Find the value of y.
1 answer:
2x + 10 and x + 40 are vertical angles. By definition, vertical angles are congruent. So let's take care of that first. 2x+10 = x+40. Subtract an x from both sides and at the same time subtract 10 from both sides to get x = 30. Ok so x = 30. So what, right? We need y. Well, 2y+x is vertical with an angle that has the exact same measure as 2y+x because vertical angles are congruent. We know that all those angles add up to equal 360, so here's our equation: 
. Combining like terms gives us 5x+4y=360. We already have a value for x, remember, so we will sub it in. x=30. 5(30)+4y=360 and 150 + 4y = 360. Subtract 150 from both sides and we have 4y = 210. Divide both sides by 4 to get that y = 52.5. There you go!
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In Right Angled Triangle the lengths of the altitude of a hypotenuse is the geometric mean of the lengths of the segments of each of the legs is TRUE
What is a Right angled triangle?
A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
The right triangle's three sides are interconnected. The Pythagorean Theorem explains this connection. This theorem states that the Hypotenuse2 = Perpendicular2 + Base2.
- The right angle, or 90°, is always one angle.
- The hypotenuse is the side with the 90° angle opposite.
- The longest side is always the hypotenuse.
- The other two inner angles add up to 90 degrees.
Let assume a right-angled triangle ABC, right-angled at A.
Let AD be the perpendicular drawn from vertex A on hypotenuse BC, intersecting BC at D.
Now, In right-angle triangle ABC,
By using Pythagoras Theorem, we have
Now, In right-angle triangle ABD
Using Pythagoras Theorem, we have
Now, In right-angle triangle ACD,
On adding equation (2) and (3), we get
Now, using equation (1), the above equation can be rewritten as
can be further rewritten as
AD is geometric mean of BD and CD
Learn more about Right angled triangle from the link below
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Answer:
1125.4 Hz
Step-by-step explanation:
The resonant frequency is the frequency at with the inductive reactance is equal to the capacitive reactance. It is given by the relation ...
where L is in henries, and C is in farads.
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For the given circuit values, the resonant frequency is ...
The resonant frequency of this circuit is about 1125.4 hertz.