98 points! identify the variables and write out the system of inequalities

X = one pound packages of Value brand.

Y = one pound packages of Superior brand.

75 pounds x 16 ounces per pound = 1200 ounces.

120 pounds x 16 ounces per pound = 1920 ounces.

Value Blend  = 4 ounces of A and 12 ounces of B

Superior blend  = 8 ounces of A and 8 ounces of B

Grade A = 4x + 8y = 1200 ounces

Grade B = 12x + 8y = 1920 ounces

Solve for X in Grade A equation:

4x + 8y = 1200

Subtract 8y from each side:

4x = 1200-8y

divide all terms by 4:

x = 300 - 2y

Replace X in the 2nd equation with the X above:

12(300-2y) + 8y = 1920

Distribute:

3600 - 24y + 8y = 1920

Combine Y terms:

3600-16y = 1920

Subtract 3600 from each side:

-16y = -1680

Divide both sides by -16:

y = -1680 / -16

y = 105

Replace y with 105 in the last X equation:

x = -2y +300

x = -2(105) + 300

x = -210 + 300

x = 90

90 one pound packages of Value brand

105 one pound packages of Superior brand

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!