Answer:
It has 10 three-point questions and 14 five-point questions
Step-by-step explanation:
Substitution (look it up it takes a long time to explain lol)
The distance between points
and
can be calculated using formula
![P_1P_2=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.](https://tex.z-dn.net/?f=P_1P_2%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D.)
1.
![AB=\sqrt{(-7-(-11))^2+(8-4)^2}=\sqrt{16+16}=\sqrt{32}=4\sqrt{2}\approx 5.657.](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%28-7-%28-11%29%29%5E2%2B%288-4%29%5E2%7D%3D%5Csqrt%7B16%2B16%7D%3D%5Csqrt%7B32%7D%3D4%5Csqrt%7B2%7D%5Capprox%205.657.)
2.
![AC=\sqrt{(-4-(-11))^2+(4-4)^2}=\sqrt{49+0}=\sqrt{49}=7.](https://tex.z-dn.net/?f=AC%3D%5Csqrt%7B%28-4-%28-11%29%29%5E2%2B%284-4%29%5E2%7D%3D%5Csqrt%7B49%2B0%7D%3D%5Csqrt%7B49%7D%3D7.)
3.
![CB=\sqrt{(-7-(-4))^2+(8-4)^2}=\sqrt{9+16}=\sqrt{25}=5.](https://tex.z-dn.net/?f=CB%3D%5Csqrt%7B%28-7-%28-4%29%29%5E2%2B%288-4%29%5E2%7D%3D%5Csqrt%7B9%2B16%7D%3D%5Csqrt%7B25%7D%3D5.)
Then
![P_{ABC}=5.657+7+5=17.657\approx 17.7](https://tex.z-dn.net/?f=P_%7BABC%7D%3D5.657%2B7%2B5%3D17.657%5Capprox%2017.7)
Answer: correct choice is C.
Answer:
2< AC<8
Step-by-step explanation:
For a triangle to exits sum of two sides must always be greater than the the third side
⇒ AC< AB+ BC =5+3=8 in
⇒AC<8 in
Also, the difference of the two sides must be smaller than the length of third side
⇒ AC> | AB-BC| = |5-3| =2
AC> 2 in
therefore, we can say 2< AC<8. Hence, AC can takes 3,4,5,6 values