The arrow on the spinner is to be spun once.
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Answer:
The value of x is .
Step-by-step explanation:
Please look at the figure attached to get more clear solution.
We have given:
FG||CB
And the line that cut the parallel line is transversal so, here BA is transversal
And alternate interior angles on transverse line are equal
So, ∠1=∠4
And ∠4=
Hence, ∠1=∠4=
And On FG the sum of angles will be
∠3+∠2+∠1=
+∠2+
=
Hence, ∠2=
Now, we know that the sum of interior angles is equal to the exterior angle:
Therefore, ∠2+∠5=∠6+∠7
On simplification we get:
Hence, the value of x is .
Two equations will be called independent if their graphs touch only on one point (they have one solution for the x-value and one solution for the y-value), and two equations will be dependent if they touch at every point (there is an infinite number of solutions).
This definition of independent and dependent equations is shown in the following diagram. Consider that there are two lines, one red line and one blue line:
They are independent if they touch only on one point and dependent if they touch at every point (they are the same line).
In our case, we are asked to write an equation in order to create an independent consistent linear system.
Note: Consistent means that the system has a solution.
First, we graph the given equation:
There are many different equations that will form an independent consistent linear system with this equation.
We are going to choose the following line equation:
Because when we graph this equation next to the previous line:
We can see that they touch at one point, thus there is a solution and the system is independent --> we have created an independent consistent linear system.
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