Mariana and bethany disagree about whether the set of polynomials is closed under addition, subtraction, and multiplication, as the set of integers is. to examine their two positions, they consider the polynomials a = 5x − 1 and b = 2x. mariana thinks these polynomials are closed under all three operations. bethany argues that these polynomials are closed under only two operations. complete the following statements, and then determine who is correct.
a + b = a − b = a • b = 10x2 + correct.

A set of polynomials is closed under an operation if the result after operation is also a polynomials.

Given A = 5x − 1 and B = 2x

A + B

= 5x - 1 + 2x

= 7x -1, a polynomials

A - B

= 5x - 1 - 2x

= 3x - 1, a polynomials

A * B

=(5x - 1)*(2x)

= 10x2 + (-2x), a polynomials

All three operations give a result in polynomials. So Mariana is correct.

i’m here for points.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places