I think you are needing the quadratic formula
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
a = 1 b = -2 c = -4 Substitute these values to find the values of 'n' that solve the equation ( I know ....it says 'x'...but you can put 'n' there)
I used a derivative calculator to find f' = (3x+1)/(sqrt(3x^2+2x)) subbing in x = 2 finds slope = 7/4 perpindicular is - 4/7
y = -4/7 x + b yielsds b = 5 1/7 at point 2,4
y = -4/7 x + 5 1/7
Picture
Second one arithmetic with d = -6 change 13 to 14.44 make it geometric with r = .76
First one Geometric ratio , r = 1/5 change 1 to -15 to make arithmetic with d = -20
You try the next one......or four.....
I think it is 7 games.... Jack wins 4 and loses 3 score 11
Mary loses 4 and wins 3 score 10
140 degrees x pi radians/180 degrees = 2.44346 R
2,44346 R x 3960 = 9676 miles
Total green beads = 861
total red beads = 128 <------ enough for 8 lizards (8 x 16 = 128)
861 green beads - 8 lizards * 94 greenbeads/lizard = 109 green beads left over after making 8 lizards.
distance/rate = time
1/5 km / 1/12 km/hr = 12/5 hr = 2 hr 24 min
5+6rt2
Roots are 5+- sqrt(25+4(a)(3) / 2a
[5 + sqrt(25+12a) - 5 + sqrt(25+12a) ] /2a = sqrt61/3
2 sqrt (25+12a)/2a = sqrt(61)/3
sqrt(25+12a)/a = sqrt(61)/3 results in a = 3