Answer:
- 13. (a) 120°, 120°, (b) 8.94 cm
- 14. (a) 17.9 cm, (b) 22.4 cm
Step-by-step explanation:
- <em>Refer to the attached sketch (not to scale)</em>
<h3>Question 13</h3>
(a) The center of the circle is also the circumcenter of the triangle PQR.
<u>Since ΔPQR is equilateral, all sides are equal, therefore opposite angles are also congruent:</u>
Sum of the three angles is 360° as cover the full circle.
<u>Each angle measure is:</u>
- ∠POQ = ∠QOR = ∠POR = 360°/3 = 120°
(b) Each side is 16 cm and the radius is 12 cm.
The distance of the midpoint M of PQ from the center O is perpendicular bisector of ΔPOQ.
<u>The segment MO is:</u>
- MO² = PO² - PM² = PO² - (PQ/2)²
- MO² = 12² - (16/2)² = 80
- MO = √80 = 8.94 cm (rounded)
<h3>Question 14</h3>
<u>ΔXYZ is isosceles with:</u>
- XY = XZ = 20 cm
- YZ = 18 cm
(a) The altitude of ΔXYZ is a perpendicular bisector of YZ. h = XM is the altitude
<u>Find h:</u>
- h² = XZ² - ZM² = XZ² - (ZY/2)²
- h² = 20² - (18/2)² = 319
- h = √319
- h = 17.9 cm (rounded)
(b) Note the ∠ZXM is half of the ∠ZOM as both the angles intercept half of the arc ZY and ∠ZOM is a central angle.
<u>Find ∠ZXM:</u>
- sin ∠ZXM = ZM/ZX = 9 / 20
- m∠ZXM = arcsin (9/20) = 26.7° (rounded)
<u>Find ∠ZOM:</u>
- m∠ZOM = 2*m∠ZXM = 2*26.7 = 53.4°
<u>Find the measure of the radius:</u>
- sin ∠ZOM = ZM/r
- sin 53.4° = 9/r
- r = 9 / sin 53.4°
- r = 11.2 cm (rounded)
<u>Find the measure of the diameter:</u>
- d = 2r = 2*11.2 cm = 22.4 cm
Answer: C) On average, the employees of Company A take more sick days than the employees of Company B.
Step-by-step explanation: USATESTPREP
Answer:
hmmmm im not the smart one but i think its k+2^(h-x)a=y
Step-by-step explanation:
Answer
18 Ft
Step-by-step explanation:
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Answer:
Multiply 1240 by 1.15 to get 1426 students enrolled this year.
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