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:
{1,4}
Step-by-step explanation:
A={3,6,9}
B={2,3,5,7}
C={1,2,3,4,5}
AUB={2,3,5,6,7,9}
(AUB)'={1,4,8,10}
(AUB)'⋂C={1,4}
Answer:36 postcards
Step-by-step explanation:
jenny bought 12 post cards
joe bought half of the postcards jenny bought = 12/2 = 6
ruth bought 3 times the postcards joe bought = 3 x 6 = 18
total postcards bought by all = 12 + 6 + 18 = 36 postcards
5/13
The x value is negative (second quadrant). 13 is the hypotenuse. So the missing side is 13^2 = (-12)^2 + y^2.
Sin theta is the opposite (5) over hypotenuse (13).
Answer:
10 teams (1 remainder)
Step-by-step explanation:
if each team has 3 players and there are 30 friends, divide that and youll end up with 10 teams. you will also have 1 remaining player
