Given parameters:
Quadratic expression:
x² - 6x + 7 = 0
Solve using quadratic formula;
x =
From the equation;
a = 1, b = -6 and c = 7
Input the parameters and solve;
x =
x =
x =
x = or
x = 7 or -1
Answers:
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Explanation for part (a)
Consider four slots labeled A,B,C,D.
We have
We started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440
You can use the nPr permutation formula as an alternative method
in this case n = 18 and r = 4. The exclamation marks indicate factorial.
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Explanation for part (b)
Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.
Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.
There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)
73440/24 = 3060
You could use the nCr combination formula to get the same result
where n = 18 and r = 4 are the same from last time.
The connection between nPr and nCr is this
which can be rearranged into
these formulas are handy to help us go back and forth between nCr or nPr.
In order to isolate any term from an equation we need to clear out any different variable or numbers different from the one we want
in this case I is being multiplied by R, so we need to do the opposite which is divide in order to eliminate
But since this is an equality we must do it on both sides so de equation does not get altered
Then we simplify the equation