CPhill

12)

Look at the graph, here :  https://www.desmos.com/calculator/wfs9ho2uyr

The graph increases from (-infinity, -4)   and from (-4/3, infinity)

The graph decreases from  (-4, -4/3)

13)

Look at the graph, here : https://www.desmos.com/calculator/n6ss75kmnc

The graph increases from ( -infinity, -1)  and from (-.366 ,  1.366)

The graph decreases from ( -1, -.366)  and from (1.366, infinity)

( 8 + 1)  x  5  =

(9) x 5  =

$45

We want to solve this

175 <  14 (x)      where  x is the number of games we are looking for

Divide both sides by 14

12.5 < x   means the same thing as  x > 12.5

So....rounding up.....Armin needs to attend 13 games to make the season pass cheaper...!!!

Slight sign error...now corrected...!!!

Let N be  the number

85 + N^2  = ( N - 17)^2  simplify

85 + N^2  = N^2  - 34N + 289    subtract N^2 from both sides

85    =  -34N + 289    subtract 289 from  both sides

85 - 289  = -34N

-204  =  -34N    divide both sides by  -34

6  = N

Answer here :

https://web2.0calc.com/questions/triangle-medians-and-altitudes

(2 ^(1/2) + 2)^2  - 2^(5/2)    =         [ a^2  = a* a ] 

(2^(1/2)  + 2) (2^(1/2) + 2)  - 2^(5/2)   =

2^(1/2) * 2^(1/2)  * 2*2^(1/2) + 2*2^(1/2)  + 2 *2   - 2^(5/2)  =    [ We are using   a*m * a^n   = a^(m + n) ]

2^(1)    +  4*2^(1/2) + 4   - 2^(5/2)  =

6  + (2)^2 * 2^(1/2)  - 2^(5/2)  = 

6 + 2^ (2 + 1/2)  - 2^(5/2)

6  + 2^(5/2)  - 2^(5/2)   =

6

Flyinindawind....a bar graph is shown....but  no data associated with it....

Note that  1/3 of the bath is filled by the frist tap each minute  and  1/2  of the bath is filled by the second tap each minute

So...the   fraction filled by both taps in one minute is (1/3) + (1/2)  =  5/6

Invert this fraction  to find the number of minutes to fill the bath  =  6/5 minutes  = 1 + 1/5  minutes =  1 min, 12 seconds  [as Melody,  Guest and  EP found !! ]

Note that the method works because   if , for example, 1/2 of the bath were filled in one minute,  the reciprocal of this fraction  tells us how many minutes it would take to  fill the bath  = 2/1   = 2  minutes  !!!

Don't know too much about this, NSS...but from some cursory reading,  we want to "attack" the highest interest rate debt, first

This is debt 3.....she  will make the minimum payment ($150) plus any surplus funds ($150)  she has allocated to pay off her debt

So... Debt  3,   ( 150 + 150)  =  $300     is the answer, NSS !!!