Answer:
Step-by-step explanation:
This is a third degree polynomial because we are given three roots to multiply together to get it. Even though we only see "2 + i" the conjugate rule tells us that 2 - i MUST also be a root. Thus, the 3 roots are x = -4, x = 2 + i, x = 2 - i.
Setting those up as factors looks like this (keep in mind that the standard form for the imaginary unit in factor form is ALWAYS "x -"):
If x = -4, then the factor is (x + 4)
If x = 2 + i, then the factor is (x - (2 + i)) which simplifies to (x - 2 - i)
If x = 2 - i, then the factor is (x - (2 - i)) which simplifies to (x - 2 + i)
Now we can FOIL all three of those together, starting with the 2 imaginary factors first (it's just easier that way!):
(x - 2 - i)(x - 2 + i) =
Combining like terms and canceling out the things that cancel out leaves us with:
Remembr that , so we can rewrite that as
and
That's the product of the 2 imaginary factors. Now we need to FOIL in the real factor:
That product is
which simplifies down to
And there you go!
Answer:
10
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors
Answer: The Area is 35 square centimeters.
Key:
B1 = Base #1
B2 = Base #2
H = height
* = multiply
/ = divide
Step-by-step explanation:
First, write down the formula needed: (B1 + B2) * H / 2 = Area
Now Fill in what you know:
(6 + 8) * 5 / 2 = Area
B1 is 6 cm
B2 is 8 cm
The Height is 5cm (TIP: the height is usually in a vertical direction).
&
The Area is still unknown
Let’s Answer the equation now:
(B1 + B2) * H / 2 = Area
(6 + 8) * 5 / 2 = Area
(14) * 5 / 2 = Area
70 / 2 = Area
Area = 35 square centimeter (cm).
I hoped this helped.
Answer:
176 mm
Step-by-step explanation:
The circumference of a circle is the perimeter of a circle (length of a circle). The circumference of a circle is given as:
Circumference (C) = 2πr = πd, where d is the diameter
The circumference of a circle with diameter 7 mm is:
C = πd = 22/7(7) = 22 mm
The length of the paper to round the cylindrical pencil is the same as the perimeter of the pencil which is 22 mm.
To round the pencil 8 times, the length of the paper needed = 8 × 22 mm = 176 mm
Answer: x - 4 without the absolute value bars surrounding it
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Explanation:
If x is larger than 4, then x-4 is positive. For example, if x = 5, then
x-4 = 5-4 = 1
So for cases when x > 4, the |x-4| and x-4 are the same identical expression. Try out more values of x to compare the two outputs. I recommend making a table with 3 columns. You'll have x in column 1, then |x-4| in column 2, and x-4 in column 3. You should find that the outputs for columns 2 and 3 are identical when x is larger than 4.
It's only when x < 4 is when |x-4| and x-4 differ. Instead we would say |x-4| = -(x-4). But we aren't focused on this case.
In short, when x > 4, we simply drop the absolute value bars to get the answer x - 4