Answer:
1. x = +/- 2
- 7
2. x =
+/- ![2i\sqrt{3}](https://tex.z-dn.net/?f=2i%5Csqrt%7B3%7D)
3. n =
+/- ![i\sqrt{2}](https://tex.z-dn.net/?f=i%5Csqrt%7B2%7D)
Step-by-step explanation:
1. Divide both sides by 2: (x + 7)^2 = 8
Square root both sides: x + 7 = +/- 2![\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D)
Subtract 7 from both sides: x = +/- 2
- 7
2. Square root both sides: x - 3 = ![\sqrt{-12}](https://tex.z-dn.net/?f=%5Csqrt%7B-12%7D)
Since there is a negative inside the radical, we need to have an imaginary number:
. So, ![\sqrt{-12} =i\sqrt{12} =2i\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B-12%7D%20%3Di%5Csqrt%7B12%7D%20%3D2i%5Csqrt%7B3%7D)
Add 3 to both sides: x =
+/- ![2i\sqrt{3}](https://tex.z-dn.net/?f=2i%5Csqrt%7B3%7D)
3. Divide by -5 from both sides: (n - 2)^2 = -2
Square root both sides: n - 2 = ![\sqrt{-2}](https://tex.z-dn.net/?f=%5Csqrt%7B-2%7D)
Again, we have to use i: ![n-2=\sqrt{-2} =i\sqrt{2}](https://tex.z-dn.net/?f=n-2%3D%5Csqrt%7B-2%7D%20%3Di%5Csqrt%7B2%7D)
Add 2 to both sides: n =
+/- ![i\sqrt{2}](https://tex.z-dn.net/?f=i%5Csqrt%7B2%7D)
Hope this helps!
Answer:
Step-by-step explanation:
The shape can be divided into two parts, let use the division in the question
So we have two rectangles
The area of a rectangle is given by l×b.
Let the big rectangle be 1
And the smaller rectangle be 2
Rectangle 1
Length is 16cm, breadth is 6cm
Area=l ×b
Area=16×6
Area=96cm^2
Rectangle two
The length will be 14-6=8cm
And the breadth will be 16-2=14cm
Then,
Area=l ×b
Area=14×8
Area=112cm^2
Total area is
Area1+Area2
112+96
Total area=208cm^2.
Answer: ±√2
Step-by-step explanation: A fraction is undefined when its denominator is =0 or undefined. so we need to get 2/3x²-6=0 or undefined. so we can also do 3x^2-6=0. Solving yields ±√2!
Answer:
-a-3b
Step-by-step explanation:
a+2b-2a-b+2(-2b)
-a+b-4b
-a-3b
-(a+3b)
The recurring decimal number 9.2424... expressed in mixed number is ![9\frac{24}{99}](https://tex.z-dn.net/?f=9%5Cfrac%7B24%7D%7B99%7D)
In the given decimal number, 2 is the digit at the tenth place and 4 is the digit at the hundredth place.
The fraction part
in the simplest form is ![\frac{8}{33}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B33%7D)
The whole number part is 9.
Therefore, the number 9.2424... as a mixed number in the simplest form is ![9\frac{8}{33}](https://tex.z-dn.net/?f=9%5Cfrac%7B8%7D%7B33%7D)