With that table of values, you can come up with a slope intersect form of a line
7 = -8m + b
1 = -5m + b
-5 = -2m + b
7-1 = -3m
6 = -3m
m = -2
1 = -5 * -2 + b
b = 1 - 10
b = -9
so it is y = -2x - 9
Now we can find where those intersect
-2x - 9 =2 (x+4)^2 - 5
-2x - 9 = 2(x^2 + 8x + 16) - 5
-2x - 9 = 2x^2 +16x + 32 -5
2x^2 + 18x +36 = 0
x^2 + 9x + 18 = 0
D = 81 - 72 = 9 = 3^2
x1 = (-9 - 3) / 2 = -6; y1 = 3
x2 = (-9 + 3) / 2 = -3; y2 = -3
so the solutions are (-6; 3) and (-3; -3)
There are 8 possible outcomes with corresponding winnings:
HHH ==> 1 + 2 + 3 = 6
THH ==> -1 + 2 + 3 = 4
HTH ==> 1 - 2 + 3 = 2
HHT ==> 1 + 2 - 3 = 0
TTH ==> -1 - 2 + 3 = 0
THT ==> -1 + 2 - 3 = -2
HTT ==> 1 - 2 - 3 = -4
TTT ==> -1 - 2 - 3 = -6
Then
Y=2x+-8.2? Hope it helps!
ST = 7.2
RT = 4.04
m∠S = 34°
Solution:
Given ΔRST is a right triangle.
RS = 6, ∠T = 56°
1.206 × 6 = ST
7.236 = ST
ST = 7.2
0.674 × 6 = RT
4.044 = RT
RT = 4.04
To find the measure of angle S.
Sum of the interior angles of the triangle = 180°
m∠R + m∠S + m∠T = 180°
90° + m∠S + 56° = 180°
m∠S + 146° = 180°
m∠S = 180° – 146°
m∠S = 34°