sr814952

06.05.2020 • 

Mathematics

In 2014, Action Comics #1, a comic book with the first appearance of Superman, was sold for about $3,200,000. This comic book was originally sold in 1938 for $0.10. How can we measure how the value of Action Comics #1 changed since 1938? Many items increase or decrease in value over time. One way to express this is by using a percent. The new price is expressed as a percentage of the old price. For example, if the new price is 50% of the old price, this means that the new price is half the old price. If the new price is 200% of the old price, this means that the new price is double the old price. One example of an object with a value that could either increase or decrease over time is a house. Many factors determine the value of a house: market, location, nearby schools, appearance, condition, etc. If any of those variables change, the value of the house could go up or down. Use the interactive below to explore this idea.

Ответ:

claudioocampo5621

24.06.2021

Mathematics

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Well, m∠1 and m∠3 are congruent by the Vertical Angle Congruent Theorem (VACT). This means that because the angles are opposite of each other, their angles are the same because they are formed by the same two intersecting lines.

Because of this, we can set m∠1 and m∠3 equal to each other:

m∠1 = m∠3

(2x + 28) = (6x + 4)

2x + 28 = 6x + 4

-4x + 28 = 4

-4x = -24

-x = -6

x = 6

Knowing that x equals 6, we can use this to find m∠2. By the Supplementary Angles Theorem (SAT), angles that are on the same line add up to equal 180°. To use the SAT, we need to plug x in to find m∠1 or m∠3, because they are both the same:

x = 6

m∠1 = (2x + 28)

m∠1 = 2(6) + 28

m∠1 = 12 + 28

m∠1 = 40°

m∠3 also equals 40°.

Now that we have the value for ∠1 (or ∠3), we can use the SAT:

m∠2 + m∠3 = 180 ← You could also use m∠1, because they both equal the same!

m∠2 + 40 = 180

m∠2 = 140°

So, the measure of ∠2 is 140°.

If you have any questions, feel free to ask! :)

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