The table below models the cost, y, of using a high-efficiency washing machine and a standard washing machine over x number of years.

i) y = 25x + 500

ii) y = 30x + 400

iii) The washing machines would cost the same amount after 20 years of use

iv) Standard machine

Step-by-step explanation:

i)

We are to determine a straight line equation that models the cost of High-Efficiency washing machine over the years;

The first step step is to determine the slope of the line,

( change in y) / ( change in x ) = (550 - 525) / ( 2 - 1) = 25

The equation is slope-intercept form will be;

y = 25x + c

Where y is the cost of the High-Efficiency washing machine and x the number of years. To determine the y-intercept, c, we use any pair of points given in the data table;

when x = 1, y = 525

525 = 25(1) + c

c = 500

Therefore;

y = 25x + 500

ii)

The straight line equation that models the cost of Standard washing machine over the years;

Slope = (460 - 430) / (2 - 1) = 30

The equation is slope-intercept form will be;

y = 30x + c

when x = 1, y = 430

430 = 30(1) + c

c = 400

Therefore;

y = 30x + 400

Where y is the cost of the standard washing machine and x the number of years.

iii)

Given the cost functions for both machines over the number of years, we simply equate the two equations and determine the value of x when both machines would cost the same amount;

We have the cost functions;

y = 25x + 500

y = 30x + 400

Equating the two and solving for x;

25x + 500 = 30x + 400

500 - 400 = 30x - 25x

100 = 5x

x = 20

Therefore, the washing machines would cost the same amount after 20 years of use.

iv)

In order to determine which machine would be the more practical purchase if kept for 9 years we use the cost functions obtained in i) and ii)

The cost function of the High-Efficiency washing machine is;

y = 25x + 500

To determine the cost, we solve for y given x = 9

y = 25(9) + 500

y = 725

The cost function of the Standard washing machine is;

y = 30x + 400

We solve for y given x = 9

y = 30(9) + 400

y = 670

Comparing the two values obtained, the cost for the Standard washing machine is more practical.

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square