Electricity provider \(A\) charges 25 cents per kilowatt hour (kWh) for electricity, plus a fixed monthly charge of $40. \begin{array} {|l|c|} Provider \(B\) charges 35 cents per kWh, with no fixed monthly charge. The graph shows how Provider \(B\) 's charges vary with the amount of electricity used in a month. --- 2 WORK AREA LINES (style=lined) --- --- 5 WORK AREA LINES (style=lined) ---
\hline
\rule{0pt}{2.5ex} \text{Electricity used in a month (kWh)} \rule[-1ex]{0pt}{0pt} & \ \ \ \ \ 0\ \ \ \ \ & \ \ \ 400\ \ \ & \ \ 1000\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Monthly charge (\$)} \rule[-1ex]{0pt}{0pt} & 40 & & 290 \\
\hline
\end{array}
Algebra, STD1 A3 2021 HSC 29
In a park the only animals are goannas and emus. Let `x` be the number of goannas and let `y` be the number of emus.
The number of goannas plus the number of emus in the park is 31. Hence `x + y = 31`.
Each goanna has four legs and each emu has two legs. In total the emus and goannas have 76 legs.
By writing another relevant equation and graphing both equations on the grid on the following page, find the number of goannas and the number of emus in the park. (4 marks)
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Number of goannas = _______________
Number of emus = _________________
Algebra, STD1 A3 2020 HSC 29
There are two tanks on a property, Tank A and Tank B. Initially, Tank A holds 1000 litres of water and Tank B is empty.
- Tank A begins to lose water at a constant rate of 20 litres per minute.
The volume of water in Tank A is modelled by `V = 1000 - 20t` where `V` is the volume in litres and `t` is the time in minutes from when the tank begins to lose water.
On the grid below, draw the graph of this model and label it as Tank A. (1 mark)
- Tank B remains empty until `t=15` when water is added to it at a constant rate of 30 litres per minute.
By drawing a line on the grid (above), or otherwise, find the value of `t` when the two tanks contain the same volume of water. (2 marks) - Using the graphs drawn, or otherwise, find the value of `t` (where `t > 0`) when the total volume of water in the two tanks is 1000 litres. (1 mark)
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Algebra, STD2 A4 SM-Bank 3
Temperature can be measured in degrees Celsius (`C`) or degrees Fahrenheit (`F`).
The two temperature scales are related by the equation `F = (9C)/5 + 32`.
- Calculate the temperature in degrees Fahrenheit when it is −20 degrees Celsius. (1 mark)
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- The following two graphs are drawn on the axes below:
`F = (9C)/5 + 32` and `F = C`
Explain what happens at the point where the two graphs intersect. (1 mark)
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