Imagine you build a house and for heating systems you have a choice between solar and air heated by natural gas. the solar heating system costs $30,000 to install, with annual operating of cost of $150 per year afterwards. the gas heating system costs $6,250 to install, with an expected annual operating cost of $1100 per year afterwards. how could you use a system of equations to solve for the time when both systems would be the same cost? how many years would that be and what is the common cost? which system would you want?

X represents years. Set the amounts equal.

$30,000 + $150(x) = $6,250 + $1100(x)

$23,750 = $950(x)

x = 25 years

Second part:

$30,000 + $150(25) = $33,750

$6,250 + $1100(x) = $33,750

Third part:

You would want the gas heating system if you were only going to have it for less than 25 years. Not completely sure what that question is asking.

answer: the four apples you took away.

step-by-step explanation:

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!