Solve: 4/3 s+4 ≥ 12

 

Solve: 15-5t ≥ 55

after dividing every term by 5 yields
 
 

simplify: cot(arcsin(-2/3))

for convenience, we write 
 
 
so that means... 
, ,  

Use the method of substitution to solve the system of linear equations. 2x-y=5, 5x-2y=13

1) 2x-y=5
2) 5x-2y=13 


5x-2(2x-5)=13
x=3 
y=2(3)-5=1

solution: (3,1)

The length of a rectangle is 4cm more than twice its width. The perimeter is 86cm. Find the width and length.

1) l=4+2w
2) 2(l+w)=86 


2) l+w=43 
replacing l...
(4+2w)+w=43
3w=39
w=13cm 



1) becomes
l=4+2*13
l=30cm

Solve: 4m-5n=8, 2m+3n=10

1) 4m-5n=8
2) 2m+3n=10 <-m2 


and after we swap their positions... 


4m+6n=20
4m-5n=8 


then subtract to get 
11n=12
n=12/11 


from 1)... 


4m-5(12/11)=8
4m=8+60/11
4m=148/11
m=37/11

domain of f(x)=log(2*x-x^2)^1/2

2x-x^2=
x(2-x) 
so the domain is 
(-oo,0)U(2,oo)