I need help with solving a system of equations using elimination

Choose whether it's always, sometimes, never

Keith_Richards [23]

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.

3 0

3 years ago

Read 2 more answers

Simplify using i 3+2i/6+5i

alukav5142 [94]

The answer for your question question is 3+ 16/3 i

5 0

2 years ago

The average systolic blood pressure was found to be 140 mm for people who have high responsibility jobs, specifically investment

9966 [12]

Answer:

Option B)

$H_{0}: \mu = 140\text{ mm}\\H_A: \mu < 140\text{ mm}$

Step-by-step explanation:

We are given the following in the question:

Hypothesis:

The doctors and u=instructor claims that practicing yoga reduces blood pressure and hence is beneficial to people.

Population mean, μ = 140 mm

Sample mean, $\bar{x}$ = 139 mm

Sample size, n = 51

Sample standard deviation, s = 5 mm

Thus, we can design the null hypothesis and alternate hypothesis as

$H_{0}: \mu = 140\text{ mm}\\H_A: \mu < 140\text{ mm}$

The null hypothesis states that the population have a blood pressure of 140 mm. The alternate hypothesis states that yoga reduces the blood pressure and the sample has a blood pressure less than 140 mm.

Thus, the correct answer is

Option B)

$H_{0}: \mu = 140\text{ mm}\\H_A: \mu < 140\text{ mm}$

3 0

2 years ago

Can anyone help me with this please???

yanalaym [24]

Triangle = 3, Square = -1, Star = 5

8 0

2 years ago

Simplify the expression r^-3 s^5 t^2/r^2 st^-2

Hoochie [10]

R/s^5t^r2st-2/r^3
hope this helps

5 0

3 years ago