The second equation shows b = 5-3a put this into the first equation for b
a^2 + (5-3a)^2 = 25 expand
a^2 + 9a^2 -30a + 25 = 25
10a^2 -30a =0
a(10a-30) = 0
a = 0 and 3 then b = 5 and -4 corrrespondingly
Take 1/2 of the 'x' coefficient , square it and add it to the expression to 'complete the square
[(1/2)(6/5) ]2 = 36/100 or 9/25 for the blank
x = 20 bill value = 20x
6x = 5 bill value = 5 (6x) = 30x values summed = 1450
20x + 30x = 1450
50x = 1450
x = 29 then 5 bill = 6x = 174 bills
Draw a Venn diagram ....you should be able to see the answer:
Angles of a triangle sum to 180 o
55o + 82o + ? = 180o Solve for ?
Arrange in y = mx+ b form m is the slope parallel slopes are =
2y-9x = 11
y = 9/2 x + 11/2
-5y + kx = 4 ( I assume you mis typed this one)
5y = kx - 4
y = k/5 x - 4/5 k/5 has to equal 9/2
k/5 = 9/2 now you can solve for 'k'
Odd multiples of 6 and odd multiples of 6 + 1 wind up in row f
2011/6 = 335 R 1
row f
Perfect squares would be 1 or 4
for ONE die
1 2 3 5 6
4 2 3 5 6
The same for the other die
so out of 36 possible rolls there are 16 rolls where ONE die has a square 16/36 = 4/9
In a triangle the 3 angles have to sum to 180 so add them up and equate them to 180:
x+2y + 6x-5y + 8x+3y = 180 when yo add them the y's will be gone....solve for x
Bowl shaped parabola.....minimum point is the vertex....to find the x value of the vertex
-b/2a = x of the vertex
16/6 sub in this for 'x' to find k which makes the equation = to 1
3 (16/6)^2 - 16 (16/6) + k = 1 k = 22 1/3
