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.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.