The first statement comes about because
a could be (say) 5
b could be (say) 6
Then c would be square root of 25 + 36 = 61 which is irrational.
I'm not sure of the wording of the second one. It reads like (5 + 6)^2 = 121 the two rationals added together make a rational number in my example. So I think that part is wrong. the second part is correct. For example sqrt(5) + sqrt(6) doesn't produce anything that is rational.
It doesn't have to. pi^2 + [cube root(10)]^2 does not produce anything rational and that is certainly not a perfect square. My first example shows that as well
I think the last one might be true.
Answer: 336.80 miles,
North of east
Step-by-step explanation:
Given
Plane lands at a point 324 miles east and 92 miles north
Distance is given by using Pythagoras theorem
![\Rightarrow d=\sqrt{324^2+92^2}\\\\\Rightarrow d=\sqrt{113,440}\\\\\Rightarrow d=336.80\ \text{miles}](https://tex.z-dn.net/?f=%5CRightarrow%20d%3D%5Csqrt%7B324%5E2%2B92%5E2%7D%5C%5C%5C%5C%5CRightarrow%20d%3D%5Csqrt%7B113%2C440%7D%5C%5C%5C%5C%5CRightarrow%20d%3D336.80%5C%20%5Ctext%7Bmiles%7D)
Direction is given by using figure i.e.
![\Rightarrow \tan \theta=\dfrac{92}{324}\\\\\Rightarrow \tan \theta=0.2839\\\\\Rightarrow \theta=15.85^{\circ}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Ctan%20%5Ctheta%3D%5Cdfrac%7B92%7D%7B324%7D%5C%5C%5C%5C%5CRightarrow%20%5Ctan%20%5Ctheta%3D0.2839%5C%5C%5C%5C%5CRightarrow%20%5Ctheta%3D15.85%5E%7B%5Ccirc%7D)
Direction is
North of east
Answer:
x = 2
Step-by-step explanation:
distribute -2 first
-2 + 8x = 3x + 8
-2 + 5x = 8
5x = 10
x = 2