Which line of music shows a glide reflection choices are below
2 answers:
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Answer: 41.5 min
Step-by-step explanation:
This problem can be solved with the Radioactive Half Life Formula:
(1)
Where:
is the final amount of the radioactive element
is the initial amount of the radioactive element
is the time elapsed
is the half life of the radioactive element
So, we need to substitute the given values and find from (1):
(2)
(3)
(4)
Applying natural logarithm in both sides:
(5)
(6)
Clearing :
This is the time elapsed
Answer:
y = 116°
Step-by-step explanation:
Given that <em>L₁ </em>|| <em>L</em>₂:
The <u>exterior angle theorem</u> states that the measure of an exterior angle of a triangle is equal to the sum of the two opposite and non-adjacent remote interior angles.
Also, ∠y° and ∠2x° are <u>same-side interior angles</u> formed by the intersection of the <em>hypotenuse</em> of the triangle that acts as a transversal to the parallel lines, <em>L₁ </em>and <em>L</em>₂. Given that ∠y° and ∠2x° are <u>same-side interior angles</u>, then it means that they are the supplements of each other, such that the sum of their measures is 180°.
Now that we have established these definitions, we can proceed with the solution.
<u>Equation 1</u>: ∠y° + ∠2x° = 180° ⇒ Same-side interior angles
<u>Equation 2</u>: ∠y° = ∠x° + ∠84° ⇒ exterior angle theorem
Substitute the value of m∠y° from Equation 2 into Equation 1 to solve for the value of x:
∠y° + ∠2x° = 180°
∠x° + ∠84° + 2x° = 180°
Combine like terms:
∠3x° + ∠84° = 180°
Subtract ∠84° from both sides:
∠3x° + ∠84° - ∠84° = 180° -∠84°
∠3x° = 180° - ∠84°
∠3x° = 96°
Divide both sides by 3 to solve for x:
∠x° = 32°
Substitute the value of x into Equation 2 to solve for y:
∠y° = ∠x° + ∠84°
∠y° = ∠32° + ∠84°
∠y° = 116°
Verify whether the values for x and y are correct by substituting their values into Equation 1 and 2:
<h3>Equation 1:</h3>∠y° + ∠2x° = 180°
116° + 2(32)° = 180°
116° + 64° = 180°
180° = 180° (True statement).
<h3>Equation 2:</h3>∠y° = ∠x° + ∠84°
116° = 32° + 84°
116° = 116° (True statement)
Therefore, the correct answer is: y = 116°.