Here is a reference to the Inscribed Quadrilateral Conjecture it says that opposite angles of an inscribed quadrilateral are supplemental.
Explanation:
The conjecture, #angleA and angleC# allows us to write the following equation:
#angleA + angleC=180^@#
Substitute the equivalent expressions in terms of x:
#x+2+ x-2 = 180^@#
#2x = 180^@#
#x = 90^@#
From this we can compute the measures of all of the angles.
#angleA=92^@#
#angleB=100^@#
#angleC=88^@#
<span>#angleD= 80^@#</span>
<span>If f(x) = 2x + 3 and g(x) = (x - 3)/2,
what is the value of f[g(-5)]?
f[g(-5)] means substitute -5 for x in the right side of g(x),
simplify, then substitute what you get for x in the right
side of f(x), then simplify.
It's a "double substitution".
To find f[g(-5)], work it from the inside out.
In f[g(-5)], do only the inside part first.
In this case the inside part if the red part g(-5)
g(-5) means to substitute -5 for x in
g(x) = (x - 3)/2
So we take out the x's and we have
g( ) = ( - 3)/2
Now we put -5's where we took out the x's, and we now
have
g(-5) = (-5 - 3)/2
Then we simplify:
g(-5) = (-8)/2
g(-5) = -4
Now we have the g(-5)]
f[g(-5)]
means to substitute g(-5) for x in
f[x] = 2x + 3
So we take out the x's and we have
f[ ] = 2[ ] + 3
Now we put g(-5)'s where we took out the x's, and we
now have
f[g(-5)] = 2[g(-5)] + 3
But we have now found that g(-5) = -4, we can put
that in place of the g(-5)'s and we get
f[g(-5)] = f[-4]
But then
f(-4) means to substitute -4 for x in
f(x) = 2x + 3
so
f(-4) = 2(-4) + 3
then we simplify
f(-4) = -8 + 3
f(-4) = -5
So
f[g(-5)] = f(-4) = -5</span>
8 because her are the multiples of 8:8, 16 , 24
In triangle, ABD,
AD²= AB²+BD²
AB² = AD²-BD²
AB² = 18²-9² = 324-81 = 243
AB = √243
In triangle, ABC,
AC² = AB²+BC²
AC² = (√243)²+(13)²
AC² = 243+169
AC = √412
AC = 20.29
Is there anything more to this question? Like are PT and TQ equal?
