This question can be solved using the Herons equation where
A = SQRT [s*(s-a)*(s-b)*(s-c)]
A = area of the triangle
a, b and c are the sides of the triangle
s = (a+b+c)/2
Since we are given the area, we can express "s" as a function of the third side c. This can be substituted in the original equation so as to obtain an expression to solve for the third side c
s = (4+10+c)/2 = (14+c)/2
using the solver function of the calculator or MS Excel, the third side is 7.21 units
Step-by-step explanation:
cot x / (1 + csc x)
Multiply by conjugate:
cot x / (1 + csc x) × (1 − csc x) / (1 − csc x)
Distribute the denominator:
cot x (1 − csc x) / (1 − csc²x)
Use Pythagorean identity:
cot x (1 − csc x) / (-cot²x)
Divide:
(csc x − 1) / cot x
Answer:
x = 20
y = 10
m∡8 = 110°
Step-by-step explanation:
m∡1 + m∡2 = 180
5x + y + 3x + y = 180
8x + 2y = 180
m∡1 = m∡8 (they are alternate-exterior angles and are congruent)
5x + y = 3x + 5y
2x = 4y
x = 2y
Substitute '2y' for 'x' in 8x + 2y = 180
8(2y) + 2y = 180
18y = 180
y = 10
x = 2(10)
x = 20
m∡8 = 3(20) + 5(10) = 110°
723/100 is the answer to your question!
Answer:
12
Step-by-step explanation:
(# of pencils)x(3/4)=9
(# of pencils)x(0.75)=9
(# of pencils)=9/(0.75)=12
