What is the LCM of 14 and 35? a. 140 b. 70 c. 56 d. 7
2 answers:
Answer: 70
Step-by-step explanation: To find the least common multiple for the integers 14 and 35, we start by making a factor tree for each of the integers.
14 factors as 2 × 7 and 35 is 7 × 5. We are looking for the factors that match up.
In this case, both integers have a factor of 7.
When finding the LCM, we multiply all the factors together, but because the 7's match up, we only need to multiply by 7 once.
So we have 2 × 7 × 5 which is 70.
Therefore, the least common multiple for 14 and 35 is 70.
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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.