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:
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Answer:
D. 7.5 inches
Step-by-step explanation:
So, we can find the ratio of the big triangle to the small one by dividing the values of the hypotenuse.
So, 18/6 = 3
Big:small = 3:1
So, using this we can make an equation to find AD.
Let's say ED=x.
AD is basically ED (x) + AE (5).
Since ED is part of the small triangle, and AD is part of the big one, we can use the 3:1 ratio from above.
So, 
=3.
Multiply both sides by x, getting x+5 = 3x.
Subtract the x: -x -x
And you get 5=2x, giving you 2.5 = x.
However, we're not done yet, as 2.5 is the value of ED, but we need AD.
Remember, AD is = ED + AE.
So, AD = 2.5 + 5.
Finally, AD = 7.5
Expression: 5+5
Equation: 5a + 2b =5
Inequality: 2x > 2+5
Answer:
3xy^3z
Step-by-step explanation:
3 is the GCF between 3 and 21
Lowest number of x's is 1
Lowest number of y's is 3
Lowest number of z's is 1
