<em>Answer: C</em>
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<em>It is C because when there is a line at the top of the number, it is infinite and repeats many times. That number in a shorter was can be written as a fraction over 990. Two of the answer choices has 990 in it which is letters B and C. This eliminates answer choices A and D. The number that is within the dot is your numerator (645) and 990 is your denominator. Overall the answer is 645/990</em>
I'll talk you through it so you can see why it's true, and then
you can set up the 2-column proof on your own:
Look at the two pointy triangles, hanging down like moth-wings
on each side of 'OC'.
-- Their long sides are equal, OA = OB, because both of those lines
are radii of the big circle.
-- Their short sides are equal, OC = OC, because they're both the same line.
-- The angle between their long side and short side ... the two angles up at 'O',
are equal, because OC is the bisector of the whole angle there.
-- So now you have what I think you call 'SAS' ... two sides and the included angle of one triangle equal to two sides and the included angle of another triangle.
(When I was in high school geometry, this was not called 'SAS' ... the alphabet
did not extend as far as 'S' yet, and we had to call this congruence theorem
"broken arrow".)
These triangles are not congruent the way they are now, because one is
the mirror image of the other one. But if you folded the paper along 'OC',
or if you cut one triangle out and turn it over, it would exactly lie on top of
the other one, and they would be congruent.
So their angles at 'A' and at 'B' are also equal ... those are the angles that
you need to prove equal.
Answer:
x=7
Step-by-step explanation:
AC=3x+3 AB=-1+2x and BC=11
AC = AB + BC
ALL THE STEPS:
3 X + 3 = - 1 + 2 X + 11
3 X + 3 = 2 X + 10
3 X + ( - 2 X ) + 3 = 2 X + ( - 2 X ) + 10
X + 3 = 10
X + 3 + ( - 3 ) = 10 + ( - 3 )
X = 7
<span>I think you know by now that I strongly encourage everyone to shoot a proper round and whatever the score is, to submit it to our Records Officer, Giles Conn. Think of it as an annual competition (a) to wear him out, and (b) to see if we can altogether, beat last year's tally. Also, for the outdoor season rounds, you can have a go at achieving the St Wilfred trophy. I've won it 3 years running (last year jointly with Terry Skinner), but they wouldn't let me keep it this time, sadly.</span>
Pythagorean theorem is formula we would use:
1.)
c^2=a^2+b^2
c^2=10^2+24^2
c^2=100+576
c^2=676
c= √676
c=26 in
2.)
c^2=7^2+14^2
c^2=49+196
c^2=245
c= √245
c~15.65 cm
