Answer:
∠ CPM = 135°
Step-by-step explanation:
given AC = BC , then Δ ABC is isosceles with base angles congruent , then
∠ ABC = =
= 70°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, then
∠ AMN + ∠ BPM = ∠ ABC , that is
25° + ∠ BPM = 70° ( subtract 25° from both sides )
∠ BPM = 45°
∠ CPM and ∠ BPM are adjacent angles on a straight line and sum to 180°
∠ CPM + 45° = 180° ( subtract 45° from both sides )
∠ CPM = 135°
Answer:
see explanation
Step-by-step explanation:
The perimeter is the sum of the 3 sides, that is
perimeter = 8 + 12 + 17 = 37 cm
To use Heron's formula for area (A)
A =
where a, b and c are the lengths of sides and s the semi perimeter
s = 37 ÷ 2 = 18.5
let a = 8, b = 12 and c = 17, then
A =
=
= ≈ 43.52 cm² ( to 2 dec. places )
Answer:
The total number of ways to form a student governance committee is 1,211,760.
Step-by-step explanation:
The students senate consists of a total of 40 students.
The students are either Sophomores or Juniors or Seniors.
The number of students in each of these categories are as follows:
Sophomores = 18
Juniors = 12
Seniors = 10
A governance committee have to be selected from the students senate.
The committee have to made up of 2 sophomores, 2 juniors and 3 seniors.
Combinations can be used to select 2 sophomores from 18, 2 juniors from 12 and 3 seniors from 10.
Combinations is a mathematical technique used to determine the number of ways to select <em>k</em> items from <em>n</em> distinct items.
The formula is:
(1)
Compute the number of ways to select 2 sophomores from 18 as follows:
Thus, there are 153 ways to select 2 sophomores from 18.
(2)
Compute the number of ways to select 2 juniors from 12 as follows:
Thus, there are 66 ways to select 2 juniors from 12.
(3)
Compute the number of ways to select 3 seniors from 10 as follows:
Thus, there are 120 ways to select 3 seniors from 10.
The total number of ways to form a student governance committee that must have 2 sophomores, 2 juniors and 3 seniors is:
Total number of ways =
Thus, the total number of ways to form a student governance committee is 1,211,760.