Answer:
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Step-by-step explanation:
Answer:
m<N = 76°
Step-by-step explanation:
Given:
∆JKL and ∆MNL are isosceles ∆ (isosceles ∆ has 2 equal sides).
m<J = 64° (given)
Required:
m<N
SOLUTION:
m<K = m<J (base angles of an isosceles ∆ are equal)
m<K = 64° (Substitution)
m<K + m<J + m<JLK = 180° (sum of ∆)
64° + 64° + m<JLK = 180° (substitution)
128° + m<JLK = 180°
subtract 128 from each side
m<JLK = 180° - 128°
m<JLK = 52°
In isosceles ∆MNL, m<MLN and <M are base angles of the ∆. Therefore, they are of equal measure.
Thus:
m<MLN = m<JKL (vertical angles are congruent)
m<MLN = 52°
m<M = m<MLN (base angles of isosceles ∆MNL)
m<M = 52° (substitution)
m<N + m<M° + m<MLN = 180° (Sum of ∆)
m<N + 52° + 52° = 180° (Substitution)
m<N + 104° = 180°
subtract 104 from each side
m<N = 180° - 104°
m<N = 76°
275 is the answer to the question
Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.
<h3>Inverse of functions</h3>
In order to determine if the function f(x) and g(x) are inverses of each other, the composite function f(g(x)) = g(f(x))
Given the function
f(x)= 5-3x/2 and
g(x)= 5-2x/3
f(g(x)) = f(5-2x/3)
Substitute
f(g(x)) = 5-3(5-2x)/3)/2
f(g(x)) = (5-5+2x)/2
f(g(x)) = 2x/2
f(g(x)) = x
Similarly
g(f(x)) = 5-2(5-3x/2)/3
g(f(x)) = 5-5+3x/3
g(f(x)) = 3x/3
g(f(x)) =x
Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.
Learn more on inverse of a function here: brainly.com/question/19859934
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