Answer:
x³ - 8x² - 11x + 148
Step-by-step explanation:
Given that x = 6 + i is a root then x = 6 - i is also a root
Complex roots occur as conjugate pairs.
The factors are therefore (x - (6 + i)) and(x - (6 - i))
Given x = - 4 is a root then (x + 4) is a factor
The polynomial is the product of the factors, that is
p(x) = (x + 4)(x - (6 + i))(x - (6 - i))
= (x + 4)(x - 6 - i)(x - 6 + i)
= (x + 4)((x - 6)² - i²)
= (x + 4)(x² - 12x + 36 + 1)
= (x + 4)(x² - 12x + 37) ← distribute
= x³ + 4x² - 12x² - 48x + 37x + 148
= x³ - 8x² - 11x + 148
<span> −3⋅(6.48)=(−3⋅6)+(−3⋅0.4)+(−3⋅0.08) </span>correctly applies the distributive property
Answer:
B) 2x - 12x - 18 = 8
Step-by-step explanation:
2x - 3y = 8
If y = 4x - 6, then substitute and solve:
2x - 3(4x - 6) = 8
2x - 12x - 18 = 8
10x - 18 = 8
10x = 8 + 18
10x = 26
x = 26/10
x = 2.6
y = 4(2.6) - 6
y = 10.4 - 6
y = 4.4
<h3>Answer: 7366.96 dollars</h3>
========================================================
Use the compound interest formula:
A = P(1+r/n)^(n*t)
where in this case,
A = 12000 = amount after t years
P = unknown = deposited amount we want to solve for
r = 0.05 = the decimal form of 5% interest
n = 1 = refers to the compounding frequency (annual)
t = 10 = number of years
-------
Plug all these values into the equation, then solve for P
A = P(1+r/n)^(n*t)
12000 = P(1+0.05/1)^(1*10)
12000 = P(1.05)^(10)
12000 = P(1.62889462677744)
12000 = 1.62889462677744P
1.62889462677744P = 12000
P = 12000/1.62889462677744
P = 7366.95904248911
P = 7366.96
