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Alex17521 [72]
3 years ago
8

This net can be folded to form a cube with a side length of 20 units

Mathematics
1 answer:
pochemuha3 years ago
8 0

Answer:

The net, when folded into a cube, has a total surface area of 2,400 sq.units

Step-by-step explanation:

The length of all sides of a cube are the same.

Now, the surface area of a cube is the sum of the area of all of its faces.

Since the length of all sides are the same and we are told that the length of a side is 20 units, thus, the area of one face is;

A = 20 x 20 = 400 sq.units

So, one the area of a face is 400 sq.units.

Now, since all the faces are the same measurement, thus each face will have an area of 400 sq.units. Cubes have 6 faces, thus the total surface Area is;

Total = 400 x 6 = 2400 sq.units

The net, when folded into a cube, has a total surface area of 2,400 sq.units

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The table below models the cost, y, of using a high-efficiency washing machine and a standard washing machine over x number of y
SSSSS [86.1K]

ANSWER:

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.

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3 years ago
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