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Lana71 [14]
3 years ago
9

Tamara was asked to write an example of a linear functional relationship. She wrote this example:

Mathematics
1 answer:
Llana [10]3 years ago
8 0

Answer:

Tamara's example is in fact an example that represents a linear functional relationship.

  • This is because the cost of baby-sitting is linearly related to the amount of hours the nany spend with the child: the more hours the nany spends with the child, the higher the cost of baby-sitting, and this relation is constant: for every extra hour the cost increases at a constant rate of $6.5.
  • If we want to represent the total cost of baby-sitting in a graph, taking the variable "y" as the total cost of baby-sitting and the variable "x" as the amount of hours the nany remains with the baby, y=5+6.5x (see the graph attached).
  • The relation is linear because the cost increases proportionally with the amount of hours ($6.5 per hour).
  • See table attached, were you can see the increses in total cost of baby sitting (y) when the amount of hours (x) increases.

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Answer:

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Step-by-step explanation:

When they ask you to make a variable the "subject of the formula", they're basically asking you to build a "machine" for it. In the expression y=mx+b, for instance, if we know what m, x, and b are, we can plug them all in and out comes a value for y! To build that machine, we need to get it by itself on one side of the equation.

So, we want to build this machine for p, and the equation we have to build it out of is

1=\dfrac{pk}{m+sp}

One think we can immediately say about this equation: for a fraction to be equal to one, its numerator and denominator have to be equal to each other. So we can say

m+sp=pk

Ok, what next? Well, if we want p by itself, we need to somehow peel it off of that <em>sp</em> and <em>pk</em>. Let's collect them on the right side by subtracting <em>sp </em>from both sides:

m=pk-sp

p is a <em>common factor</em> of both <em>sp </em>and <em>pk</em>, so we can peel it away using the distributive property:

m=p(k-s)

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\dfrac{m}{k-s}=p or p=\dfrac{m}{k-s}

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Step-by-step explanation:

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<u>-1           -1 </u>

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Step-by-step explanation:

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