CPhill

-4(x+2y)=      just distribute the -4 over the terms in the parentheses on the left side

-4x - 8y

And that's it.....!!!!!

[ 6 + 1/4] * [ 5 + 3/4] =

[25/4] * [ 23/4]  =

575/16 =

35 + 15/16

9(2x-9)=99    distribute the 9 over terms inparenthesis on the lefy

18x - 81  = 99     add 81 to bth sides

18x = 180          divide both sides by 18

x = 10

2(1)^2 , 2(2)^2 , 2(3)^2, 2(4)^2, 2(5)^2  =

2, 8, 18, 32, 50

arcos (1/2) = pi/3

So

sin(pi/3) =

√3 / 2

The f third and fourth functions all have a different slope from the given one......so....they will each intersect the given equation in exactly one point.

The first equation has the same slope but a different y intercept from the given one.....thus, these two functions will never intersect......and thus, have no solution in common.....

The second function is exactly the same as the given one......thus....this "system"  will have infinite solutions....

All  rhe 8 digit numbers  are from  10,000,000 to 99,999,999

And there are (99,999,999 - 10,000,000,000) + 1 = 90,000, 000 of these

So, we have 45,000,000 pairs  and each pair sums to (10,000,000 + 99,999,999).....the sum is just    (10,000,000 + 99,999,999) * (45,000,000) = 4,949,999,955,000,000

And all the 10 digit numbers are from  1,000,000,000 to 9,999,999,999

And there are (9,999,999,999 - 1,000,000,000) + 1 =  9,000,000,000 of these

So, we have 4,500,000,000 pairs of these.......and each pair sums to (1,000,000,000 + 9,999,999,999).....so the total sum is just (1,000,000,000 + 9,999,999,999) * (4,500,000,000)  = 4,949,999,999,550,0000,000

So the total sum is 4,949,999,955,000,000 +  49,499,999,995,500,000,000  =  49,504,949,995,455,000,000   

Let your current age be  A .....so  your age one year from now is A + 1 and one year ago was A- 1   ....and we have

For the first part, we have

(4/5)(A) > (3/4)(A + 1)    multiply through by the common denominator of 4 and 5, i.e., 20

16A > 15(A + 1)   simplify

16A > 15A + 15    subtract 15A from both sides

A > 15

And for the second part, we have

(4/5)A > (5/6)(A - 1)     multiply through by the common denominator of 5 and 6, i.e., 30

24A > 25(A - 1)      simplify

24A > 25A - 25      add 25 to both sides and subtract 24A from both sides

25 > A      or, expressed another way.....

A < 25

So.....using both solutions, we have

15 < A < 25       {your possible age is greater than 15 but less than 25 }

I get the same answer as Alan....but with a slightly different explanation...

The first spy can sit in any of the first four "vertical" benches . The next spy has three vertical benches to choose from. The third spy has two and the last one has one. That's 4 x 3 x 2 x 1 = 4! ways = 24 ways. But, once seated, we can also arrange these vertical columns in 4! ways.....so....4! x 4!  = 24 x 24 = 576.

This is a Pythagorean "Triple"  .......

y = ±√[13^2 - (-5)^2]  = ±  12

So.....the tanΘ = y/ x     and so we have

tan Θ  =  ±  12 / 5