m∠DWC=138°, ∠AWB = 138°, ∠AWD = 42°, ∠BWC = 42°
Solution:
Line 
intersect at a point W.
Given 
.
<em>Vertical angle theorem:</em>
<em>If two lines intersect at a point then vertically opposite angles are congruent.</em>
<u>To find the measure of all the angles:</u>
∠AWB and ∠DWC are vertically opposite angles.
Therefore, ∠AWB = ∠DWC
⇒ ∠AWB = 138°
Sum of all the angles in a straight line = 180°
⇒ ∠AWD + ∠DWC = 180°
⇒ ∠AWD + 138° = 180°
⇒ ∠AWD = 180° – 138°
⇒ ∠AWD = 42°
Since ∠AWD and ∠BWC are vertically opposite angles.
Therefore, ∠AWD = ∠BWC
⇒ ∠BWC = 42°
Hence the measure of the angles are
m∠DWC=138°, ∠AWB = 138°, ∠AWD = 42°, ∠BWC = 42°.
Use the following identity:
cos(2x)=1-2sin^2(x)
Im pretty sure that it would be 600%. If it was 600% that would be 600 over 100 which would be 6
<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>
