Step-by-step explanation:
- Since m∠ACM = 90°, then by angle addition, m∠ACP + m∠PCM = 90°.
- Since CP⊥ AM, then by definition of perpendicular, m∠APC = 90°. Since angles of a triangle add up to 180°, that means m∠PAC + m∠ACP = 90°.
- By substitution, m∠PCM = m∠PAC.
- Since m∠PCM + m∠CMP = 90°, then by substitution, m∠CMP = m∠PAC.
- Therefore, by AAA, △ACP and △CMP are similar.
Having proven that the triangles are similar, we can write the proportion:
AP / CP = CP / MP
9 / CP = CP / 16
CP² = 144
CP = 12
Now, we can simply use Pythagorean theorem to find the other sides.
AC² = AP² + CP²
AC² = 9² + 12²
AC = 15
CM² = CP² + PM²
CM² = 12² + 16²
CM = 20
Answer:
28.56/linear yard
32.2256/linear meter
121.77984k
Step-by-step explanation:
a) Scale = k9.52*3 = 28.56/linear yard
b) Scale = k9.52*3.28 = 32.2256/linear meter
c) Cost = 3.9 * 32.2256 = 121.77984k
Answer:
1 / 51
Step-by-step explanation:
Given that :
Number of cards in a deck = 52
Number of heart suit = 13
Number of kings = 4
Recall:
Probability = (required outcome / Total possible outcomes)
P(first card is king) = 4/52 = 1/13
P(second card is heart) = 13/51
Hence,
P(first card is king) * P(second card is heart)
(1/ 13) * (13/51) = 13 / 663 = 1/ 51
Answer:
124
Step-by-step explanation:
