Question

select the correct answer from each drop - down menu.
lionel uses two functions to model the costs of having a problem diagnosed and repaired by two appliance repair companies.
he models the cost, in dollars, of having phil’s appliances handle the repair job, requiring x hours of labor, with function p: ( p(x)=68x + 81 ).
he models the cost of having quality electric handle the same repair with function q: ( q(x)=51x + 90 ).
the function drop - down menu with options ( s(x)=119x + 171 ), ( s(x)=17x + 171 ), ( s(x)=17x + 9 ), ( s(x)=17x - 9 ) represents the amount, in dollars, lionel will save by having quality electric handle an x - hour repair instead of phil’s appliances.
lionel will save drop - down menu or calculation part by having quality electric for a repair needing 2 hours of labor.
reset and next buttons

Explanation:

To determine the function for the amount Lionel saves and the value for a 2 - hour repair, we follow these steps:

Step 1: Find the savings function \(s(x)\)

The savings function \(s(x)\) is the difference between the cost of Phil's Appliances \(p(x)\) and the cost of Quality Electric \(q(x)\).
Given \(p(x)=68x + 81\) and \(q(x)=51x+90\).
We calculate \(s(x)=p(x)-q(x)\)
\[

$$\begin{align*} s(x)&=(68x + 81)-(51x + 90)\\ &=68x+81 - 51x-90\\ &=(68x-51x)+(81 - 90)\\ &=17x-9 \end{align*}$$

\]

Step 2: Find the savings for \(x = 2\) hours of labor

We substitute \(x = 2\) into the savings function \(s(x)=17x-9\)
\[

$$\begin{align*} s(2)&=17\times2-9\\ &=34 - 9\\ &=25 \end{align*}$$

\]

For the first drop - down (savings function):

The correct function is \(s(x)=17x - 9\)

For the second drop - down (savings for 2 - hour repair):

When \(x = 2\), \(s(2)=17\times2-9=34 - 9 = 25\) (if we assume the options are related to the value of \(s(2)\), but since the options for the second part are not fully visible, based on the calculation of the function, the savings function is \(s(x)=17x - 9\))

If we consider the first drop - down menu for the savings function:
The correct function is \(s(x)=17x-9\)

If we consider the second part (savings for 2 - hour repair), we substitute \(x = 2\) into \(s(x)=17x - 9\) and get \(s(2)=17\times2-9 = 25\)

For the first drop - down (the savings function):

To find the savings function, we subtract the cost function of Quality Electric (\(q(x)\)) from the cost function of Phil's Appliances (\(p(x)\)). Given \(p(x)=68x + 81\) and \(q(x)=51x + 90\), we calculate \(s(x)=p(x)-q(x)=(68x + 81)-(51x+90)=17x-9\).

Step 1: Identify the savings function

We have already found that \(s(x)=17x-9\)

Step 2: Substitute \(x = 2\) into the function

We substitute \(x = 2\) into \(s(x)=17x-9\)
\[s(2)=17\times2-9=34 - 9=25\]

Answer:

\(s(x)=17x - 9\)

For the second part (savings for 2 - hour repair):