Answer:
x = - 8, x = - 4
Step-by-step explanation:
Given
x² + 15x + 30 = 3x - 2 ( subtract 3x - 2 from both sides )
x² + 12x + 32 = 0 ← in standard form
Consider the factors of the constant term (+ 32) which sum to give the coefficient of the x- term (+ 12)
The factors are + 8 and + 4 , since
8 × 4 = + 32 and 8 + 4 = + 12 , then
(x + 8)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 8 = 0 ⇒ x = - 8
x + 4 = 0 ⇒ x = - 4
Answer:
14
Step-by-step explanation:
The law of cosines is a² = b²+c²-2bc(cos A).
We will use s in place of a, since it is the unknown side. This makes b and c 8 and 9.
Angle A will be the angle opposite side a, or in this case side s. This makes it 111.
This gives us
s² = 8²+9²-2(8)(9)(cos 111)
s² = 64+81-2(8)(9)(cos 111)
s² = 145-144(cos 111)
s² = 196.605
Take the square root of each side:
√(s²) = √(196.605)
s = 14.02 ≈ 14
The volume of a triangular prism by definition is given by:
V = (Area of the base) * (height)
Substituting the values we have:
V = (30) * (6)
V = 180 in ^ 3
Answer:
The volume of the sail in the form of a triangular prism is:
V = 180 in ^ 3
