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Anvisha [2.4K]
3 years ago
13

PLS ANSWER what is the rate of change for these tables please answer in y over x form

Mathematics
1 answer:
Airida [17]3 years ago
5 0

Answer:

1)\frac{-36}{5}

2)\frac{42}{5}

3)\frac{96}{1}

4)\frac{202}{2}

Step-by-step explanation:

Given is four pair of coordinates.

We have to find rate of change for these.

'Rate of change' is nothing but slope that is calculated as,

\frac{rise}{run} = \frac{y2-y1}{x2-x1}

1)

\frac{y2-y1}{x2-x1} \\\frac{12--24}{-6--1} \\\frac{36}{-5}\\\frac{-36}{5}

2)

\frac{6-48}{-3-2}\\\frac{-42}{-5}\\\frac{42}{5}

3)

\frac{-6-90}{3-4}\\\frac{-96}{-1}\\\frac{96}{1}

4)

\frac{-10-192}{6-8}\\\frac{-202}{-2}\\\frac{202}{2}

Therefore these are the required \frac{y}{x} form.

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B= # of pounds of British blend

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This is a linear programming problem. In order to solve it we need to determine how we are going to use the provided data and we need to keep in mind what we need to maximize (or minimize depending on the problem)

So, the problem states that "The goal of Fine Coffees, Inc. Is to maximize profits." This last sentence will tell us what the objective function will be. The objective function must model the desired value we want to maximize. So the objective function should represent the profits of selling the two tipes of cofee blends.

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"Each pount of American blend cofee requires 12 oz of Colombian beans and 4 oz. of Dominican beans, while a pound of British blend coffee uses 8 oz of each type of bean." Again, this data will help us find the restrictions for our linear programming problem, since they will tell us how much coffe we can manufacture, so they are not needed to find the objective function.

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We set A to be the number of pounds of American blend and B to be the number of pounds of British blend. So the profit for American blend is found by using the following equation:

P_{American}=$2.00*A

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P_{British}=$1.00*B

so the total profit is found by adding the two given profits, so we get:

P_{total}=P_{American}+P_{British}

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P_{total}=$2.00A+$1.00B

which can be simplified to:

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