The set of rental car rates making it more economical for Jamal than employing taxi services is outlined as A = {x | 0 ≤ x < 26} [where x represents dollars]. The step-by-step breakdown is as follows: Let the rental cost be $x per day. With Jamal's trip extending over 4 days, factoring in $24 for gas, and estimating taxi costs at around $128, an inequality emerges: 128 > 24 + 4x. Thus simplifying leads to 4x < 104 and consequently x < 26.
The domain refers to all potential input values, specifically represented by the x-axis on a graph. Conversely, the range includes all possible output values, depicted along the y-axis.
The graph clearly extends horizontally from (-∞,∞) on the x-axis, indicating that its domain is (-∞,∞).
Similarly, it can be seen that the graph stretches vertically from (-∞,∞) on the y-axis, denoting that the range is also (-∞,∞).
This indicates the function includes an infinite array of values. Therefore, there are no limitations on either the domain or the range for this function.
When there is one table (t=1), you can place 6 chairs (c=6) around it: 2 along the length of each side and 1 at each end.
With t=2, where the tables are positioned end to end (joined at the width), c=10, that means 4 chairs along each side of the joined tables and 1 chair at each end. Each additional table increases the number of chairs by 4, thus we can express this as c=4t+2, with the constant 2 representing the individual chair at each end. If the tables are spread apart, then c=6t.
The equivalence exists because tenths represent one-tenth of a whole. Having 20 tenths means multiplying 20 by 1/10, resulting in 20/10, which simplifies to 2 wholes. Conversely, expressing 2 as 20 tenths yields the same amount.
