Answer:
![P\approx 28.872\,\text{units}](https://tex.z-dn.net/?f=P%5Capprox%2028.872%5C%2C%5Ctext%7Bunits%7D)
Step-by-step explanation:
We are given coordinates of each of the vertices of the triangle ABC, hence we can use the distance formula to find the lengths of each of the side.
the distance formula is generally written as:
![r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28x_1-x_2%29%5E2%2B%28y_1-y_2%29%5E2%2B%28z_1-z_2%29%5E2%7D)
for the side AB: A(-2,2,3) and B(4,-4,3)
![AB = \sqrt{(-2-4)^2+(2-(-4))^2+(3-3)^2}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%28-2-4%29%5E2%2B%282-%28-4%29%29%5E2%2B%283-3%29%5E2%7D)
![AB = \sqrt{(-6)^2+(6)^2+(3-3)^2}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%28-6%29%5E2%2B%286%29%5E2%2B%283-3%29%5E2%7D)
![AB = \sqrt{72}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B72%7D)
for the side BC: B(4,-4,3) and C(7,6,4)
![BC = \sqrt{(4-7)^2+((-4)-6)^2+(3-4)^2}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%284-7%29%5E2%2B%28%28-4%29-6%29%5E2%2B%283-4%29%5E2%7D)
![BC = \sqrt{110}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B110%7D)
for the side CA: C(7,6,4) and A(-2,2,3)
![CA = \sqrt{(7-(-2))^2+(6-2)^2+(4-3)^2}](https://tex.z-dn.net/?f=CA%20%3D%20%5Csqrt%7B%287-%28-2%29%29%5E2%2B%286-2%29%5E2%2B%284-3%29%5E2%7D)
![CA = \sqrt{98}](https://tex.z-dn.net/?f=CA%20%3D%20%5Csqrt%7B98%7D)
Now we all the sidelengths:
to find the perimeter we need to just sum the three side lengths:
![P = AB + BC + CA](https://tex.z-dn.net/?f=P%20%3D%20AB%20%2B%20BC%20%2B%20CA)
![P = \sqrt{72} + \sqrt{110} + \sqrt{98}](https://tex.z-dn.net/?f=P%20%3D%20%5Csqrt%7B72%7D%20%2B%20%5Csqrt%7B110%7D%20%2B%20%5Csqrt%7B98%7D)
![P\approx 28.872\,\text{units}](https://tex.z-dn.net/?f=P%5Capprox%2028.872%5C%2C%5Ctext%7Bunits%7D)
this is the perimeter of triangle ABC
No, -8 - 2(3 + 2n) + 7n is not equivalent to -30 - 13n
Step-by-step explanation:
Let us revise the operation of the negative and positive numbers
- (-) + (-) = (-)
- (-) × (-) = (+)
- (-) + (+) = the sign of greatest [(-) if the greatest is (-) or (+) if the greatest is (+)]
- (-) × (+) = (-)
- (-) - (+) = (-)
- (+) - (-) = (+)
∵ The expression is -8 - 2(3 + 2n) + 7n
- Simplify it
∵ 2(3 + 2n) = 2(3) + 2(2n) = 6 + 4n
∴ -8 - 2(3 + 2n) + 7n = -8 - (6 + 4n) + 7n
- Multiply the bracket by (-)
∴ -8 - (6 + 4n) + 7n = -8 - 6 - 4n + 7n
- Add the like terms
∴ -8 - (6 + 4n) + 7n = (-8 - 6) - 4n + 7n
∴ -8 - (6 + 4n) + 7n = -14 + 3n
∴ -8 - 2(3 + 2n) + 7n is equivalent to -14 + 3n
∵ -14 + 3n ≠ -30 - 13n
∴ -8 - 2(3 + 2n) + 7n is not equivalent to -30 - 13n
No, -8 - 2(3 + 2n) + 7n is not equivalent to -30 - 13n
Learn more:
You can learn more about the directed numbers in brainly.com/question/10364988
#LearnwithBrainly
Answer:
86
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
it is the smallest number on a number line which is kind of what a thermometer is