What is linear equation?
An equation between two variables that gives a straight line when plotted on a graph.
2x + 5xy - 3 = 0
x (2 + 5y) -3 = 0
x ( 2 + 5y ) = 3
2 + 5y = 3 / x
5y = (3/x) - 2
y = ( (3/x) - 2) / 5
According to the graph i don't think it's a linear equation.
Triangle EFG can also be proven to be a right triangle by using the following: D. Prove that KL is equal to c by Pythagorean Theorem.
<h3>What is the Pythagorean Theorem?</h3>The Pythagorean theorem states that the square of the longest side of a right triangle, which is the hypotenuse (c²) equals the sum of the squares of the other two legs of the right triangle (a² + b²).
If we apply the Pythagorean theorem, we would find the length of KL. If KL has the same length as c in triangle EFG, then we can say that triangle EFG is also a right triangle.
Therefore, the answer is: D. Prove that KL is equal to c by Pythagorean Theorem.
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From the given information,
a. The length of the belt is 180.28 ft
b. The height of the window from the ground is 100 ft
c. The length of the ramp needed is 141.42 ft
<h3>What is the Pythagorean theorem's formula?</h3>The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs of the triangle. I.e., (hypotenuse)² = (opposite)² + (adjacent)²
<h3>Calculation:</h3>It is given that,
The height of the silo is 150 feet
The distance from the belt to the silo is 100 feet
With the given measurements, a right-angled triangle is formed.
a. Finding the length of the belt:
From the diagram,
The height of the silo, sh = 150 ft
The base distance, sb = 100 ft
So, the length of the conveyor belt is the hypotenuse (bh) of the triangle formed.
On applying the Pythagorean theorem,
bh² = sb² + sh²
⇒ bh² = (100)² + (150)²
⇒ bh² = 32500
⇒ bh = √32500 = 50√13
∴ bh = 180.28 ft
Thus, the length of the belt is 180.28 ft.
b. Finding the height of the window from the ground:
It is given that the angle of elevation from the lower end of the belt(b) to a window(w) on the side of the silo is 45°.
This creates a special right-angled triangle. I.e.,
The angles of the new triangle are 90°- 45°. So, the third angle also becomes 45° (Since the sum of angles in a triangle is 180°)
So, the new triangle has angles of 90°- 45°- 45°
Thus, the new triangle is said to be an isosceles right angled triangle.
So, the two legs of the triangle are equal. I.e., sb = sw = 100 ft
Therefore, the height of the window from the ground(sw) is 100 ft
c. Finding the length of the ramp(bw) to the window:
Since we have
sw = 100 ft and sb = 100 ft
On applying Pythagora's theorem,
bw² = sb² + sw²
⇒ bw² = (100)² + (100)²
⇒ bw = √20000 = 141.42 ft
Therefore, the length of the ramp to the window is 141.42 ft.
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