1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
elena-14-01-66 [18.8K]
3 years ago
9

Choose whether it's always, sometimes, never 

Mathematics
2 answers:
Keith_Richards [23]3 years ago
3 0

Answer: An integer added to an integer is an integer, this statement is always true. A polynomial subtracted from a polynomial is a polynomial, this statement is always true. A polynomial divided by a polynomial is a polynomial, this statement is sometimes true. A polynomial multiplied by a polynomial is a polynomial, this statement is always true.

Explanation:

1)

The closure property of integer states that the addition, subtraction and multiplication is integers is always an integer.

If a\in Z\text{ and }b\in Z, then a+b\in Z.

Therefore, an integer added to an integer is an integer, this statement is always true.

2)

A polynomial is in the form of,

p(x)=a_nx^n+a_{n-1}x^{x-1}+...+a_1x+a_0

Where a_n,a_{n-1},...,a_1,a_0 are constant coefficient.

When we subtract the two polynomial then the resultant is also a polynomial form.

Therefore, a polynomial subtracted from a polynomial is a polynomial, this statement is always true.

3)

If a polynomial divided by a polynomial  then it may or may not be a polynomial.

If the degree of numerator polynomial is higher than the degree of denominator polynomial then it may be a polynomial.

For example:

f(x)=x^2-2x+5x-10 \text{ and } g(x)=x-2

Then \frac{f(x)}{g(x)}=x^2+5, which a polynomial.

If the degree of numerator polynomial is less than the degree of denominator polynomial then it is a rational function.

For example:

f(x)=x^2-2x+5x-10 \text{ and } g(x)=x-2

Then \frac{g(x)}{f(x)}=\frac{1}{x^2+5}, which a not a polynomial.

Therefore, a polynomial divided by a polynomial is a polynomial, this statement is sometimes true.

4)

As we know a polynomial is in the form of,

p(x)=a_nx^n+a_{n-1}x^{x-1}+...+a_1x+a_0

Where a_n,a_{n-1},...,a_1,a_0 are constant coefficient.

When we multiply the two polynomial, the degree of the resultand function is addition of degree of both polyminals and the resultant is also a polynomial form.

Therefore, a polynomial subtracted from a polynomial is a polynomial, this statement is always true.

jeka57 [31]3 years ago
3 0

1) an integer added to an integer is an integer - Always

(adding two integers always results in an integer, if the two integers are positive, their sum will be positive, if two integers are negative, they will yield a negative sum)

2) a polynomial subtracted from a polynomial is a polynomial - Always

(if the polynomials are subtracted vertically, then the signs of the subtracted polynomial's need to be flipped to their opposites)

3) a polynomial divided by a polynomial is a polynomial - Sometimes

(this depends on the degree of polynomials in the numerator and the denominator)

4) a polynomial multiplied by a polynomial is a polynomial - Always

(when two polynomials are added, the product function is the addition of degree to both the polynomials)

You might be interested in
I need help with this please i have a test
zaharov [31]
Equation : (7x-4)+(3x-3)+(x) = 180
In the equation the sum of the internal angle in the triangle is 180 degrees. Use this equation to figure the sum of angle in any quadrilateral 180*(number of sides-2)
Solve the equation
Put all similar variable on one side
7x+3x+x-4-3=180
11x-7=180
11x=180+7
11x=187
x = 187/11
x = 17
Now find the angles by plugging in x
Angle F (7*17-4) = 115 degrees
Angle G (x) = 17 degrees
Angle E (3*17-3) = 48 degrees
If you add 115+48+17 you will get a sum of 180 this shows your answer is right


Angle F = 115
Angle G = 17
Angle E = 48
4 0
2 years ago
20 pts need this question asap
AlekseyPX
It's D because 140÷3.50 is 40
7 0
3 years ago
In one region, the september energy consumption levels for single-family homes are found to be normally distributed with a mean
tatyana61 [14]
The probability would be 0.1971.

We will calculate a z-score for each end of this interval.

z = (X-μ)/σ

For the lower limit:
z = (1100-1050)/218 = 50/218 = 0.23

For the upper limit:
z = (1225-1050)/218 = 175/218 = 0.80

Using a z-table (http://www.z-table.com) we see that the area under the curve to the left of, less than, the lower limit is 0.5910.  The area under the curve to the left of, less than, the upper limit is 0.7881.  To find the area between them, we subtract:

0.7881 - 0.5910 = 0.1971
6 0
3 years ago
Read 2 more answers
Mrs. Johnson has 159 chickens that she puts in shelters at night to keep safe. She places 12 chickens in a shelter and continues
Lesechka [4]

Answer:

3

Step-by-step explanation:

159-12=147-12=... keep going until you get to

15-12=3

8 0
3 years ago
Plzzz helppp giving brainiest to the first one
aniked [119]

Answer:

Arsenic-74-is used to locate brain tumors. It has a half-life of 17.5 days. ... C. Find the amount remaining after 6 days from a 90-mg sample

4 0
2 years ago
Read 2 more answers
Other questions:
  • Which function represents g(x), a reflection of f(x) =4(1/2)x across the x-axis?
    7·2 answers
  • 461÷301 give the answer​
    8·1 answer
  • How much does the atmosphere weigh over each square meter of surface? express this in tonnes (units of 1000 kg). recall the conv
    15·1 answer
  • The gross weight of a truck containing 30 pigs is 8 tons 1,123 pounds and 6 ounces. The average weight of one pig is 95 pounds 1
    10·1 answer
  • 5 friends go out for pizza the total bill comes up to £43.85 how much should each of the friends pay
    7·1 answer
  • The product of 7 and b is less than -35.
    8·2 answers
  • What’s the fraction of 65 percent
    12·1 answer
  • gọi (c) là đồ thị hàm số y = x ^ 4 + x tiếp tuyến. tiếp tuyến (C) vuông góc với đường thẳng d: x+ 5y =0 có phương trình là
    10·1 answer
  • A single die is rolled once. Find the probability of rolling a number less than 7.
    10·1 answer
  • Which of the following is equivalent to this expression?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!