geno3141

Originally, the game show host has two doors and you have one.

Therefore, the game show host has a 2 to 1 advantage over you.

So, you want to switch with the host and then you will have the 2 to 1 advantage. (The fact that the host shows you a losing door does not change the odds; it just confuses the problem.)

If you keep your original door, you have a 1/3 probability of winning.

If you switch, you have a 2/3 probability of winning.

9² + 12²  =  c²

81 + 144  =   c²

225  =   c²

c = √225  =  15

If you mean ab², then you have 6·(-3)²  =  6·9  =  54

Solving  a|x + b| = c

Divide both sides by a:  |x + b| = c/a

If the fraction, c/a, is negative, then any "answer" that you get is extraneous.

None.

When r = 7.999, floor(r) = 7, and their sum is 14.999.

When r = 8, floor(r) = 8, and their sum is 16.

All values of 15 are skipped.

Maybe only a coincidence, but when, in those four cases, the positive answer was a whole number, it gave you the negative answer. ???

The factors of 24 are:

   1 x 24

   2 x 12

   3 x 8

   4 x 6

A linear equation (straight line). 

-4(3x - 5) > -28

Use the distributive law on the left side:

(-4)(3x) - (-4)(5) > -28

-12x + 20 > -28

Subtract 20 from both sides:

-12x > -48

Divide both sides by -12:

(When you multiply or divide both sides of an inequality by a negative number, you must change the direction of the inequality; you don't change the direction if you are adding or subtracting or if you are multiplying or dividing by a positive number.)

x < 4

√(90) · √(14) · √(70)    

Factoring these, you can get:

=  √( 9 · 10 · 7 · 2 · 7 · 10 )

Rearranging:

=  √(9) · √(10 · 10) · √(7 · 7) · √(2)

=  √(9) · √(100) · √(49) · √(2)

= 3 · 10 · 7 · √(2)

=  210√(2)