Answer:

Step-by-step explanation:
Set builder notation-
It is a notation for representing a set by enumerating its elements and stating the properties that its members must satisfy.
The given set is,

This set is comprised of all negative integers. So symbol Z should be used in this case.
The set builder notation for this set is,

Answer:
1. 
2. 
Step-by-step explanation:
1. You know that the average mass of an onion is 115 grams and Bill needs 4.0 pounds.
Then, since
, we can make the following conversion:

Then, the number of onions Bill needs is:
≈ 
2. Since
, we can make the following conversion:

Knowing that all the potatoes sold today at the store bring in $1,420 and 4.98 kilograms of potatoes is $1.75, we can calculate the amount of kilograms the grocery shoppers bought:

Explanation:
Factoring to linear factors generally involves finding the roots of the polynomial.
The two rules that are taught in Algebra courses for finding real roots of polynomials are ...
- Descartes' rule of signs: the number of positive real roots is equal to the number of coefficient sign changes when the polynomial is written in standard form.
- Rational root theorem: possible rational roots will have a numerator magnitude that is a divisor of the constant, and a denominator magnitude that is a divisor of the leading coefficient when the coefficients of the polynomial are rational. (Trial and error will narrow the selection.)
In general, it is a difficult problem to find irrational real factors, and even more difficult to find complex factors. The methods for finding complex factors are not generally taught in beginning Algebra courses, but may be taught in some numerical analysis courses.
Formulas exist for finding the roots of quadratic, cubic, and quartic polynomials. Above 2nd degree, they tend to be difficult to use, and may produce results that are less than easy to use. (The real roots of a cubic may be expressed in terms of cube roots of a complex number, for example.)
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Personally, I find a graphing calculator to be exceptionally useful for finding real roots. A suitable calculator can find irrational roots to calculator precision, and can use that capability to find a pair of complex roots if there is only one such pair.
There are web apps that will find all roots of virtually any polynomial of interest.
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<em>Additional comment</em>
Some algebra courses teach iterative methods for finding real zeros. These can include secant methods, bisection, and Newton's method iteration. There are anomalous cases that make use of these methods somewhat difficult, but they generally can work well if an approximate root value can be found.
Answer:
Arc length of the partial circle = 3π units
Step-by-step explanation:
Given question is incomplete; please find the complete question attached.
Formula for the arc length of a circle = 
Here θ is the angle formed by the sector at the center.
Angle that is formed at the center of the circle is = 360° - 90°
= 270°
So, length of the arc = 
= 3π
Therefore, length of the given partial circle is 3π units.
Answer:
x = 30
Step-by-step explanation:
Put in proportions
= 
Cross multiply and get 27x = 45 x 18
OR...
27x = 810.
THEN...
divide by 27 on both sides to get 30
x = 30