Answer:
6.75 × 10^3
Step-by-step explanation:
Move the decimal 3 times to the left so that the resulting number, m = 6.75, is greater than or equal to 1 but less than 10
Since we moved the decimal to the left the exponent n is positive
n = 3
Write in the scientific notation form, m × 10^n
6.75 × 10^3
A(-5,5)
B(4,5)
C(2,0)
D(-5,-2)
AB,BC,CD,DA
AB = [4-(-5)),5-5]=[9,0]
Lenght
![AB= \sqrt{9^2+0^2}= \sqrt{81} =9](https://tex.z-dn.net/?f=AB%3D%20%5Csqrt%7B9%5E2%2B0%5E2%7D%3D%20%5Csqrt%7B81%7D%20%20%3D9)
BC = [2-4,0-5]=[-2,-5]
Lenght
![BC=\sqrt{(-2)^2+(-5)^2}=\sqrt{4+25}=\sqrt{29}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%28-2%29%5E2%2B%28-5%29%5E2%7D%3D%5Csqrt%7B4%2B25%7D%3D%5Csqrt%7B29%7D)
CD = [-5-2,-2-0]=[-7,-2]
Lenght
![CD=\sqrt{(-7)^2+(-2)^2}=\sqrt{49+4}=\sqrt{53}](https://tex.z-dn.net/?f=CD%3D%5Csqrt%7B%28-7%29%5E2%2B%28-2%29%5E2%7D%3D%5Csqrt%7B49%2B4%7D%3D%5Csqrt%7B53%7D)
DA =[-5-(-5),-2-5]=[0,-7]
Lenght
![DA=\sqrt{0^2+(-7)^2}=\sqrt{49}=7](https://tex.z-dn.net/?f=DA%3D%5Csqrt%7B0%5E2%2B%28-7%29%5E2%7D%3D%5Csqrt%7B49%7D%3D7)
sorted from longest to shortest:
AB, CD,DA,BC
Answer:
![Distance = 3](https://tex.z-dn.net/?f=Distance%20%3D%203)
Step-by-step explanation:
Given
-12 and -15
Required
Solve the difference
The question you posted included the solution. However, the solution is incorrect;
The absolute difference is represented as:
![Difference = \vert a - b \vert](https://tex.z-dn.net/?f=Difference%20%3D%20%5Cvert%20a%20-%20b%20%5Cvert)
In this case:
![a = -12](https://tex.z-dn.net/?f=a%20%3D%20-12)
![b = -15](https://tex.z-dn.net/?f=b%20%3D%20-15)
So, the distance is calculated as:
![Distance = |-12 - (-15)|](https://tex.z-dn.net/?f=Distance%20%3D%20%7C-12%20-%20%28-15%29%7C)
Open bracket
![Distance = |-12 +15|](https://tex.z-dn.net/?f=Distance%20%3D%20%7C-12%20%2B15%7C)
![Distance = |3|](https://tex.z-dn.net/?f=Distance%20%3D%20%7C3%7C)
![Distance = 3](https://tex.z-dn.net/?f=Distance%20%3D%203)
(4,-2) (6,-2) (4,1) are co ordinates for the triangle after the movement
Answer:
13 is the number.
Step-by-step explanation:
Given:
Twice the difference of a number and 9 equals 8.
Let the unknown number be 'x'.
Therefore, as per question:
The difference of 'x' and 9 = ![x-9](https://tex.z-dn.net/?f=x-9)
Twice the difference means 2 times the difference. So, we multiply 2 to the difference. Therefore,
![2(x-9)](https://tex.z-dn.net/?f=2%28x-9%29)
Now, the above expression is equal to 8. So, we equate the above expression to 8. This gives,
![2(x-9)=8](https://tex.z-dn.net/?f=2%28x-9%29%3D8)
Solving for 'x', we get:
Using distributive property of addition and distributing 2 inside the bracket. This gives,
![2\times x-2\times 9=8\\\\2x-18=8\\\\2x=8+18\\\\2x=26\\\\x=\frac{26}{2}=13](https://tex.z-dn.net/?f=2%5Ctimes%20x-2%5Ctimes%209%3D8%5C%5C%5C%5C2x-18%3D8%5C%5C%5C%5C2x%3D8%2B18%5C%5C%5C%5C2x%3D26%5C%5C%5C%5Cx%3D%5Cfrac%7B26%7D%7B2%7D%3D13)
Therefore, the unknown number is 13.
Now, we can verify our answer.
![2(13-9)=26-18=8](https://tex.z-dn.net/?f=2%2813-9%29%3D26-18%3D8)
Therefore, the answer is correct.