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:
8x^3-7x^2-11x+9
Step-by-step explanation:
(8x^3-5x-1)-(7x^2+6x-10)
remove unnesasary ( )
8x^3-5x-1 -(7x^2+6x-10)
the distribute
8x^3-5x-1 -7x^2-6x+10
combine like terms
8x^3-11x+9-7x^2
use the communative property to reorder the equation
8x^3-7x^2-11x+9
