Answer and Step-by-step explanation:
f(x) = x³ + x² - 4x - 4
Using the rational roots theorem we can determine that 2 is a root of this equation:
f(2) = 2³ + 2² - 4.2 - 4 = 8 + 4 - 8 - 4 = 0
By using Ruffini's rule we can find the others roots
2 | 1 1 -4 -4
1 3 2 0
x² + 3x + 2 = 0
S = -3 P = 2
x' = -1
x" = -2
roots are: -2 -1 2
sign before -2: f(-3) = -10 < 0
sign between -2 and -1: f(-1.5) = 0.875 > 0
sign between -1 and 2: f(0) = -4 < 0
sign after 2: f(3) = 20 > 0
This way, we can see the behaviour of the function
Answer:
2 hours
Step-by-step explanation:
Distance = Rate * Time
If we replace these with the numbers in the problem and use "t" as the variable, it becomes:
30 miles = 15 mph * t
Now, to solve:
30 = 15t
<em>divide both sides by 15</em>
t = 2
add the units
time = 2 hours
Answer:
The discriminant is 0
Step-by-step explanation:
Since the graph of the quadratic equation has only one x-intercept, we can conclude that the quadratic has only one real root.
If a quadratic equation has only one real root, then the discriminant is 0
If x = -3 is the only x-intercept of the graph of a quadratic equation then the discriminant is 0
For the answer to this questions,<span>a. P (z ≤ z0) = 0.0401=P(z ≥ z0) = 1-0.0401 = 0.9599 = P(z ≤ -z0) = 0.9599
From tables z0 = -1.75
b. P (-z0 ≤ z ≤ z0) = .95 = P (z ≤ z0)- P (z ≤ -z0) = P (z ≤ z0)- P (z ≥ z0) =
P (z ≤ z0)-(1- P (z ≤ z0))
P (z ≤ z0) = (0.95+1)/2=0.975
From tables z0 = 1.96
c. P (-z0 ≤ z ≤ z0) = 0.90
the procedure is the same that exercise b P (z ≤ z0) = (0.9+1)/2=0.95
From tables the nearest value is z0 = 1.64
</span>d. P (-z0 ≤ z ≤ 0) = 0.2967= P (z ≤ 0) - P (z ≤ -z0) = P (z ≤ 0) - P (z ≥ z0) =
<span>P (z ≤ 0) - (1- P (z ≤ z0)) </span>
<span>P (z ≤ z0) = 0.2967 + 1 - P (z ≤ 0)= 0.2967 + 1 - 0.5 = 0.7967 </span>
<span>From tables z0 = 0.83
</span><span>
I hope my answer helped you
</span>
Answer: 8
Step-by-step explanation:
1. Rewrite the equation:
-2x^3 - 3x^2 + 4 x = -2
2. Plug in the value of x, -2
-2(-2)^3 - 3(-2)^2 + 4
3. Use order of operations (PEMDAS):
-2(-8) - 3(4) + 4
= 16 - 12 + 4
= 8