Recall that the diagonals of a rectangle bisect each other and are congruent, therefore:
Substituting the given expression for each segment in the first equation, we get:
Solving the above equation for x, we get:
Substituting x=10 in the equation for segment EI, we get:
Therefore:
Now, to determine the measure of angle IEH, we notice that:
therefore,
Using the facts that the triangles are right triangles and that the interior angles of a triangle add up to 180° we get:
Question 1:
For this case we have the following equation:
We observe that the equation is a polynomial of the second degree.
Therefore, the equation has two possible solutions.
The variable of the equation for this case is x.
In this case, we have an open equation because we have a variable.
Rewriting the equation we have:
Answer:
open, there is a variable.
Question 2:
For this case we have the following equation:
From here, we must clear the value of x.
For this, we follow the following steps:
1) Pass the value of 8x adding:
2) Pass the value of 6 adding:
3) Add the values on the same side of equality:
4) Pass the 8 to divide:
Answer:
The value of x is given by:
Question 3:
For this case we have the following equation:
The ordered pair solution is the one that satisfies both sides of the equation.
For the point (6, 2) we have:
Substituting values we have:
We observe that both sides of the equation are equal.
Therefore, the ordered pair solution is (6, 2)
Answer:
An ordered pair that is a solution of the equation y = x-4 is:
(6, 2)