Answer:
a. attached graph; zero real: 2
b. p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)
c. the solutions are 2, -3-3i and -3+3i
Step-by-step explanation:
p(x) = x³ + 4x² + 6x - 36
a. Through the graph, we can see that 2 is a real zero of the polynomial p. We can also use the Rational Roots Test.
p(2) = 2³ + 4.2² + 6.2 - 36 = 8 + 16 + 12 - 36 = 0
b. Now, we can use Briott-Ruffini to find the other roots and write p as a product of linear factors.
2 | 1 4 6 -36
1 6 18 0
x² + 6x + 18 = 0
Δ = 6² - 4.1.18 = 36 - 72 = -36 = 36i²
√Δ = 6i
x = -6±6i/2 = 2(-3±3i)/2
x' = -3-3i
x" = -3+3i
p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)
c. the solutions are 2, -3-3i and -3+3i
Answer:
no its not
Step-by-step explanation:
Answer:
Step-by-step explanation:
The equation that will model this situation will be of the form
where 
is the time in hours john has traveled since the gas station, and 
is the distance.
Now we know that John has already traveled 20 miles when he is at the gas station, this means at 
, 
; or
Thus we have
.
Now we need to figure out 
When John reaches home 2 hours later he notes that he has traveled 30 miles, which means he has traveled 30 - 20 = 10 miles; thus we have
Now we have the full equation:
Answer:
60% decrease
Step-by-step explanation:
To work out percentage change you takeaway the original number by the new number (New number-Original number) in this case 24-60=(-36), then divide the decreased amount by the original number and multiply the answer by 100 (Decrease amount ÷ Original number x 100) for this question you'd do (-36)÷60=(-0.6) then (-0.6)x100=(-60).
The minus shows its a decrease in percentage by 60%
(I hope this helps srry if it doesn't make sense)
Answer:
See attachment
Step-by-step explanation:
The given inequality is 
By the definition of the absolute value function, we obtain the compound inequality.
When we simplify we get:
The graph for the solution set is shown in the attachment
