Answer:

Step-by-step explanation:
The triangles are drawn below.
CD is perpendicular to AB as CD is height to AB.
Therefore, angles
°
So, triangles ΔCBD and ΔCAD are right angled triangles.
Now, from the right angled triangle ΔABC,

From ΔCBD,
is same as
.
So, 

Now, from ΔCAD,
is same as 
So, 

Hence, the unknown angles of both the triangles are:

Answer:
13.60 See the note below.
Step-by-step explanation:
Remark
This is just the reverse of the question you just did. This time you are trying to solve for c
Givens
Solution
c^2 = a^2 + b^2 Substitute the givens.
c^2 = 8^2 + 11^2 Expand
c^2 = 64 + 121 Combine the right side by adding
c^2 = 185 Take the square root of both sides.
sqrt(c^2) = sqrt(185) Complete the operation
c = 13.601 Round to the nearest 1/100 th
c = 13.60 Note: the zero must be there or the answer does not show the nearest 1/100 th
4x - 1 < 11
Add 1 to both sides
4x < 12
Divide both sides by 4
x < 3
x is less than 3
Answer:

Step-by-step explanation:
Given
Let
Undergraduates
Graduates
So, we have:
-- Total students
--- students to select
Required

From the question, we understand that 2 undergraduates are to be selected; This means that 2 graduates are to be selected.
First, we calculate the total possible selection (using combination)

So, we have:





Using a calculator, we have:

The number of ways of selecting 2 from 3 undergraduates is:




The number of ways of selecting 2 from 5 graduates is:




So, the probability is:




Answer:
Step-by-step explanation:
ABCD is a square.
side = 24 cm
Area of square = side * side = 24 * 24 = 576 cm²
Semicircle:
d = 24 cm
r = 24/2 = 12 cm
Area of semi circle =πr²
= 3.14 * 12 * 12
= 452.16 cm²
Area of shaded region = area of square - area of semicircle + area of semicircle
= 576 - 452.16 + 452.16
= 576 cm²
Perimeter:
Circumference of semicircle = 2πr
= 2 * 3.14 * 12
= 75.36
Perimeter = 2* circumference of semicircle + 24 + 24
= 2 * 75.36 + 24 + 24
= 150.72 + 24 + 24
= 198.72 cm