CPhill

We can't do anything, here......if it was a right triangle, we'd need to know another side or angle.

If it was any other kind of triangle, we'd need to know two angles and a side or two sides and an included angle or all three sides.

0.844444..... = [84 -8]  /90   = 76/90

0.4444.....  =  4/9 

So .....   76/90  - 4/9   =   [9(76) - 4(90)]/ [9 * 90] =   [684 - 360] / 810  = 324/810  = 162/405 = [2*81] /[5 * 81]  =  2/5

1 Drink = p

3 Drinks = 3p

Medium Pizza = 2 x the cost of 1 drink  = 2p

Large Pizza = 3 x the cost of 1 drink = 3p

So.....assuming that she bought 3 drinks and both pizza types, she would have

30 - (3p + 2p + 3p) =    $ [ 30 - 8p  ]  left

The "bar" over the .009 indicates that this part repeats.....  so.....we have .009009009009.....etc. .....and we can write this as  9 / [ a number having the same number of 9's as the number of digits in the repeating cycle length ]

And notice that we have 3 digits in the repeating cycle length......so the denominator of the above fraction is just 999.......

.009009009  =   9/999  = 1/111

And 1 * 111 =   111

9 laps  x (1/8) miles per lap = 9/8 miles

2min 30 sec = 2.5 min  = 2 +1/2 min = 5/2 min  ...so....

D /T = R

(9/8)miles / (5/2) min  =

(9/8) x (2/5) =   18/40  = 9/20 miles per minute....

The diagonals form right angles......so we have

[(1/2) the shorter diagonal]^2 + [(1/2) the longest diagonal]^2  = [(1/4) perimeter]^2

6^2  + d^2  = 9^2      where d is 1/2 the length of the longer diagonal......so.....by the Pythagorean Theorem, we have

√[9^2 - 6^2]  = √[81 - 36 ] = √45  =  3√5 = d   ......   and twice this = 6√5 = about 13.416

Yeah, Alan......I hadn't noticed that....72°  is definitely not correct.....it would mean that the shortest side would be opposite the intermediate angle....impossible.....!!!

(x + 1)^2 + (y - 3)^2  = 36

I think this is supposed to be

2^x=9^(x-9 )