Answer:
Yes, △ABC ∼ △FED by AA postulate.
Step-by-step explanation:
Given:
Two triangles ABC and FED.
m∠A = m∠B
m∠C = m∠A + 30°
m∠E = m∠F = 
m∠D = 
°.
Now, let m∠A = m∠B = 
So, m∠C = m∠A + 30° = 
Now, sum of all interior angles of a triangle is 180°. Therefore,
m∠A + m∠B + m∠C = 180
Therefore, m∠A = 50°, m∠B = 50° and m∠C = m∠A + 30° = 50 + 30 = 80°.
Now, consider triangle FED,
m∠D+ m∠E + m∠F = 180
Therefore, m∠F = 50°
m∠E = 50° and
m∠D = 
So, both the triangles have congruent corresponding angle measures.
m∠A = m∠F = 50°
m∠B = m∠E = 50°
m∠C = m∠D = 80°
Therefore, the two triangles are similar by AA postulate.
Step-by-step explanation:
sin(2x) + cos(3x)
Use double angle formula sin(2x) = 2 sin x cos x.
Use triple angle formula cos(3x) = 4 cos³x − 3 cos x.
Substitute:
2 sin x cos x + 4 cos³x − 3 cos x
Answer:
10n
Step-by-step explanation:
n represents number, its like using X, since we don't have the information on it, we replace it with a letter.
Answer:
1312.5 minutes
Step-by-step explanation:
For her phone service, Lucy pays a monthly fee of $25, and she pays an additional $0.06 per minute of use. The least she has been charged in a month Is $103.72
What are the possible numbers of minutes she has used her phone in a month?
Use m for the number of minutes, and solve your inequality for m.
The term least = ≥ = greater than or equal to
Our inequality equation is given as:
$25 + $0.06 × m ≥ $103.72
25 + 0.06m ≥ 103.72
0.06m ≥ 103.72 - 25
0.06m≥ 78.75
m ≥ 78.75/0.06
m ≥ 1312.5 minutes
The possible number of minutes she used is 1312.5 minutes
if its diameter is 8 cm, then its radius is half that, or 4 cm.
