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:
meter
Step-by-step explanation:
We have to write first what is known from the information.
Let's say, length is L, width is W, and height is H
1. The length of the box is 2 1/2 m = 2,5 m = 5/2 m, it is 1 9/16 = 25/16 times it's width (L). So we have the equation :
L ≡ 
Then we find the W. From the fraction above, we found W equals to 
meter
2. What is the height of the box, if its volume is 12 3/4 m^3 = 51/4 m^3
Formula of a volume is :
The area wide times the height
In this problem, the equation is :
L × W × H = Volume
Insert the numbers,
× 
× H = 
From the fraction above, we can find that H equals to
meter
Assuming that he read at the same speed last summer, 2,724 pages.
a. The speed is represented by 7 miles an hour
b. f(t)=7t
c. 28 miles
Answer:
n= 4f/5+90
Step-by-step explanation:
f= 5(n−90)
/4 (simplify)
f * 4=5(n−90) (multiply 4 on both sides)
4f=5(n−90) (regroup)
4f/5
=n−90 (divide 5 on both sides)
4f/5
+90=n (add 90 to both sides)
