Answer:
A. The length of the third side is approximately 5 feet.
B. A =
, B =
and C =
.
Step-by-step explanation:
Let the triangle be ABC. Given two sides and an included angle, let us apply the cosine rule to determine the third length.
A. Let side a = 6 feet and c = 3 feet, thus;
=
+
- 2ac Cos B
=
+
- 2(6 x 3) Cos 
= 36 + 9 - 36 x 0.5
= 45 - 18
= 27
b = 
= 5.1962
b = 5.2 feet
b ≅ 5 feet
The length of the third side is approximately 5 feet.
B. Given that B =
, then let us apply the Sine rule to determined the measure of A.
=
So that,
= 
Sin A = 
Sin A = 0.99923
A =
0.99923
= 87.75
A ≅ 
Since the sum of angle in a triangle =
.
Then,
A + B + C = 
+
+ C = 
+ C = 
C =
- 
= 
C = 
Thus,
A =
, B =
and C =
.
The answer is B. (y = 4)
Further explanation:
–4y + 8 = 4(2y – 2) – 2(–16 + 8y)
= -4y + 8 = 4 * (2y -2) - 2 * (-16 + 8y)
= -4y + 8 = ( 4 * 2y - 4 *2 ) - (2 * -16 - 2 * 8y )
= -4y + 8 = 8y - 8 - ( -32 - 16y)
= -4y + 8 = 8y - 8 + 32 + 16y
Move y’s to the left & numbers to the right
= -4y - 8y - 16y = -8 + 32 - 8
= 12y - 16y = -16 + 32
Y = 16 / 28
Y = 4 = (B choice)
Answer:A
Step-by-step explanation:positive is bigger then negative.
When you factor you get (x-2)(x-3)=0 then x=2 and x=3