Why is
[tex] \sqrt{2x} [/tex]
is not a polynomial but
[tex] \sqrt{2}x [/tex]
is a polynomial?​

Answers

Answer 1

Answer:

Only natural numbers (i.e., non-negative integers) can be the exponents of variables in a polynomial.

Step-by-step explanation:

The exponent of variables in a polynomial should be natural numbers ([tex]0[/tex], [tex]1[/tex], [tex]2[/tex], [tex]3[/tex], [tex]\dots[/tex].)

[tex]\sqrt{2\, x}[/tex] is equal to [tex]\sqrt{2}\, x^{1/2}[/tex]. In this expression, [tex]x[/tex] is the variable. Its exponent is [tex]1/2[/tex], which isn't a natural number. On the other hand, [tex]\sqrt{2}\, x[/tex] is equivalent to [tex]\sqrt{2}\, x^{1}[/tex]. The exponent of variable [tex]x[/tex] is [tex]1[/tex], which is indeed a natural number.

[tex]\sqrt{2\, x}[/tex] isn't a polynomial because the exponent of variable [tex]x[/tex] isn't a natural number. On the other hand, [tex]\sqrt{2}\, x[/tex] is indeed a polynomial over the set of real numbers.


Related Questions

Mario completely covered a square floor using 98.5 ft ^2 of hardwood without any overlap
Which measurement is closest to the side length of this floor in feet?
9.5 ft
10 ft
25 ft
49 ft

Answers

The answer is 10 ft. I took the test but it didn't explain why it was the answer.

Question 12
What is the length of a segment with endpoints at (-3, 4) and (4, 4)?

Answers

Answer:

7 units. count from -3 to 4 on a number line

Step-by-step explanation:

Answer:(4,5)

Step-by-step explanation:

hi:) I need help with 11(a) , thanks!:))

Answers

Answer:

18.95

Step-by-step explanation:

ln 2 x ln (4x) = 3

ln 4x = = 3 / ln 2

ln4x =  3 / 0.69315 = 4.3281

4x = e^4.328 = 75.80

x =  18.95.

What is a sufficient sample?

Answers

Answer:

A good maximum sample size is usually 10% as long as it does not exceed 1000. A good maximum sample size is usually around 10% of the population, as long as this does not exceed 1000. For example, in a population of 5000, 10% would be 500. In a population of 200,000, 10% would be 20,000.

Step-by-step explanation:

help!! Will mark brainliest! Thank you

Answers

Answer:

34

Step-by-step explanation:

7y - 3x

7(4) - 3(-2)

28-(-6)

34

Solve. And Explain. r/9 = -4

Answers

Answer:

Step-by-step explanation:

r/9 = -4

then multiply 9 to -4 which equals -36

at last, r is equal to -36

So you need to have the variables on one side and the constants on another.

Since r is divided by 9 on the left side, you have to get rid of the 9 by multiplying. r/9 times 9 equals r, and -4 times 9 equals -36.

So r = -36

Hope this helped!

Given that (y+2), (y+3)and (2y^2+1) are consecutive terms of an arithmetic progression find the value of x

Answers

Answer:

In an arithmetic sequence, the difference between any consecutive terms should be always the same, then we have:

(y + 3) - (y + 2) = D

(2*y^2 + 1) - (y + 3) = D.

From the first equation, we can find the value of D:

y + 3 - y - 2 = D

1 = D.

Replacing this in the second equation, we have:

(2*y^2 + 1) - (y + 3) = 1

Now we can solve this equation:

2*y^2 + 1 - y - 3 - 1 = 0

2*y^2 - y - 3 = 0.

The solutions of this quadratic equation can be found with the Bhaskara's equation:

[tex]y = \frac{1 +- \sqrt{1^2 - 4*2*(-3)} }{2*2} = \frac{1+-\sqrt{25} }{4} = \frac{1+-5}{4}[/tex]

Then the possible values of y are:

y = (1 + 5)/4 = 6/4

y = (1 - 5)/4 = -1

Please help meeee > THANK YOU!!!!!

Answers

Answer:

39.   An adult male Western Banded Gecko is 5 1/2 (or 5.5) inches long.

41.    13,000 feet long, because 1 4/9 of 9,000 is 13,000.

43.  to answer the question we need to know if 35 out of 50 states is equal or greater than 3/4 if that is the case, the Constitution will be ammended, and that is represented like this:

35/50 >= 3/4

that inequality is saying that 35 states out of 50 is equal or greater than 3/4, lets simplify and modify the fractions to compare easily:

35/50 >= 3/4

7/10 >= 3/4

now we need to find the least common multiplier of 10 and 4 to take the fractions to a common denominator and compare easy. Lets multiply numerator and denominator for a correct number to get the fractions to denominator common 20, the lcm:

7/10 >= 3/4

(2/2)(7/10) >= (5/5)(3/4)

2*7/2*10 >= 5*3/5*4

14/20 >= 15/20

we can see that the inequality does not hold, so,

35/50 >= 3/4

does not hold either, therefore the Constitution cannot be ammended

40.  10 students play chess and sudoku,

30*2/5 is 12, out of 12; the number of students that play chess,5/6 play sudoku.

So..12*5/6 is 10 and that is the number of students that play both sudoku and chess.

42. Four fifths of 7/8 will be less than 7/8 (because you've multiplied by a number less than 1).

Similarly, 7/8 of 4/5 will be less than 4/5.

This means that the product will be less than each of the original factors.  

answer: no

44.  The answer is 7/12 because 3/4 - 1/6= 7/12

3/4 converts to 9/12 and 1/6 converts to 2/12. The domanaters stay the same, but 9-2=7. that is how you get 7/12

The direction angle of a vector is 135o. The x-component of the vector is -3. What is the y-component of this vector

Answers

Answer:

3

Step-by-step explanation:

the vector somewhat looks like this:

 ^

_\|_             the angle is 135 degrees, and the x component is -3

    |               To find the y component given the direction angle and x component, use the formula y_comp = tan(angle) * x_comp

tan (135 degrees) * -3 = 3

You can also use the graph and geometry, but that method is not recommended for beginners as it is very easy to make a mistake. The graph should be used to check if your answer makes sense.

Create a real-world problem that represents 2/3 and 2/5.

Answers

Answer: Hi!

Sara had 2/3 of a piece of cake. Jasmine had 2/5 of a piece of cake. How much cake did Sarah and Jasmine have in total?

Hope this helps!

Answer:

If Kaylah had 2/5 of a pizza, and Allia had 2/3 of a pizza how much would they eat together?

Which statement is true about the end behavior of the function represented by the graph?

As x approaches 1, f(x) approaches 25.
As x approaches −∞, f(x) approaches −∞, and as x approaches ∞, f(x) approaches −∞.
As x approaches −∞, f(x) approaches −4, and as x approaches ∞, f(x) approaches 7.
As x approaches −∞, f(x) approaches −∞, and as x approaches ∞, f(x) approaches ∞.

Answers

End behavior always involves x approaching positive and negative infinity. So we'll cross off the choice that says "x approaches 1".

The graphs shows both endpoints going down forever. So both endpoints are going to negative infinity regardless if x goes to either infinity.

Answer: Choice BAs x approaches −∞, f(x) approaches −∞, and as x approaches ∞, f(x) approaches −∞.

Another way to phrase this would be to say "f(x) approaches negative infinity when x goes to either positive or negative infinity"

End behavior always involves x approaching positive and negative infinity. So we'll cross off the choice that says "x approaches 1".

The graphs shows both endpoints going down forever. So both endpoints are going to negative infinity regardless if x goes to either infinity. (Option B)

What is end behavior in graphs?

End behavior refers to the behavior of a graph as the x-values approach positive or negative infinity.

It describes how the graph behaves at the far left and far right ends.

End behavior can be categorized as increasing or decreasing, and it helps understand the long-term trend or direction of the graph.

Learn more about end behavior at:

https://brainly.com/question/12619590

#SPJ2

What is The equation of the line that passes through the point (4,8) and has a slope of 0

Answers

Answer:

y = 8

Step-by-step explanation:

Plug in the point and slope into the equation y = mx + b to solve for b:

8 = 0(4) + b

8 = b

Then, plug this back into the equation:

y = 0x + 8

y = 8 will be the equation

Answer: y=8

Step-by-step explanation:

concept to know: when it is a horizontal line, the slope is zero, when it is a vertical line, the slope is undefined.

---------------------

If it is required to have a slope of 0, then it is a horizontal line.

y=b (this is the equation for some line that slope is 0)

We then should find the b, or the y-intercept

The question did not provide us with a point of y-intercept, BUT since it is a horizontal line, the y value of any point is the same, including y-intercept (when x value is 0)

Therefore, the y-intercept will be (0, 8), and the equation will be

y=8

How many pennies could you have if: When you Break de Pennies into groups of 2, you have 1 penny left over, AND when you break the pennies into groups of 3, and you have 1 penny left over, AND when you break the pennies into groups of 5, you have 1 penny left?

Answers

Answer:

The answer is 31 pennies

Step-by-step explanation:

we have to find a number that gives a remainder of 1 when divided by both 2, 3 and 5.

The easiest way to do this is to list the factors of 5, add 1 to it, and test them until we find the one with a remainder of 1 by all three divisors. This is done as follows:

1) factor: 5 (+1) = 6

6 ÷ 2 = 3 remainder 0

6 ÷ 3 = 2 remainder 0

since there is a remainder of 0, when divided by 3, 6 is wrong

2) factor; 10 (+1) = 11

11 ÷ 3 = 3 remainder 2 ( 11 is not the correct answer

3) factor : 15 (+1) = 16

16 ÷ 2 = 8 remainder 0 ( 16 is  not the correct answer

4) factor : 20(+1) = 21

21 ÷ 3 = 7 remainder 0 ( 21 is wrong)

5) factor : 25(+1) = 26

26 ÷ 2 = 13 remainder 0 ( 26 is wrong)

6) factor : 30(+1) = 31

31 ÷ 2 = 15 Remainder 1

31 ÷ 3 = 10 Remainder 1

31 ÷ 5 = 6 Remainder 1

since all three divisors give a remainder of 1, the correct answer is 31

Therefore you have 31 pwnnies


Mia's kitten weighs of 3/5 a pound. The mother cat weighs 14 times as many pounds as the kitten. How much does the mother cat weigh.

Answers

Answer:

8.4

Step-by-step explanation:

You must multiply 0.6 or 3/5 by 14. 6x14=84, but you must divide that by 10 which would give you a total answer of 8.4 pounds

The weight of the mother cat is 8[tex]\frac{2}{5}[/tex] pounds

The weight of the mother cat can be determined by multiplying the weight of the kitten by 14

Weight of the mother cat = weight of kitten x 14

[tex]\frac{3}{5}[/tex] x 14

= [tex]\frac{42}{5}[/tex]

Convert the improper fraction to a mixed fraction

[tex]\frac{42}{5} = 8\frac{2}{5}[/tex] pounds

To learn more about  fractions, please check:

https://brainly.com/question/21449807?referrer=searchResults

I NEED URGENT HELP PLEASE

Answers

Answer:

x'9(3√y) is the correct answer.

-First apply the exponent multiplication rule of algebra

Which statement is true? Question 3 options: 0 is a natural number -9 is a whole number 4.6 is a rational number 81−−√ is an irrational number

Answers

Answer:

the true statement, 0 is a natural number

Plz Help ASAP WILL MARK YOU BRAINLIEST

Answers

Answer: D

Step-by-step explanation:

It is D because it forms a right angle. perpendicular lines must form a right angle so it is D.

Answer:

D.

Step-by-step explanation:

The 2 lines that cross form a 90 degree angle, therefore it is perpendicular.

(3x+6) + (5x - 7) =​

Answers

Answer:

8x - 1

Step-by-step explanation:

(3x+6) + (5x - 7) =3x+6 + 5x - 7=3x +5x +6 - 7=8x - 1

Hope this helps.. Good luck!

What is the distance between 4.5 and - 3.75

Answers

the distance between 4.5 and -3.75 is .75 you simply subtract 3.75 from 4.5

square root of -19 in terms of i​

Answers

Answer:

i√19

Step-by-step explanation:

Because √(-19) = √(-1)√19, and because √(-1) = i, we get i√19

PLZZ ANSWER ASAP PLZZZ HELP MEEE

Answers

___________________________________

Answer: There is no answer because this is a multi step question.

___________________________________

Step-by-step explanation:

A singular unit in this problem can be found by doing 25.00/2.

This is 12.50. You then use this to answer all the questions.

1.A) She earns 12.50 per hour.

1.B)  (Idk if this is right but I'm answering the question) Kate will never have more then Jocelynn if they work the same amount of hours because Jocelynn is simply paid more.

Melissa has three different positive integers. She adds their reciprocals together and gets a sum of $1$. What is the product of her integers?Melissa has three different positive integers. She adds their reciprocals together and gets a sum of $1$. What is the product of her integers?

Answers

Answer:

One possible answer is 0,1,1

Step-by-step explanation:

-1x-1 is 1

Which angle measures are correct? Select three options,

OmZX= 55°

OmZW = 125°

OmZW = 55°

mZZ = 125°

mZZ = 55°

PLEASE ANSWER FAST TIMED TEST

Answers

Answer:

m∠W = 125°

m∠X = 55°

m∠Z = 55°

Step-by-step explanation:

The shape is parallelogram WXYZ. m∠Y = 125.

A parallelogram is a quadrilateral shape in which both opposite sides and opposite angles are equal to each other. The diagonals of a parallelogram bisect each other. Also consecutive angles in a parallelogram are supplementary.

Therefore in parallelogram WXYZ:

m∠Z + m∠Y = 180° (Consecutive angles in a parallelogram are supplementary)

m∠Z + 125 = 180

m∠Z = 180 - 125

m∠Z = 55°

m∠W = m∠Y (Opposite angles are equal)

m∠W = 125°

m∠W + m∠X = 180° (Consecutive angles in a parallelogram are supplementary)

m∠X + 125 = 180

m∠X = 180 - 125

m∠X = 55°

Joan saved $2.34 on an item that is usually $7.89. What percent did she save

Answers

(2.34/ 7.89) times 100 = ˜29.65%

Joe bought a box of laundry detergent that contains 195 scoops. Each load of laundry
2 scoops. How many loads of laundry can he do with this one box? The box of
detergent was $19.99. How much is he paying for each load that he washes?
uses

Answers

Answer:

at least 97 loads

Step-by-step explanation:

Write the quotient 7+5i÷1-4i in standard form.​

Answers

Answer:

7+i

Step-by-step explanation:

(7+5i)/1-4i = 7+i

Answer:

[tex]-\frac{13}{17} + \frac{33}{17} i[/tex]

Step-by-step explanation:

(see attached)

Please solve these. Will rate you 5 star! ​

Answers

Answer: Hi!

To find the answer for question 24, we would first find the square root of 20 and 5. The square root of 20 is about 4.47 (I used a calculator for convenience) and the square root of 5 is about 2.24. Now we need to add these:

4.47 + 2.24 = 6.71

Now we divide 30 by this:

30/6.71 = 4.47

Now, we'll evaluate the answer choices.

a) is equal to 1.49

b) is equal to 13.4

c) is equal to 4.47

d) is equal to 26.88

The answer choice that is correct is c, because it is what we got for the problem that we were supposed to solve in the beginning.

Hope this helps!

If tan fº = 2/1 and the measure of yw is 8 units, what is the measure of xw?

2units

4units

7units

8 units

Answers

*see attachment for the figure referred to

Answer:

4 units

Step-by-step explanation:

Given that [tex] tan(f) = \frac{2}{1} [/tex], therefore, it follows that:

[tex] tan(f) = \frac{opp}{adjacent} = \frac{YW}{XW} = \frac{8}{XW} [/tex],

If the ratio of YW to XW = 2:1, therefore, [tex] \frac{2}{1} = \frac{8}{XW} [/tex]

Cross multiply to find XW

[tex] XW*2 = 8*1 [/tex]

[tex] XW = \frac{8}{2} = 4 units[/tex]

Answer:

the answer is B

Step-by-step explanation:

I took the test and got it right

In between what two integers is the \large \sqrt{77}

Answers

Answer:

8 and 9

Step-by-step explanation:

Since 77 is between 64= 8² and 81= 9²

√64 < √77 < √818 < √77 < 9

what is the answer for b
[tex]2(b - 3)[/tex]

Answers

Answer:

B

Step-by-step explanation:

Answer:

2b-6

Step-by-step explanation:

[tex]2(b-3)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=2,\:b=b,\:c=3\\=2b-2\times \:3\\=2b-6[/tex]

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