Answer= x³+4x²+16x+64
Expand the following:(x + 4 i) (x - 4 i) (x + 4)
(x - 4 i) (x + 4) = (x) (x) + (x) (4) + (-4 i) (x) + (-4 i) (4) = x^2 + 4 x - 4 i x - 16 i = -16 i + (4 - 4 i) x + x^2:
-16 i + (-4 i + 4) x + x^2 (4 i + x)
| | | | x | + | 4 i
| | x^2 | + | (4 - 4 i) x | - | 16 i
| | | | (-16 i) x | + | 64
| | (4 - 4 i) x^2 | + | (16 + 16 i) x | + | 0
x^3 | + | (4 i) x^2 | + | 0 | + | 0
x^3 | + | 4 x^2 | + | 16 x | + | 64:
Answer: x^3 + 4 x^2 + 16 x + 64
Answer:
- Dilation
- Reflection
- Translation
- Rotation
- Reflection
- Translation
Step-by-step explanation:
<em>Dilation</em>
Dilation multiplies the distance from a point to the center of dilation by the dilation factor. It does this for every point.
The center of dilation itself has zero distance from the center of dilation. Multiplying that by the dilation factor still gives zero, so the point that is the center of dilation remains unchanged.
<em>Reflection</em>
Reflection mirrors a point across some line. Each point ends up the same distance on the other side of the line that it was originally from the line.
The segment joining a point with its reflection is perpendicular to the line, so the line of reflection is the perpendicular bisector of the segment joining any point with its image.
<em>Rotation</em>
The angle defined by a point, the center of rotation, and the point's image is the angle of rotation. It is the same for every point.
The center of rotation doesn't go anywhere; it is "invariant".
<em>Translation</em>
Moving an image without changing its size or orientation is translation. Every point moves the same distance in the same direction, so any lines in the original figure have the same length and orientation in the translated figure: they are parallel.
To solve the problem shown above, you must follow the proccedure shown below:
1. By definition, Completary angles are those angles whose sum is 90 degrees and Suplementary angles are those angles whose sum is 180 degrees.
2. Keeping the information above on mind, you have:
<span>
(a) An angle measures 43 . What is the measure of its complement?
=90°-43°
=47°
(b) An angle measures 81 . What is the measure of its supplement?
</span>
=180°-81°
=99°
The answers are:
a) 47°
b) 99°
S= one length of square 1
S+1 = one length square 2
S+2= one length square 3
Our equation would be
S^2+(S+1)^2+(S+2)^2=365
Idk if it would be called distribute but.. distribute
S^2+S^2+2S+1+S^2+4S+4=365
Add like terms
3S^2+6S-360=0
Divide everything. By 3
S^2+2S-120=0
Factor
(S-10)(S+12)=0
The two solutions are:
S-10=0
S=10
S+12=0
S=-12
Since a length can’t be a negative the only possible solution would be 10
Since a perimeter is all lengths added together we can multiply the length by four to get the perimeter
Square 1
10*4=40
Perimeter is 40cm
Square 2
S+1 =11
11*4=44
Perimeter is 44cm
Square 3
S+2=12
12*4=48
Perimeter is 48cm
Add all the perimeters together to get the total perimeter:
Total perimeter:
40+44+48=132
The total perimeter is 132cm
I hope this helps. Sorry if I messed up anything on here it was kinda hard to keep track of everything. Feel free to ask if you need anything cleared up :)
