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The measure of the angle ∠PQR is 90 degrees
<h3>How to prove that ∠PQR is 90 degrees?</h3>
The equation of the line PQ is given as:
3x - y - 2 = 0
The coordinates of the QR are given as:
(0, -2) and (6, -4)
Make y the subject in 3x - y - 2 = 0
y = 3x - 2
The slope of the above line is
m1 = 3
Next, we calculate the slope (m2) of points Q and R.
So, we have:
m2 = (y2- y1)/(x2 - x1)
This gives
m2 = (-4 + 2)/(6 - 0)
Evaluate
m2 = -1/3
The slopes of perpendicular lines are opposite reciprocals.
m1 = 3 and m2 = -1/3 are opposite reciprocals.
This means the lines PQ and QR are perpendicular lines.
The angle at the point of perpendicularity is 90 degrees
Hence, the measure of the angle ∠PQR is 90 degrees
Read more about linear equations at:
brainly.com/question/15602982
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Total number of wheels in the toy shop = 37 wheels
Number of wheels for tricycles = 3
Number of wheels for go-carts = 5
- Since the total number of tricycles and go-carts are not given, we solve this question using Assumption.
- Let's assume: We have 4 tricycles and 4 go-carts
(4 x 3) + (4 x 5)
= 12 + 20
= 32 wheels. This assumption is wrong.
- Let's assume: We have 4 tricycles and 5 go-carts
(4 x 3) + (5 x 5)
= 12 + 25
= 37 wheels. This assumption is correct.
Therefore, we have 4 tricycles and 5 go-carts in the toy shop.
To learn more, visit the link below:
brainly.com/question/23264573
I think this is how you do it...
Answer:
x<4
Step-by-step explanation:
3x < 12
Divide with 3 on each side
x< 4
In words x has all the real numbers that are less than 4 or x belongs to any number from -ve infinity to 4.
