Answer:
Step-by-step explanation:
According to the Alternate Exterior Angles Theorem, "when two lines are cut by a transversal, the resulting alternate exterior angles are congruent."
This means that the two expressions above are to be set equal to each other because they are representative of two alternate exterior angles, which are congruent:
Add to both sides of the equation:
Subtract from both sides of the equation:
Divide both sides of the equation by the coefficient of , which is
:
~
Check your work by substituting for
in the initial equation:
It's correct!
Answer:
18
Step-by-step explanation:
From the given figure, we can see that angle (4x - 11) will be equal to angle 1 since they are corresponding angles
We notice that angle 1 is vertically opposite to angle (2x + 25)
Hence,
angle (4x - 11) = angle 1 = angle (2x + 25)
So, we can say that angle (4x - 11) = angle (2x + 25)
Now, solving for x:
4x - 11 = 2x + 25
2x = 36
x = 18
To find the vertical asymptotes set denominator as 0
Divide both sides of the equation by-3
Write -x as a difference
Factor out x from the expression
Factor out -3 from the expression
Factor out x+2 from the expression
When the product of factors equals 0, at least one factor is 0
Solve the equations for x
We are given, cost of the robot for 0 number of year = $16,000.
0 represents initial time of the robot.
After 10 year cost of the robot is = $0
The problem is about the number of the years and cost of the robot over different number of years.
So, we could take x coordinate by number of hours and y coordinate for y number of hours.
So, from the problem, we could make two coordinates for the given situation.
(x1,y1) = (0, 16000) and (x2,y2) = (10, 0).
In order to find the function of time, we need to find the rate at which robot rate depreciates each year.
Slope is the rate of change.
So, we need to find the slope of the two coordinates we wrote above.
We know, slope formula
Plugging values in formula, we get
Brecasue of depreciation we got a negative number for slope or rate of change.
Therefore, rate of depreciation is $1600 per year.
We already given inital cost, that is $16,000.
So, we can setup an a function
f(x) = -1600x + 16000.
But the problem is asked to take the variable t for time.
Replacing x by t, we get
f(t) = -1600t + 16000.
