When working out an equation, if the result comes out like : x = 2, or y = 4.....a variable equal to a number, then there is 1 solution
if the result comes out like : 0 = 4, or 2 = 6...no variable and an incorrect result, then the equation has no solutions because ur lines are parallel.
if the result comes out like : 2 = 2 or 5 = 5...no variable and a true statement, then there will be infinite solutions because ur lines are coincident...they are the same line
Answer:
g(x) = -f(x)
Step-by-step explanation:
When we have a point (x, y) and we reflect it over the x-axis, the result of the reflection is the point (x, -y)
In this problem why is the easiest to substitute.
Just set the equations equal to each other because they both equal y
-x + 4 = 2x - 8
(You want to get all the x's to one side so add x to each side)
4 = 3x - 8
(next add 8 to both sides)
12 = 3x
(lastly divide 3 from both sides)
4 = x
You have got your x so now it is time to find that y just replace x to either of the two equations
y = 2(4) -8 or y = -(4) + 4
y = 8 - 8 y = 0
y = 0
Final Answer: y=0, x=4
To calculate the distance between two points, we can use a formula that is a variation Pythagorean Theorem. Look:
![\mathsf{d=\sqrt{(x_Q-x_P)^2+(y_Q-y_P)^2}}](https://tex.z-dn.net/?f=%5Cmathsf%7Bd%3D%5Csqrt%7B%28x_Q-x_P%29%5E2%2B%28y_Q-y_P%29%5E2%7D%7D)
"d" represents the distance and coordinates are expressed as follows: (x, y)
Let's go to the calculations.
![\mathsf{d=\sqrt{(x_Q-x_P)^2+(y_Q-y_P)^2}}\\\\ \mathsf{d=\sqrt{(7-3)^2+(4-(-8))^2}}\\\\ \mathsf{d=\sqrt{(4)^2+(4+8)^2}}\\\\ \mathsf{d=\sqrt{16+(12)^2}}\\\\ \mathsf{d=\sqrt{16+144}}\\\\ \mathsf{d=\sqrt{160}}\\\\ \mathsf{d=12,649110640673...}\\\\ \underline{\mathsf{d\approxeq12,6}}](https://tex.z-dn.net/?f=%5Cmathsf%7Bd%3D%5Csqrt%7B%28x_Q-x_P%29%5E2%2B%28y_Q-y_P%29%5E2%7D%7D%5C%5C%5C%5C%20%5Cmathsf%7Bd%3D%5Csqrt%7B%287-3%29%5E2%2B%284-%28-8%29%29%5E2%7D%7D%5C%5C%5C%5C%20%5Cmathsf%7Bd%3D%5Csqrt%7B%284%29%5E2%2B%284%2B8%29%5E2%7D%7D%5C%5C%5C%5C%20%5Cmathsf%7Bd%3D%5Csqrt%7B16%2B%2812%29%5E2%7D%7D%5C%5C%5C%5C%20%5Cmathsf%7Bd%3D%5Csqrt%7B16%2B144%7D%7D%5C%5C%5C%5C%20%5Cmathsf%7Bd%3D%5Csqrt%7B160%7D%7D%5C%5C%5C%5C%20%5Cmathsf%7Bd%3D12%2C649110640673...%7D%5C%5C%5C%5C%20%5Cunderline%7B%5Cmathsf%7Bd%5Capproxeq12%2C6%7D%7D)
The answer is 12,6 u.c.
8 becuase C(2) x B(4) = 8