Answer:
Parallel lines are lines <u>in the same plane</u> that do not intersect, like lines on notebook paper.
The "in the same plane" requirement is important! Take a look at the attached image. Lines AD and DC don't intersect, but they are <u>not</u> in the same plane (face of the rectangular solid). We don't call those parallel, we call them skew lines.
Step-by-step explanation:
1/3x-10/3=-4
1/3x=-4+10/3
1/3x=-2/3
x=-2
X = 30
3x-5=x+55
2x=60
x=30
2(6-7x) = -8(x+6)
multiply the numbers inside the parenthesis with the numbers outside of them:
12 -14x = -8x-48
add 12 to each side:
-14x =-8x -36
add 8x to both sides
-6x = -36
divide both sides by-6
x = 6
For -1 <= x <= 1:
We can see that the graph forms a line parallel to the x-axis with a constant value 4.
Therefore of this interval : f(x) = 4
For 3 <= x <= 5:
We can see that the graph forms a linear function.
The equation for a linear function is : f(x) = mx + c where m is the slope and c is the intercept.
points (3,2) and (5,4) lie on this graph, we can use them to calculate the slope as follows:
m = (y2-y1) / (x2-x1) = (4-2) / (5-3) = 2/2 = 1
point (3,2) satisfies the equation as follows:
2 = 1(3) + c ............> c = -1
We can check the value of c using the other point (5,4) as follows:
4 = 1(5) + c ..............> c = -1
Based on the above calculations:
For the given interval: f(x) = x -1
