Refer to the attached image.
Given:
The measure of
and
.
Also, Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.
To Prove:
is a right angle.
Proof:
Statements Reasons
1.
Given
2.
Given
3.
The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.
4.
Substitution property of equality
5.
Simplification
6.
JML is a right angle. Definition of right angle
Answer:
k = 30, 
Step-by-step explanation:
Since
is a solution, then it must satisfy the differential equation. So, we calculate the derivatives and replace the value in the equation. We have that

Then, replacing the derivatives in the equation we have:

Since
is a positive function, we have that
.
Now, consider a general solution
, then, by calculating the derivatives and replacing them in the equation, we get

We already know that r=5 is a solution of the equation, then we can divide the polynomial by the factor (r-5) to the get the other solution. If we do so, we get that (r-6)=0. So the other solution is r=6.
Therefore, the general solution is

Answer: Maria has 10 bills of 5€ and 10 bills of 10€.
She has a total of 150€.
Step-by-step explanation:
Let be "f" the number of 5€ bills that Maria has and "t" the number of 10€ bills that Maria has.
Set up a system of equations:

Use the Substitution method to solve the system of equations:
1. Solve for "f" from the first equation:

2. Substitute the equation obtained into the second equation and solve for "t".
Then:

3. Substitute the value of "t" into the equation
and evaluate:

Therefore, Maria has 10 bills of 5€ and 10 bills of 10 €.
So the total amount of money she has, is:

She has a total of 150€.
Answer:
38
Step-by-step explanation:
substitute the value of the variable into an equation, then simplify
Step-by-step explanation:
-10 or -20 satisfies the equation.
But when you substitute 10 in:
30-40<-50+8
-10<-42(wrong)
it's wrong