The three lines 8x+3y=12, 6y-7x=24, x+9y+33=0 intersect to form a triangle. Find the coordinates of its centroid
1 answer:
Answer:
coordinates of its centroid=(-1,-1)
Step-by-step explanation:
The given three lines are:
8x+3y=12, (1)
6y-7x=24 (2)
and x+9y+33. (3)
Multiplying equation (1) by 2 and subtract the equation (2), we get
23x=0⇒x=0,
Putting the value of x=0 in equation (2), we get
6y=24
y=4
Now, multiply the first equation by 3 and subtract the equation (3), we get
23x=69⇒x=3
Putting the value of x=3 in equation (1), we get
24+3y=12
3y=-12
y=-4
Also, multiplying the equation (3) by 7 and add the equation (2), we get
69y=-207
y=-3
Putting the value of y=-3 in equation (2), we get
6(-3)-7x=24
-18-24=7x
x=-6
So the centroid is located at (the average of the three vertices):
and
.
Thus, the coordinates of its centroid=(-1,-1)
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Answer:
We know that:
She makes $19 per hour of lifeguarding.
She makes $8 per hour walking dogs.
She can work at most 7 hours per week.
She must earn a minimum of $80 per week.
If x represents the number of hours lifeguarding and y represents the number of hours walking dogs, the inequalities will be:
x + y ≥ 7 hours.
(this says that she can work at most 7 hours per week)
x*$19 + y*$8 ≥ $80
(this says that she can earn a minimum of $80)
Then the system of inequalities is:
x + y ≥ 7 hours.
x*$19 + y*$8 ≥ $80
To graph these two we can write them as lines in standard form and simply graph both inequalities, the solution of the system will be the intersection between the solutions of each inequality.
Here we also should add the inequalities:
x ≥ 0
y ≥ 0
So we only look at the first quadrant.
The graph can be seen in the image below: (the dark blue is the solution region for the first inequality, the light blue one is the solution region for the second inequality)
One possible solution can be:
x = 4 and y = 1
or
x = 4 and y = 2
and there are a lot of other possible solutions.
