CPhill

We have the form

ax^2  + bx   + c  = 0

Where  a = 1, b = - 2  and c = 6

The discriminant  is     b^2 - 4ac.....if this is < 0, we have no real solutions...so...

(-2)^2   - [ 4 * 1 * 6 ]    =

4 - [ 24]   =   -20

So....no real solutions......

You got that part correct....but we need to compare that with how much she would spend on a policy if she quit smoking.....which is   4 * 3.50 * 12   = $168

So...the amount she would save is the difference between these.....

x^2  + 9x - 15   = 0 

Not too much math to do here, NSS

The quadratic formula  will  have "-9"  as the first term in the numerator, so we can eliminate A and B 

Further, the dscriminant   =  9^2 -  [4*1 * -15]   =  81 - (-60) =   81 + 60   = 141

This will be the integer under the radical.....so....

"C"  is correct     !!!!

x^2 + 9x - 36  = 0         factor   and set = 0

(x + 12) ( x - 3)   = 0

Set each factor to 0, solve for x and we get that

x = -12   or   x   = 3

Presently....she would spend   4 * 5.25 * 12 = $252

If she quit smoking, she would spend   4 * 3.50 *12   = $168

So...she would save  $[ 252 - 168 ]  = $84 per year

As Rom points out....5!!   + 7!!   +  9!!   +  .....+  49!!    will end in 5

[ Each term  will have 5 * an odd product ...i.e., ending in a "5"....and we will have 23 terms....so....an odd number of summed  terms ending in "5" will also end in "5"  ]

And   

1!!   = 1

3!! = 3

So....the sum ends in   1 + 3   + 5   =    9

3  =  -4g   - 5       add 5 to both sides

8  =  -4g      divide both sides by  -4

-2  =    g

5 .

An equilateral triangle has every interior angle  = 60°

So

7x - 3    =   60        add 3 to both sides

7x  = 63      divide both sides by 7

x   = 9    

4 .

This is an equilateral triangle....so.....all sides are equal....so we can set any two sides equal and solve for x

4x - 10   = 3x + 2       add 10 to both sides.....subtract 3x from both sides

x  =   12

3.   Similar to 2

Because angle ACB  = angle ABC   then   AB   = AC

So

2x - 24   =  x - 2      add  24 to both sides, subtract x from each side    

x  =   22  =   BC