Hakims car travels 600 feet in 20 seconds. Andres mortar cycle travels 300 feet in 12 seconds. Which is faster, the car or the m
otorcycle?
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2 answers:
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Normally, we could add exponents.
however, that only is possible when the bases are the same
recall what exponents mean
12³=12*12*12
so we cannot add exponents for 12³*11³ because that means 12*12*12*11*11*11
it would not equal 12⁶ or 11⁶
or you could refer to the rule
notice when x=x then we can add the bases
fun fact below
we can reverse a previous exponential rule like this
since
then 
therefor
we can't add the exponents because the bases are not the same
however, that only is possible when the bases are the same
recall what exponents mean
12³=12*12*12
so we cannot add exponents for 12³*11³ because that means 12*12*12*11*11*11
it would not equal 12⁶ or 11⁶
or you could refer to the rule
notice when x=x then we can add the bases
fun fact below
we can reverse a previous exponential rule like this
since
therefor
we can't add the exponents because the bases are not the same
Let x be the number of weeks; therefore, the two linear equations are
Where T stands for the punches on the tea punch card and C for the punches on the coffee punch card.
Solving by substitution. Set T=C, then
Thus, substitute the value of x=3 into the first equation,
Thus, after 3 weeks, Josiah will have the same number of punches on each card, and he will have 23 punches on each card.