Shayna pays 20 for 5 bottles of juice. What is the unit price for the bottles of juice?
1 answer:
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Answer with positive exponent = or
Answer with negative exponent =
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Explanation:
The rule we use is
If we multiply two exponential expressions with the same base, then we add the exponents.
The base for each is 5. The exponents 4 and -7 add to -3.
This means
To convert to a positive exponent, we apply the reciprocal to the base. We go from 5, aka 5/1, to 1/5.
So,
First we assume that this is equal to zero
so what we notice is this is a sum of 2 perfect cube
recall that
a^3+b^3=(a+b)(a^2-ab+b^2)
125x^3+343=
(5x)³+(7)³=(5x+7)(25x²-35x+49)
now solve the part in second parenthasees because we can see that the first parenthasees (5x+7) is going to have a real root
remember quadratic formula
for ax^2+bx+c=0
x=
a=25
b=-35
c=49
x=
x=
x=
x=
x=
x=
x=
the comlex roots are
x=
and 
so what we notice is this is a sum of 2 perfect cube
recall that
a^3+b^3=(a+b)(a^2-ab+b^2)
125x^3+343=
(5x)³+(7)³=(5x+7)(25x²-35x+49)
now solve the part in second parenthasees because we can see that the first parenthasees (5x+7) is going to have a real root
remember quadratic formula
for ax^2+bx+c=0
x=
a=25
b=-35
c=49
x=
x=
x=
x=
x=
x=
x=
the comlex roots are
x=