Answer:
1) ΔACD is a right triangle at C
=> sin 32° = AC/15
⇔ AC = sin 32°.15 ≈ 7.9 (cm)
2) ΔABC is a right triangle at C, using Pythagoras theorem, we have:
AB² = AC² + BC²
⇔ AB² = 7.9² + 9.7² = 156.5
⇒ AB = 12.5 (cm)
3) ΔABC is a right triangle at C
=> sin ∠BAC = BC/AB
⇔ sin ∠BAC = 9.7/12.5 = 0.776
⇒ ∠BAC ≈ 50.9°
4) ΔACD is a right triangle at C
=> cos 32° = CD/15
⇔ CD = cos32°.15
⇒ CD ≈ 12.72 (cm)
Step-by-step explanation:
In accordance with <em>propositional</em> logic, <em>quantifier</em> theory and definitions of <em>simple</em> and <em>composite</em> propositions, the negation of a implication has the following equivalence:
(Correct choice: iii)
<h3>How to find the equivalent form of a proposition</h3>
Herein we have a <em>composite</em> proposition, that is, the union of <em>monary</em> and <em>binary</em> operators and <em>simple</em> propositions. According to <em>propositional</em> logic and <em>quantifier</em> theory, the negation of an implication is equivalent to:
To learn more on propositions: brainly.com/question/14789062
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First of all we have to arrange the data in ascending order as shown below:
28, 40, 43, 43, 45, 50, 50
Total number of values = 7
Since the number of values is odd, the median will be the middle value i.e. 4th value which is 43. Median divides the data in two halves:
1st Half = 28, 40, 43
2nd Half = 45, 50, 50
Q1 or the First Quartile is the middle value of the lower or 1st half which is 40.
Q3 or the Third Quartile is the middle value of the upper or second half, which is 50.
IQR or the Inter Quartile Range is the difference of Q3 and Q1.
So, IQR= Q3 – Q1 = 50 – 40 = 10
Thus, IQR for the given data is 10
Answer:
1. Sides 1 and 2 are congruent so sides 3 are also congruent
2. Since angles D and R are the same and the two sides are the same, the triangles are the same
Answer:
y = -3x - 6
Step-by-step explanation:
