Determine whether the lines are parallel, perpendicular or neither: Line 1:4y−12=3x Line 2:2y−1.5x=−14
1 answer:
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We manipulate the expressions to model them in the pending-intersection form
Line 1:
Line 2:
By definition, we have that if two lines are parallel then their slopes are equal. It is observed that the slopes of both lines are equal, so the lines are parallel.
ANswer:
The lines are parallel
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The start price of it in t=0 is 3,500, as we can see on the graph. Then, the function becomes
Let's see at t=2, where the price is g=2000:
Take natural logarithm:
So, the difference between t=0 and t=2 is
And then we get the change of x in one year equal to 0.035.
So, the final equation is
You can insert any t and see that it is correct, for example t=7
Answer:
where y is positive.
The 2y in the denominator is not inside the fourth root
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Work Shown:
The idea is to get something of the form in the denominator. In this case,
To be able to reach the , your teacher gave the hint to multiply top and bottom by
For more examples, search out "rationalizing the denominator".
Keep in mind that only works if y isn't negative.
If y could be negative, then we'd have to say . The absolute value bars ensure the result is never negative.
Furthermore, to avoid dividing by zero, we can't have y = 0. So all of this works as long as y > 0.
Answer:
x=-2
Step-by-step explanation:
Given points are (-2,2) and (-2,-3).
Now we need to find equation of the line passing through the given points.
So let's begin by finding slope
which is undefined. That means graph of the line must be vertical as you can see that in given points, x-value is not changing.
Equation of vertical line is given by x=k where k is the fixed value of x-coordinate.
x-coordinate is -2 in given points.
Hence final equation is x=-2.