Answer:
Δ JKL is similar to Δ ABC ⇒ D
Step-by-step explanation:
Similar triangles have equal angles in measures
In ΔABC
∵ m∠A = 15°
∵ m∠B = 120
∵ The sum of the measures of the interior angles of a Δ is 180°
∴ m∠A + m∠B + m∠C = 180°
→ Substitute the measures of ∠A and ∠B
∵ 15 + 120 + m∠C = 180
→ Add the like terms in the left side
∴ 135 + m∠C = 180
→ Subtract 135 from both sides
∴ 135 - 135 + m∠C = 180 - 135
∴ m∠C = 45°
The similar Δ to ΔABC must have the same measures of angles
If triangles ABC and JKL are similar, then
m∠A must equal m∠J
m∠B must equal m∠K
m∠C must equal m∠L
∵ m∠J = 15°
∴ m∠A = m∠J
∵ m∠L = 45°
∴ m∠C = m∠L
∵ m∠J + m∠K + m∠L = 180°
→ Substitute the measures of ∠J and ∠L
∵ 15 + m∠K + 45 = 180
→ Add the like terms in the left side
∴ 60 + m∠K = 180
→ Subtract 60 from both sides
∴ 60 - 60 + m∠K = 180 - 60
∴ m∠K = 120°
∴ m∠B = m∠K
∴ Δ JKL is similar to Δ ABC
Answer:
(a) 95% of people have an IQ score between 66 and 134.
(b) 32% of people have an IQ score of less than 83 or greater than 117.
(c) 16% of people have an IQ score greater than 117
Step-by-step explanation:
To prove the similarity between the two circles we must translate circle A by <- 1, 1> and dilate the figure by a factor of 2.
<h3>How to prove that two circles are similar</h3>
Herein we must prove that two circles are similar by taking advantage of two key characteristics: (i) Center, (ii) Radius. Based on such facts, we must apply the following <em>rigid</em> transformation:
- Translating the circle from A to B.
- Enlarging the circle A by a <em>dilation</em> factor.
Step 1 - Traslating the circle from A to B: Translation vector - (- 1, 1).
(x, y) = (2, 3) + (- 1, 1)
(x, y) = (1, 4)
Step 2 - Dilate the circle by a factor of 2.
r = 2 · 5
r = 10
To prove the similarity between the two circles we must translate circle A by <- 1, 1> and dilate the figure by a factor of 2.
To learn more on transformation rules: brainly.com/question/9201867
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Answer:
The probability that more than 30 minutes will elapse before the next fraudulent corporate tax return is discovered=0.1353
Step-by-step explanation:
We are given that
We have to find the probability that more that 30 minutes will elapse before the next fraudulent corporate tax return is discovered.
Using exponential distribution
The probability that more than 30 minutes will elapse before the next fraudulent corporate tax return is discovered
The probability that more than 30 minutes will elapse before the next fraudulent corporate tax return is discovered
Hence, the probability that more than 30 minutes will elapse before the next fraudulent corporate tax return is discovered=0.1353
