For a perfect square
b² = 4*a*c
Comparing ax² + bx + c = 0 to x² + bx + 16
a = 1, c = 16
<span>b² = 4*a*c
</span>
<span>b² = 4*1*16
</span>
<span>b² = 64
</span>
b = √64
b = 8
The value of b = 8.
Answer: 24 cups.
Step-by-step explanation:
Let be "x" the amount of cups of peaches that Fred will need to make 60 cups of fruit salad.
According to the information given in the exercise, you know that the ratio of cups of peaches to cups of cherries is the one shown below:

Which can also be written as a fraction:

Then, if he uses 2 cups of peaches and 3 cups of cherries, he will get 5 cups of fruit salad.
Knowing the above, you can set up the following proportion:

Now you must solve for "x" in order to find its value. This is:

The answer is B: a^3b^4<span>
Proof:
Simplify the following:
(a^7 b^8)/(a^4 b^4)
Combine powers. (a^7 b^8)/(a^4 b^4) = a^(7 - 4) b^(8 - 4):
a^(7 - 4) b^(8 - 4)
7 - 4 = 3:
a^3 b^(8 - 4)
8 - 4 = 4:
Answer: a^3 b^4
PS: I just wish that you put the equation down as it's intended i.e.
a^7b^8/a^4b^4 is not the same as (<span>a^7b^8)/(a^4b^4)</span>
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