Answer:
1/15
Step-by-step explanation:
Dividing a fraction can sometimes be seen as multiplying it by another fraction.
So instead of doing (1/5)/3 we can write it like this:
1/5 * 1/3
And since multiplying something by one third is equivalent to dividing it by three, nothing has really changed.
So now we can multiply the fractions.
First we'll take the numerator (the number above the line) of 1/5 and multiply it by the numerator or 1/3.
1 * 1 = 1
Then we do the same for the two denominators (the numbers <em>below</em> the line)
5 * 3 = 15
So now we've turned 1/3 * 1/5 into: (1*1)/(3*5),
Then simplified it to:
1/15
Answer:
Fourth degree polynomial (aka: quartic)
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Work Shown:
There isnt much work to show here because we can use the fundamental theorem of algebra. The fundamental theorem of algebra states that the number of roots is directly equal to the degree. So if we have 4 roots, then the degree is 4. This is assuming that there are no complex or imaginary roots.
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If you want to show more work, then you would effectively expand out the polynomial
(x-m)(x-n)(x-p)(x-q)
where
m = 4, n = 2, p = sqrt(2), q = -sqrt(2)
are the four roots in question
(x-m)(x-n)(x-p)(x-q)
(x-4)(x-2)(x-sqrt(2))(x-(-sqrt(2)))
(x-4)(x-2)(x-sqrt(2))(x+sqrt(2))
(x^2-6x+8)(x^2 - 2)
(x^2-2)(x^2-6x+8)
x^2(x^2-6x+8) - 2(x^2-6x+8)
x^4-6x^3+8x^2 - 2x^2 + 12x - 16
x^4 - 6x^3 + 6x^2 + 12x - 16
We end up with a 4th degree polynomial since the largest exponent is 4.
Answer:
The two numbers are 52 and 12.
Step-by-step explanation:
x+y=64
x=16+3y
Now, substitute the second equation into the first one.
16+3y+y=64
16+4y=64
4y=48
y=12
Substitute 12 into one of the equations in order to find x.
x=16+3(12)
x=16+36
x=52
