Math Is Fun Forum

[this problem has 3 questions]

Use the law of detachment or the law of sylogism to determine a conclusion that follows from statements (1) and (2)
If a valid conclusion does not follow, write no valid conclusion.

(1) if a triangle is a right triangle , then it has two acute anges.
(2) triangle ABC is a right triangle

I wrote:
p = a triangle is a right triangle
q = it has two acute angles
p --> q
law of detachment

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(1) if three points are noncollinear,then they determine a plane
(2) points A,B,and C are coplanar

I wrote :
Law of Syllogism
a implies b, b impies c, a implies c
a -->b , b-->c, a--.c

noncollinear- points that do not lie on a single line
coplanar - lying in the same plane , any sets of three points are coplanar

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(1) all circles have diameters whose measure is twice the measure of the radius.
(2) AB is a radius of circle B

I wrote:
p = all circles have diameters
q = measure is twice the measure of the radius

p --> q
LAW OF DETACHMENT

( teacher gave me an x...no what can  i do )

csc^2 x - cot^2 x 
--------------------- = cos^2 x
1 + tan^2 x

csc^2 x - cot^2 x 
--------------------- = cos^2 x
1 + tan^2 x

  1               cos^2x
  -----     -    ---------
  sin^2x         sin^2x
-----------------------    =   cos^2x
   cos^2x         sin^2x
  --------   +   --------
   cos^2x         cos^2x

but 1 - cos^2 x = sin^2x, and Sin^2x + cos^2x  = 1, so the whole thing boils down to

         1
---------------   =   cos^2x
          1
      --------
       cos^2 x

fred can complete 5 jobs in 4 hours
when barney helps him, they can complete 9 jobs in 6 hours
how long would it take barney to complete 1 job

ok i think this is wrong but you tell me :

9/6 = 1/x
9x = 6
x = 6/9
x = 2/3
x = 0.6

help

Which congruence test can be used to prove that triangle GHI =~ triangle LKJ?

ok                            __      __
angle G =~ angle L    GJ =~ LJ
                                __      __
angle H =~ angle K    HJ =~ KH
                                      __       __
angle GHJ =~ angle LKJ    HG =~ LK

NOW WHAT.

how many ml of a 3 1/2%  salt solution must be added to 176ml of a 4 3/4% salt solution that is 45% salt?

three students must be chosen to serve on a panel out of a class of 12 students . in how many different ways can they be chosen?

well 12 students in total
1 2 3 4 5 6 7 8 9 10 11 12
3 must be chosen
so it can be
123
456
789
10 11 12
or
234
567
89 10
11 12 1
or
345
678
9 10 11
12 1 2

correct
so there are  12 ways

how many different ways can 5 objects be arranged in a circle????????