Answer plss!
if the measure of angle 3 is 130 degrees, what is the measure of angle 7? why?

the measure of angle 7 is 130 degrees.

Step-by-step explanation:

The two blue lines are parallel. Therefore, angle 3 and angle 7 are corresponding angles. Corresponding angles are equal. Therefore, If the measure of angle 3 is 130 degrees, then the measure of angle 7 is also 130 degrees.

We can check by the following means:

The sum of the angles on a straight line is 180 degrees. Therefore,

Angle 4 = 180 - angle 3 = 180 - 130 = 50 degrees. Angle 4 and angle 6 are equal because they are alternate angles. Angle 6 and angle 7 are on a straight line. Therefore, angle 7 = 180 - angle 6 = 180 - 50 = 130 degrees

Both given solutions form a fundamental set of solutions, since they are solutions of the given differential equation and their Wronskian is which is different than 0, thus the solutions are linearly independent.

Step-by-step explanation:

In order to verify that the given functions form a fundamental set of solutions of the differential equation, we need to replace them on the differential equation. After we have verified both solutions, we can find the Wronskian to show that they are linearly independent.

Verifying the given functions as solutions of the given ODE.

For we can find the first derivative using product rule.

And the second derivative will be

Replacing on the given ODE we get

Combining like terms.

We can repeat the process for , so using product rule we have

And the second derivative is

Replacing on the given ODE we get

Combining like terms we get

Thus we have verified that the functions are solutions of the differential equation on the indicated interval.

Verifying that the solutions are linearly independent.

We can use the first derivatives to find the Wronskian

So we get

Simplifying we get

Using Pythagorean identity we get

So it is not 0, thus we have verified that the solutions are linearly independent, thus they form a fundamental set of solutions.