The table below gives data from a linear function. find a formula for the function.

1 answer:

4 0

Given the following table that gives data from a linear function:

$\begin {tabular}
{|c|c|c|c|}
Temperature, $y = f(x)$ (^\circ C)&0&5&20 \\ [1ex]
Temperature, $x$ (^\circ F)&32&41&68 \\ 
\end {tabular}$

The formular for the function can be obtained by choosing two points from the table and using the formular for the equation of a straight line.

Recall that the equation of a straight line is given by
$\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}$

Using the points (32, 0) and (41, 5), we have:
$\frac{y-0}{x-32} = \frac{5-0}{41-32}= \frac{5}{9} \\ \\ \Rightarrow y=\frac{5}{9}(x-32)$

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Before a bag of flour can be sold, it must be 40 kilograms but can be within 0.5

Serjik [45]

Answer:

The minimum acceptable weight of the flour bag is 39.5 kg,

and its maximum acceptable weight is 40.5 kg

Step-by-step explanation:

Notice that the selling weight of the bag to be sold (x) needs to differ from 40 kg at most 0.5 kg. Therefore, we can write the following inequality:

$|x-40|\leq 0.5$

The inequality can be solve once we remove the absolute value symbol, and solve for the unknown "x". Recall that in order to solve it, we need to consider the two possible cases:

a) that the expression within the absolute value symbol is larger than or equal to zero, and b) that the expression is less than zero.

a) If $x-40\geq 0$ then its absolute value is equal to itself (x-40), and when we remove the absolute value symbols, we get: