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:
x = 3, y = 2
Step-by-step explanation:
Substitute the values of x from each alternative in the previous <em>question</em>, then solve for y. This is depicted below.
- <em>A. y = -7, x = 5, 4(5) + 2y + 3 = 19</em>
- <em>B. y = 0 and x = 4, 4(4) + 2y + 3 = 19</em>
- <em>C. y = 2 and x = 3, 4(3) + 2y + 3 = 1</em>
- <em>D. y = 4, x = 2, 4(2) + 2y + 3 = 19</em>
Only the third option has a y value that is <em>comparable</em> to the value in the computations, according to the calculations.
As a result, the letter C is the correct response.
Answer:
2.9375 inches or 2 15/16"
Step-by-step explanation:
23 1/2 feet equals 282 inches
(1/8 ÷ 12) = (x ÷ 282)
cross-multiply:
35.25 = 12x
x = 2.9375 or 2 15/16 inches
Answer: 20
Step-by-step explanation:
Follow order of operations (PEMDAS)
20÷1÷[(10÷5)÷2] Given
20÷1÷[(2)÷2] Do 10÷5 in parenthesis
20÷1÷[(1)] Do (2)÷2
20÷1 Do 1÷[(1)]
20 Do 20÷1, and that is your answer
