Determine if the function defines an inner product for polynomials p(x) = a0 + a1x anxn and q(x) = b0 + b1x bnxn. (select all that apply.) p, q = a0b0 + a1b1 + + anbn in pn satisfies p, q = q, p does not satisfy p, q = q, p satisfies p, q + w = p, q + p, w does not satisfy p, q + w = p, q + p, w satisfies c p, q = cp, q does not satisfy c p, q = cp, q satisfies p, p ? 0, and p, p = 0 if and only if p = 0 does not satisfy p, p ? 0, and p, p = 0 if and only if p = 0

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.

chemists are often responsible for designing a chemical reaction and analyzing the products obtained from it. one significant part of designing a chemical reaction is determining the amount of each reactant that is needed and the amount of each product that will be produced. in order to do so, chemists use stoichiometry, the quantitative relationships between reactants and products.

26- 6 = 20. erica has 20 bottles left