A spherical balloon is inflated with gas at a rate of 600 cubic centimeters per minute.

Drag the expressions into the boxes to correctly complete the table.

lora16 [44]

Answer:

SUMMARY:

$x^4+\frac{5}{x^3}-\sqrt{x}+8$ → Not a Polynomial

$-x^5+7x-\frac{1}{2}x^2+9$ → A Polynomial

$x^4+x^3\sqrt{7}+2x^2-\frac{\sqrt{3}}{2}x+\pi$ → A Polynomial

$\left|x\right|^2+4\sqrt{x}-2$ → Not a Polynomial

$x^3-4x-3$ → A Polynomial

$\frac{4}{x^2-4x+3}$ → Not a Polynomial

Step-by-step explanation:

The algebraic expressions are said to be the polynomials in one variable which consist of terms in the form $ax^n$ .

Here:

$n$ = non-negative integer

$a$ = is a real number (also the the coefficient of the term).

Lets check whether the Algebraic Expression are polynomials or not.

Given the expression

$x^4+\frac{5}{x^3}-\sqrt{x}+8$

If an algebraic expression contains a radical in it then it isn’t a polynomial. In the given algebraic expression contains $\sqrt{x}$ , so it is not a polynomial.

Also it contains the term $\frac{5}{x^3}$ which can be written as $5x^{-3}$ , meaning this algebraic expression really has a negative exponent in it which is not allowed. Therefore, the expression $x^4+\frac{5}{x^3}-\sqrt{x}+8$ is not a polynomial.

Given the expression

$-x^5+7x-\frac{1}{2}x^2+9$

This algebraic expression is a polynomial. The degree of a polynomial in one variable is considered to be the largest power in the polynomial. Therefore, the algebraic expression is a polynomial is a polynomial with degree 5.

Given the expression

$x^4+x^3\sqrt{7}+2x^2-\frac{\sqrt{3}}{2}x+\pi$

in a polynomial with a degree 4. Notice, the coefficient of the term can be in radical. No issue!

Given the expression

$\left|x\right|^2+4\sqrt{x}-2$

is not a polynomial because algebraic expression contains a radical in it.

Given the expression

$x^3-4x-3$

a polynomial with a degree 3. As it does not violate any condition as mentioned above.

Given the expression

$\frac{4}{x^2-4x+3}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}$

Therefore, is not a polynomial because algebraic expression really has a negative exponent in it which is not allowed.

SUMMARY:

$x^4+\frac{5}{x^3}-\sqrt{x}+8$ → Not a Polynomial

$-x^5+7x-\frac{1}{2}x^2+9$ → A Polynomial

$x^4+x^3\sqrt{7}+2x^2-\frac{\sqrt{3}}{2}x+\pi$ → A Polynomial

$\left|x\right|^2+4\sqrt{x}-2$ → Not a Polynomial

$x^3-4x-3$ → A Polynomial

$\frac{4}{x^2-4x+3}$ → Not a Polynomial

3 0

3 years ago

Select the graph that shows the solution set for the following system.<br> x + y < 2<br> x>2

kompoz [17]

Answer:

Answer is in the attachment.

Step-by-step explanation:

To graph x>2 consider first x=2. x=2 is a vertical line and if you want to graph x>2 you need to shade to the right of the vertical line.

To graph x+y<2, I will solve for y first.

x+y<2

Subtract x on both sides:

y<-x+2

Consider the equation y=-x+2. This is an equation with y-intercept 2 and slope -1 or -1/1. So the line you have in that picture looks good for y=-x+2. Now going back to consider y<-x+2 means we want to shade below the line because we had y<.

Now where you see both shadings will be intersection of the shadings and will actually by your answer to system of inequalities you have. In my picture it is where you have both blue and pink.

I have a graph in the picture that shows the solution.

Also both of your lines will be solid because your question in the picture shows they both have equal signs along with those inequality signs.

Just in case my one graph was confusing, I put a second attachment with just the solution to the system.

5 0

3 years ago

What is the effect on the graph of the function f(x) = V3x when f(x) is replaced with f(x + 4)?

andreev551 [17]

Answer:Replacing x with -x will reflect a graph across the y-axis. Multiplying x by 3 before the function is applied will compress the graph horizontally. This means the correct choice is D.

8 0

3 years ago

How do i completely factor 9c^4-36c^2?

VLD [36.1K]

You take out the biggest factor of 9 and 36 which is 9c^2. The factors both have the c variable in common so you take the least exponent and put it with the gcf.

9c^2(c^2+4)

8 0

3 years ago

Read 2 more answers

Carolyn says that point A and point B represent opposite integers. a. What is the opposite of the integer represent by point A?

zysi [14]

we are given

point-A= -7

point-B=8

(a)

opposite of point-A is negative of point-A value

so,

opposite of point-A is -(-7)

opposite of point-A is 7

opposite of point-B is negative of point-B value

so,

opposite of point-B is -8

opposite of point-B is -8

(b)

we can see that

opposite of point-A is 7

opposite of point-B is -8

they are not equal

so, this argument is FALSE.......Answer

4 0

3 years ago