Answer: BC is 9 units long
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Work Shown:
Let x be the length of segment BC.
BC is parallel to DE, so this means that triangle ABC is similar to triangle ADE.
Side AB pairs with side AD (both are horizontal sides of triangle ABC and triangle ADE respectively)
Side BC pairs with side DE (both are vertical sides of triangle ABC and triangle ADE respectively)
Because of those facts above, we can end up with this proportion
AB/AD = BC/DE
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Let's plug in the given values and isolate x
AB/AD = BC/DE
12/20 = x/15
12*15 = 20*x ... cross multiply
180 = 20x
20x = 180
20x/20 = 180/20 ... divide both sides by 20
x = 9
Segment BC is 9 units long.
note: There is no need to calculate the length of segment AE. Though you are correct in stating that AE = 25.
The domain of the equation are all the possible values of the independent variables that would make the equation reasonable, possible or true. In this item, the independent variable is r. This could take a value of 0 up to the point when m is equal to zero.
m = 30 - 3r = 0
r = 10
The domain is therefore [0, 10].
The range is the value of the dependent variable which would be from 0 to the point when no video game is played. This is, [0, 30].
The function is discrete because r and m cannot take every value in the number line.
It is in simplest form. Decimal form is 14.4