Answer:1. 22
2. 35
Step-by-step explanation:
Part 1: If the roots of a polynomial are a, b, and c, then the factors can be written in the form (x - a), (x - b), and (x - c). In this case, we have (x - 3), (x - [3 + i]), and (x - [3 - i]). The three factors are (x - 3)(x - 3 - i)(x - 3 + i).
Part 2: The two factors with complex terms are (x - 3 - i)(x - 3 + i), and multiplying these terms as a difference of two squares can give:
(x - 3)^2 - i^2 = x^2 - 6x + 9 - (-1) = x^2 - 6x + 10
Part 3: We now multiply (x^2 - 6x + 10) by the remaining factor of (x - 3). This results in the cubic expression:
(x^2 - 6x + 10)(x - 3)
= x^3 - 3x^2 - 6x^2 + 18x + 10x - 30
= x^3 - 9x^2 + 28x - 30
Answer:
65.03square units.
Step-by-step explanation:
Find the diagram in the attachment below.
Area of the sector HJK = theta/360° × πr²
theta is the angle subtended by the sector = ∠HJK = 92°
r is the radius = HJ = 9units.
Substituting the given values in the formula:
Area of sector HJK = 92°/360° × π(9)²
Area of sector HJK = 23,399.28/360
Area of sector HJK = 65.03 square units to nearest hundredth
10% of $15 = 15/10= 1.5
1.5 x 2= 3 = 20%
15-3=12
Therefore the towel will be $12 with a 20% of coupon
