g^4 + 18g^2 + 24 "complete the square" on g
g^4 + 18g^2 + 81 + 24 - 81
(g^2 + 9)^2 - 57
c= 1
p = 9
q = -57
x^2 + 5x + 1 complete the square on x
x^2 + 5x + 25/4 +1 - 25/4 =
(x + 5/2)^2 + 4/4 - 25/4
(x + 5/2)^2 - 21/4
b + c = 5/2 - 21/4 = 10/4 - 21/4 = -11 / 4
sqrt (2) , sqrt (10) , 5sqrt (2) rewrite as
sqrt (2) , sqrt (5)*sqrt (2) , 5sqrt (2)
The common ratio is 5 sqrt (2) /( sqrt (5) * sqrt (2) ) = sqrt (5)
The 7th term is
sqrt (2) * (sqrt (5))^6 =
sqrt (2) (5^(1/2))^6 =
sqrt (2) * 5^3 =
125 sqrt (2)
p(1,-1) = 1 - 2(-1) = 3
p(-5,2) = -5 -2(2) = -9
So we have
p (3, -9) = 3 - 2 (-9) = 3 -18 = -15
B
2
A C
If tan B = 5.....then the ratio of AC / BA = 5/1 ....so .... AC = 5BA
Using the Pythagorean Theorem
BA^2 + AC^2= BC^2
BA^2 + (5 BA)^2 = 2^2
BA^2 + 25 BA^2 = 4
26 BA^2 = 4
BA^2 = 4 /26 = 2 /13
BA = sqrt (2/13) = 2sqrt (13) / 13 ≈ .392
Y
W
X Z
Angle YXZ = 60°
Angle XYZ = 45°
So angle XZY = 180 - 60 - 45 = 75° = angle XZW
Since XW bisects angle YXZ.....then angle WXZ = 30°
Then in triangle XWZ ,angle WXZ = 30° and angle XZW = 75°
So angle XWZ = 180 - 30 - 75 = 75°
x = -2y^2 -3y + 5 - y^2 + 6 simplify as
x = -3y^2 - 3y + 11
This is a parabola that opens to the left.....the line will intercept the parabola at its vertex
The y coordinate of the vertex = - (-3) / ( 2 * -3) = 3/ -6 = -1/2
The x coordinate is -3(-1/2)^2 -3(-1/2) + 11 = -3/4 + 3/2 + 11 = 11+3/4 = 11.75
The equation of the line is x = the x cordinate of the vertex = 11.75
500 * 5 = $2500 = total money taken in = revenue
1(750) + 2(250) + 5(125) = $1875 = prize money paid out
Profit = 2500 - 1875 = $625
% of revenue that was profit = 625 / 2500 = .25 = 25 %
Let two points on the line be (0, 18) and (x , 0)
We can solve this
[ 0 -18 ] / [ x - 0 ] = 3/7
-18 / x = 3/7
-18 (7/3) = x
(-18/3)(7) = x
-42 = x = the x intercept
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