Answer:
A) 2 + i
Step-by-step explanation:
F(x) = x^3 - 3x^2 + x + 5
0 = x^3 - 3x^2 + x + 5
0 = (x+1)(x^2 - 4x + 5)
Great, now we can separate these two parenthesis expressions because of the Zero Product Property. Start with the simple one:
0 = x + 1
<u>x = -1</u>
We have our first real root! But it doesn't look like that's one of the answer choices, so move on to the other expression:
0 = (x^2 - 4x +5)
This expression can't be factored, so we will use the quadratic formula (which is x = 
).
First solve for the positive part:
= (4 + sqrt(16-20)) / 2
= 4 + sqrt(-4) / 2
= 4 + 2i / 2
<u>= 2 + i</u>
Then for the negative part:
= (4 - sqrt(16-20)) / 2
= 4 - sqrt(-4) / 2
= 4 - 2i / 2
<u>= 2 - i</u>
<u></u>
<u>2 + i</u> is answer choice A! Our other roots, <u>2 - i</u> and <u>-1</u>, aren't answer choices.
Using translation concepts, it is found that the equation that represents the new function is:
The cube root parent function is given by:
![y = \sqrt[3]{x}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5D%7Bx%7D)
<h3>Translation:</h3>
The function goes through these following translations:
- Vertically stretched by a factor of 3, that is, it is multiplied by 3, hence
![y = 3\sqrt[3]{x}](https://tex.z-dn.net/?f=y%20%3D%203%5Csqrt%5B3%5D%7Bx%7D)
.
- Reflected over the x-axis, that is, it is multiplied by -1, hence
![y = -3\sqrt[3]{x}](https://tex.z-dn.net/?f=y%20%3D%20-3%5Csqrt%5B3%5D%7Bx%7D)
.
- Translated 8 units down, that is, 8 is subtracted from the function, hence
![y = -3\sqrt[3]{x} - 8](https://tex.z-dn.net/?f=y%20%3D%20-3%5Csqrt%5B3%5D%7Bx%7D%20-%208)
.
Then, the equation is:
To learn more about translation concepts, you can take a look at brainly.com/question/13671886
Answer:
A is the anser
Step-by-step explanation:
Answer:
-(5 n + 6)
Step-by-step explanation:
Simplify the following:
-4 (n + 1) - (n + 2)
-4 (n + 1) = -4 n - 4:
-4 n - 4 - (n + 2)
-(n + 2) = -n - 2:
-4 - 4 n + -n - 2
Grouping like terms, -4 - 4 n - 2 - n = (-4 n - n) + (-4 - 2):
(-4 n - n) + (-4 - 2)
-4 n - n = -5 n:
-5 n + (-4 - 2)
-4 - 2 = -(4 + 2):
-5 n + -(4 + 2)
4 + 2 = 6:
-5 n - 6
Factor -1 out of -5 n - 6:
Answer: -(5 n + 6)
Put the value of x = -3 to the expression x · x - 2x:
<h3>(-3)(-3) - 2(-3) = 9 + 6 = 15</h3>
