The denominators stay the same and only the numerator changes.
-5 + 8i - 5 - 8i
Standard form is a + bi.
Combine like terms when adding or subtracting complex numbers.
-10 is the correct answer. Letter D
Answer:
The length is 6 meters.
Step-by-step explanation:
If its width is x meters then its length is 2x + 2 meters and we have the equation:
2x + 2(2x + 2) = 16
2x + 4x + 4 = 16
6x = 16 - 4
6x = 12
x = 2 meters.
Thus x is the width and the length is 2(2) + 2 = 6 meters.
Answer:
<em>B. (U+V)(U-V)</em>
Step-by-step explanation:
<u>Factoring</u>
The given expression is:
![4x^2-9y^6](https://tex.z-dn.net/?f=4x%5E2-9y%5E6)
It should be noted that both terms are perfect squares:
![(2x)^2=4x^2](https://tex.z-dn.net/?f=%282x%29%5E2%3D4x%5E2)
![(3y^3)^2=9y^6](https://tex.z-dn.net/?f=%283y%5E3%29%5E2%3D9y%5E6)
Since it's a difference of squares, we need to use the following pattern to factor the required expression:
![(U^2-V^2)=(U+V)(U-V)](https://tex.z-dn.net/?f=%28U%5E2-V%5E2%29%3D%28U%2BV%29%28U-V%29)
Thus, the answer is
B. (U+V)(U-V)
Answers: choice C) -4
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Explanation:
There are two basic ways to find the slope.
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The first way is where we use the slope formula
m = (y2-y1)/(x2-x1)
The two points are (x1,y1) = (-1,8) and (x2,y2) = (2,-4)
Plug the coordinate of those points into the slope formula, then simplify
m = (y2-y1)/(x2-x1)
m = (-4-8)/(2-(-1))
m = (-4-8)/(2+1)
m = (-12)/(3)
m = -4
The slope is -4
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The second way is to use a more visually oriented approach.
Start at (-1,8).
Draw a straight vertical line through this point. Then move to the point (2,-4) and draw a completely flat horizontal line through this point.
Mark the intersection between these two lines (vertical and horizontal) as point A
Now go back to (-1,8). Count the number of spaces you must move down to go from (-1,8) to point A. You should count out 12 spaces. This is the run, which in this case is negative since we're going downhill as we move from left to right
Then count 3 spaces to go from point A to (2,-4). This is the run
Rise = -12
Run = 3
Slope = Rise/Run = -12/3 = -4
As you can probably see, this effectively mirrors some parts of the slope formula above
No matter which method you use, the slope is -4
-4 is the same as -4/1
A slope of -4/1 means we go down 4 units and then move to the right 1 unit
So that means rise/run = -12/3 is the same as saying rise/run = -4/1