1680 - x) (.07) =  ( x) (.04) + 20.80

117.6  - .07x  = .04 x + 20.80

117.6 - 20.80  = .11x

96.8 =  .11x

96.8 / .11 = x  = $880  at 4%

(x + 3)/ ( x + 5)   =  ( x + 1) / ( x + 2)       cross-multiply

(x + 3) (x + 2) =  (x + 5) ( x + 1)

x^2  + 5x + 6 =    x^2 + 6x + 5    simplify as

1 =  x

Rearrange as

-3x^2 +  15x

The max value occurs when x =   -(15) / (2 * -3)  =   -15 / -6  =  5/2 =  2.5

And the max is

-3 (2.5)^2  + 15 (2.5)  = 

18.75

5p - (5 + 125i)  = 10000

5p - 5 - 125i  = 10000

5p - 125i =  10005          let p   = ( 2001 + 25i)

5 ( 2001 + 25i) - 125 i  =  10005

10005 + 125i - 125i  = 10005

10005 = 10005

The discriminant of   x^2 + bx + 68   must be < 0

So

b^2 - 4(1) (68)  < 0

b^2  - 272 < 0

b^2  < 272

This will be true when      -sqrt (272) < x < sqrt (272)

Greatest integer value for b =   floor[ sqrt (272) ] =    16

(1/2)  /(7/8)   =   (1/2) *(8/7)  =  8 / 14  =   4 / 7

Call the part of the bike that Brandon  can assemble in one hr =  1/  x

Call the part that Maria can  assemble in one hour   =  1 / ( x + 2)

Working together  they assemble   1 /x + 1/(x +2)    part of the bike   

So

Part of the bike they can  assemble in 3 hours + part Maria can assemble in one  hour =  1

3 [1/x + 1 / (x + 2)]  + (1)( 1/(x+ 2))  = 1

3/x +   ( 4) / (x + 2)  = 1

[ 3( x + 2) + 4x ] / [ x * (x + 2) ] =  1

7x + 6 =  x^2 + 2x 

x^2 - 5x - 6 =  0

( x - 6) (x + 1)  =  0

Take the first factor and  set =  0 

x = 6

It takes Maria       x + 2 =    8 hours to  assemble the  bike  by herself