Given:
The inequalities are:
To find:
The integer values that satisfy both inequalities.
Solution:
We have,
For , the possible integer values are
...(i)
For , the possible integer values are
...(ii)
The common values of x in (i) and (ii) are
Therefore, the integer values -1, 0 and 1 satisfy both inequalities.
Answer:
Step-by-step explanation:
Orthocenter is the intersection of altitudes.
We'll calculate the slopes of the two sides and their altitudes ad find the intersection.
<h3>Side QR</h3><u>Perpendicular slope:</u>
<u>Perpendicular line passes through S(-1, -2):</u>
<u>Perpendicular slope:</u>
<u>Perpendicular line passes through Q(-1, 5):</u>
The intersection of the two lines is the orthocenter.
<u>Solve the system of equations to get the coordinates of the orthocenter:</u>
<u>Find y-coordinate:</u>
The orthocenter is (1, 3)
If we plot the points, we'll see it is inside the triangle
