S, Y, R, and V are used to make 5-letter codes
you want only one S
there are 5 positions
S can be in position 1, for position 2 you can choose from 3 letters, for position 3 you can choose from 3 letters, for position 4 you can choose from 3 letters, and for position 5 you can choose...

4x^(-2)-11x^(-1)-20=0
let u=√x^(-2) so u^2 would equal x^(-2)
√x^(-2)=√(1/x^2)=1/x
so u=1/x and u^2=1/x^2=x^(-2)
substitute
4u^2-11u-20=0
4*20=2*2*2*2*5=(2*2*2*2)*5 and 16-5=11
factor
(u-4)(4u+5)=0
u-4=0
u=4
4u+5=0
4u=-5
u=-5/4
we...

let C be angle C
let C+16 be angle A
let (C+16)/3 be angle B
C+(C+16)+(C+16)/3=180
C+C+16+(C+16)/3=180
2C+16+(C+16)/3=180
2C+(C+16)/3=180-16
2C+(C+16)/3=164
multiply both sides by 3
3*2C+3*(C+16)/3=3*164
6C+C+16=492
7C+16=492
7c=492-16
7C=476
C=476/7
C=68...

(x-1)^2=9
x^2-2x+1=9
x^2-2x+1-9=0
x^2-2x-8=0
factor
(x-4)(x+2)=0
x-4=0
x=4
x+2=0
x=-2
(x-1)^2=25
x^2-2x+1=25
x^2-2x+1-25=0
x^2-2x-24=0
factor
(x-6)(x+4)=0
x-6=0
x=6
x+4=0
x=-4...

√(x+2)=x-4
square both sides
x+2=x^2-8x+16
x^2-8x+16-x-2=0
x^2-9x+14=0
factor
(x-7)(x-2)=0
x-7=0
x=7 (answer)
x-2=0
x=2 but 2 makes the left side equal to 2 and the right side equal to -2 so disregard the answer of 2 !!!

4, 11, 25, 53, 109, 221, 445, ...

√4+√4+√4+4=10
(4+[4/4])*√4=10
4+4+4-√4=10

√4√6√x^2√x√y^10√y
2*√6*x*√x*y^5√y
2xy5√(6xy)

1.
ln(x+2)-ln(x)=ln(x+5)
ln([x+2]/x)=ln(x+5)
(x+2)/x=x+5
x+2=x(x+5)
x+2=x^2+5x
x^2+5x-x-2=0
x^2+4x-2=0
using the quadratic formula
[-4±√(16+8)]/2
(-4±2√6)/2
-2±√6
x=-2+√6
2....

width=w
length=2w+11
diagonal=2w+13
use the Pythagorean Theorem
(2w+13)^2=w^2+(2w+11)^2
4w^2+52w+169=w^2+4w^2+44w+121
simplify
52w+169=w^2+44w+121
w^2+44w-52w-169+121=0
w^2-8w-48=0
factor
(w-12)(w+4)=0
w-12=0
w=12...

I think there's a typo in 3 so I'll do it with what I think is correct.
(10^(1-n)^n)/(1000^n)^n+1 is the left side which I'll do first
(10^(n-n^2))/[(10^3)^n]^(n+1)
[10^(n-n^2)]/[(10)^3n]^(n+1)
[10^(n-n^2)]/[10^(3n^2+3n)
when you divide you subtract...

(65+98+80+87+T)/5=80 where T=next test score
(330+T)/5=80
330+T=5*80
330+T=400
T=400-330
T=70

ab is the number
a+b=12
10a+b=13a
b=13a-10a
b=3a
substitute into a+b=12
a+3a=12
4a=12
a=3
b=9
39 is the number

ratio 4 to 7
Group 1 Group 2
4 7
8 14
12 ...

xy-4xz=5
factor out the "x"
x(y-4z)=5
divide both sides by (y-4z)
x=5/(y-4z)

(1/2)x-(5/3)=(-1/2)x+(19/4)
add (1/2)x to both sides
x-(5/3)=(19/4)
add (5/3) to both sides
x=(19/4)+(5/3)
x=(57/12)+(20/12)
x=77/12
x=6 5/12

g/b=9/4
9/4=g/20
5*4=20 so 5*9=45 girls
or...
9/4=g/20
cross multiply
4*g=9*20
4g=180
g=180/4
g=45
45+20=65 students altogether

n(U)=60
h=# of elements in G
4h=# of elements in H
h+4h=60
5h=60
h=60/5
h=12
n(G)=12 and n(H)=4*12=48

x^(-2)=16
x^(-2)=1/x2
1/x2=16
take the reciprocal of both sides
x2=1/16 answer

(x-h)^2+(y-k)^2=r^2, where (h,k) is the center and r is the radius
x^2+y^2-12x+2y+33=0
rearrange terms
x^2-12x +y^2+2y =-33
complete the square for x and for y
12/2=6 and 6^2=36
2/2=1 and 1^2=1
add 36 and...