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.
A fifty-fifty sugar-water solution would contain the same amount of water by weight as by sugar, that is, 0.5 lb water.
In other words, a solution that is made up of 0.5 lb sugar and 0.5 lb water is a 50% sugar concentration.
Usually, you create the inequality by casting the problem statement into mathematical terms. Then, solving the inequality can answer the question posed by the problem statement.
Example:
I want to carpet my 1600 ft² house, but I can only afford to spend $3000. Tax and installation costs are expected to add 20% to the total cost of the carpet. What price range of carpet should I be looking at in term of dollars per square yard?
Solution:
Let p represent the price per square yard of carpet. The problem statement tells me
(1600 ft²)×((1 yd)/(3 ft))²×p×(1 + 0.20) ≤ $3000 . . . . . created inequality
p×((1600×1.20)/9 yd²) ≤ $3000 . . . . . . . . . . . . . . . . . simplify left side
p ≤ $14.06/yd²
I can afford carpet that costs less than $14.06 per square yard.
Answer:
4x<=100
Step-by-step explanation:
she has 4 friends to spend the 100 dollars on because she wants to spend the same amount on each friend you can multiply 4x. you can't spend more than 100 but you can spend 100$ so it would be <=100
Answer:
A. Rational
B. Irrational
C. Rational
D. Rational
i'm 100% sure! just finished my quiz
<em>hope this helps </em>^.^ !!!!
