Step-by-step explanation:
![slope = \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 7 - 13}{5 - ( - 3)} \\ = \frac{ - 20}{8} \\ = \frac{ - 2 \times 10}{2 \times 4} \\ = \frac{ - 10}{4} \\ = \frac{ - 2 \times 5}{ 2 \times 2} = \frac{5}{2}](https://tex.z-dn.net/?f=slope%20%3D%20%20%5Cfrac%7Brise%7D%7Brun%7D%20%20%3D%20%20%5Cfrac%7By2%20-%20y1%7D%7Bx2%20-%20x1%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B%20-%207%20-%2013%7D%7B5%20-%20%28%20-%203%29%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B%20-%2020%7D%7B8%7D%20%20%5C%5C%20%3D%20%20%20%5Cfrac%7B%20-%202%20%5Ctimes%2010%7D%7B2%20%5Ctimes%204%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B%20-%2010%7D%7B4%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B%20-%202%20%5Ctimes%205%7D%7B%202%20%20%5Ctimes%202%7D%20%3D%20%20%5Cfrac%7B5%7D%7B2%7D%20%20)
Answer:
(a+b,c)
Step-by-step explanation:
Note that the midpoint formula is:
![(\frac{x_{1} +x_{2}}{2}, \frac{y_{1} +y_{2}}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx_%7B1%7D%20%2Bx_%7B2%7D%7D%7B2%7D%2C%20%5Cfrac%7By_%7B1%7D%20%2By_%7B2%7D%7D%7B2%7D%29)
Point A (0,0) and Point C (2a+2b,2c)
It follows that:
![(\frac{(2a+2b +0}{2}, \frac{2c+0}{2})\\(\frac{(2(a+b)}{2}, \frac{2c}{2})\\\\(a+b,c)](https://tex.z-dn.net/?f=%28%5Cfrac%7B%282a%2B2b%20%2B0%7D%7B2%7D%2C%20%5Cfrac%7B2c%2B0%7D%7B2%7D%29%5C%5C%28%5Cfrac%7B%282%28a%2Bb%29%7D%7B2%7D%2C%20%5Cfrac%7B2c%7D%7B2%7D%29%5C%5C%5C%5C%28a%2Bb%2Cc%29)
Using this table as a reference, you can see the following: A kilogram is 1,000 times<span>larger than one gram (so 1 kilogram = 1,000 grams). A centimeter is </span>100 times<span>smaller than one meter (so 1 meter = 100 centimeters). A dekaliter is </span>10 times<span>larger than one liter (so 1 dekaliter = 10 liters).</span>
Given:
The expression is:
![(-4)\times ...\times (-4) (11\text{ times})](https://tex.z-dn.net/?f=%28-4%29%5Ctimes%20...%5Ctimes%20%28-4%29%20%2811%5Ctext%7B%20times%7D%29)
To find:
The exponential notation for the given expression.
Solution:
We know that
...(i)
We have,
![(-4)\times ...\times (-4) (11\text{ times})](https://tex.z-dn.net/?f=%28-4%29%5Ctimes%20...%5Ctimes%20%28-4%29%20%2811%5Ctext%7B%20times%7D%29)
Using (i), the given expression can be written as:
![(-4)\times ...\times (-4) (11\text{ times})=(-4)^{11}](https://tex.z-dn.net/?f=%28-4%29%5Ctimes%20...%5Ctimes%20%28-4%29%20%2811%5Ctext%7B%20times%7D%29%3D%28-4%29%5E%7B11%7D)
Therefore, the exponential notation of the given expression is
.
Answer:
-14 - 12i
Step-by-step explanation:
Apply complex arithmetic rule: (ai)(b + ci) = -ac + abi
a = 2, b = 6, c = -7
-( -2(-7) + 2*6i )
-( 14 + 12i)
-14 - 12i