C = 2(PI)r multiply 2 x 3.14 x (whatever the radius is!
Answer:
There are 150 blue marbles in Alex's bag.
Step-by-step explanation:
Let 
, 
, 
be the quantities of red, blue and yellow marbles, respectively. From statement we derive three rational equations for initial and final ratios:
Initial ratio
(1)
(2)
Final ratio
(3)
After some algebraic handling we get the following system of linear equations:
(1)
(2)
(3)
The solution of the system of linear equations is:
, 
, 
There are 150 blue marbles in Alex's bag.
Let s represent the short side of the triangle. The long sides of the triangle are each s+1, and the triangle's perimeter is
... s + (s+1) + (s+1) = 3s+2
The length of one side of the square is s-2, and its perimeter is 4 times that, 4(s-2) = 4s-8. The square and triangle have the same perimeter, so
... 3s+2 = 4s-8
... 10 = s . . . . . . . . add 8-3s to both sides
The length of the shorter side of the triange is 10 units.
The blanks are as follows:
- Angle addition postulate
- Subtraction property of equality
- Corresponding sides of similar triangles are proportional
- Multiplication property of equality
The answer is -30 (from calculator)
