Answer:
SUMMARY:
→ Not a Polynomial
→ A Polynomial
→ A Polynomial
→ Not a Polynomial
→ A Polynomial
→ 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
.
Here:
= non-negative integer
= 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](https://tex.z-dn.net/?f=x%5E4%2B%5Cfrac%7B5%7D%7Bx%5E3%7D-%5Csqrt%7Bx%7D%2B8)
If an algebraic expression contains a radical in it then it isn’t a polynomial. In the given algebraic expression contains
, so it is not a polynomial.
Also it contains the term
which can be written as
, meaning this algebraic expression really has a negative exponent in it which is not allowed. Therefore, the expression
is not a polynomial.
Given the expression
![-x^5+7x-\frac{1}{2}x^2+9](https://tex.z-dn.net/?f=-x%5E5%2B7x-%5Cfrac%7B1%7D%7B2%7Dx%5E2%2B9)
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](https://tex.z-dn.net/?f=x%5E4%2Bx%5E3%5Csqrt%7B7%7D%2B2x%5E2-%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7Dx%2B%5Cpi)
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](https://tex.z-dn.net/?f=%5Cleft%7Cx%5Cright%7C%5E2%2B4%5Csqrt%7Bx%7D-2)
is not a polynomial because algebraic expression contains a radical in it.
Given the expression
![x^3-4x-3](https://tex.z-dn.net/?f=x%5E3-4x-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}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7Bx%5E2-4x%2B3%7D)
![\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5C%3Aa%5E%7B-b%7D%3D%5Cfrac%7B1%7D%7Ba%5Eb%7D)
Therefore, is not a polynomial because algebraic expression really has a negative exponent in it which is not allowed.
SUMMARY:
→ Not a Polynomial
→ A Polynomial
→ A Polynomial
→ Not a Polynomial
→ A Polynomial
→ Not a Polynomial
4+3.5=7.5
7.5x =180
180/7.5
=24 (answer)
For this case we have a function of the form:
![y = A * (b) ^ n ](https://tex.z-dn.net/?f=y%20%3D%20A%20%2A%20%28b%29%20%5E%20n%0A)
Where,
A: initial amount
b: growth rate (if b> 1)
n: time in hours
Substituting values we have:
![s (n) = 20 * b ^ n ](https://tex.z-dn.net/?f=s%20%28n%29%20%3D%2020%20%2A%20b%20%5E%20n%0A)
We have then that the initial amount is:
![A = 20 ](https://tex.z-dn.net/?f=A%20%3D%2020%0A)
If b = 1.85 then the growth percentage is:
Answer:
here were initially 20 bacteria.
The hourly percent growth rate of the bacteria would be 85%
You will receive a free beverage and free desert on your 60th visit.
Beverage- 1, 2, 3, 4, 5, 6
Visits- 12, 24, 36 ,48 ,60
Desert- 1, 2, 3 ,4
Visits- 15, 30, 45, 60
Notice how for beverages at 60 visits you get your 6th drink for free, and for deserts, at you 60 visits you receive your 4 free desert.
So, since both numbers have the same number (60) of visits which is their common multiple between the 2, you answer is 60.
![f(x)=\frac{(x-1)(x+2)(x+4)}{(x+1)(x-2)(x-4)}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B%28x-1%29%28x%2B2%29%28x%2B4%29%7D%7B%28x%2B1%29%28x-2%29%28x-4%29%7D)
The denominator of a fraction can't be equal to 0.
![(x+1)(x-2)(x-4) \not= 0 \\ x+1 \not=0 \ \land \ x-2 \not= 0 \ \land \ x-4 \not= 0 \\ x \not= -1 \ \land \ x \not = 2 \ \land \ x \not= 4](https://tex.z-dn.net/?f=%28x%2B1%29%28x-2%29%28x-4%29%20%5Cnot%3D%200%20%5C%5C%0Ax%2B1%20%5Cnot%3D0%20%5C%20%5Cland%20%5C%20x-2%20%5Cnot%3D%200%20%5C%20%5Cland%20%5C%20x-4%20%5Cnot%3D%200%20%5C%5C%0Ax%20%5Cnot%3D%20-1%20%5C%20%5Cland%20%5C%20x%20%5Cnot%20%3D%202%20%5C%20%5Cland%20%5C%20x%20%5Cnot%3D%204)
The function is undefined at x=-1, x=2, x=4, because for these values the denominator of the function would equal 0, and it's impossible to divide by 0.
Edward is correct.