Total cost = d
Original cost per person = d/3
New cost per person = d/5
d/5 = d/3 - 11
11 = d/3 - d/5
11 = 2d/15
11*15/2 = d
d = 82.5 dollars
30x = 42 (mod 47)
30x = 47n + 42. n is an integer.
6(5x - 7) = 47n. 47 is prime so n must be a multiple of 6
n. 5x
1*6. 54. Not divisible by 5
2*6. 101. Not divisible by 5
3*6. 148. Not divisible by 5
4*6. 195. So x = 195/5.
x = 39
If the j, g and c represent units (joules, grams, celcius?) then the result is 0.4333*2*412.1 j
or 357.126 j
.
The distance between (x1, y1) and (x2, y2) is given by sqrt( (x1-x2)^2 + (y1-y2)^2 )
Just plug in your numbers.
x + y = 0. y = -x
8x - 7y = 75. 8x - 7(-x) = 75. 15x = 75. x = 5. y = -5
See the answer given here: http://web2.0calc.com/questions/find-a-b_1#r1
To add (subtract) two matrices you add (subtract) corresponding elements. So here you have:
A+ B = [ 9 14 14
12 10 12]
Like so:
\(\text{area = } \frac{1}{2}\left| \begin{array}{rrrrr}0 & 0 & 1 \\ 20 & 0 & 1 \\ 20 & 6 & 1\end{array}\right| \\ \\ \text{area = } (0*(0*1 - 6*1) - 0*(20*1 - 20*1) + 1*(20*6 - 20*0))/2 \\ \\ \text{area = } 60 \\ \\ \)
Here's another approach:
+33667 
