The quadratic can be written as (x-3)^2+51 so b+c=48

:D

Assuming that you mean 3pi/4, we know that a circle has 2pi radians so 3pi/4 is 3/8 of it. The circumference is 96 mm so the length of the arrc is 36pi mm

Out of 3 consecutive numbers, one must be divisible by 2 and one must be divisible by 3 so the product must be divisible by 6. There are 79 integers from 2 to 80.

Cases

3 is rolled before even numbers: 1/4

3 is rolled after 1 even numbers: 3/16

7/16

We're looking for (-3+5i)(-3-5i) which is 9+25=34.

For any z in the form a+bi, z multiplied by its conjugate will be equal to a^2+b^2.

My idea:

Pick which attribute(s) (color, shape, number, shading) is similar. Make all of the other one's different. Count the cases and multiply.

You have to pick 3 vertices of the hexagon so there are 6choose3= 20 ways

Here are the numbers I got

111

123

132

213

222

231

312

321

333

9 numbers

1/3

Using similar triangles, TRQ is similar to TPS with an area ratio of 1/16 so the area of PQRS is 405/17

Using Simons favorite factoring trick gets us (p-2)(q-2)=6 so (p-2) can be either 1,2,3, or 6 meaning p is 3,4,5, or 8. 2/5