Multiply the binomials: (2c - d) (3c + d)

Mathematics

1 answer:

slega [8]3 years ago

3 0

Answer:

6c^2-cd-d^2

Step-by-step explanation:

How you get the answer is you use the process called FOIL. The F is front, so you multiply the 2c and the 3c to get 6c^2. The O is the outer, so you multiply the 2c and the d(because they are on the outer sides of the parenthesis) to get 2cd. The I is the inner, so you multiply the -d and the 3c(because they are on the inner sides of the parenthesis) to get -3cd. The L is the last, so you multiply d and -d to get -d^2. The 2cd and the -3cd are the same so you have to minus them to get -cd. So the answer is:

6c^2-cd-d^2.

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1) The dependent variable is the boiling point of water and the independent variable is the altitude.

2) The slope would represent the average decrease of the boiling point of water per every one thousand feet that the altitude increase.

Explanation:

1) given

Table:

<span>Altitude (in thousands of feet)    Boiling Point of Water (Fahrenheit)

(sea level) 0    212
0.5                                               211.1
1.0                                               210
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2) The independent variable is the input of the function, and the dependent variable is the output of the function.

The input determines the output once the rule is established.

Therefore:

a) the independent variable is the altitude, and
b) the dependent variable is the boiling point of water in Farenheit.

3) The slope of the graph would be:

                 change in the dependent variable          change in boiling point
slope = --------------------------------------------------- = ---------------------------------
</span>                 change in the independent variable          change in altitude

Therefore, the slope represents the average change in the boiling boilin point of water every one thousand feet on change of altitude.

If the relationship is not linear, then the slope is not constant, and you will have different slopes for different parts.

If the slope is negative, means that as the altitude increase the boiling point of water decrease.

You can calculate the slope using any two pair of points (data)

              212 - 210           2
slope =---------------- =   ------- = - 2
                0 - 1            - 1

or, using other pair of points:

                204.8 - 210           -5.2
slope = --------------------- =   --------- = -2.6
                  4.0 - 2.0               2.0

As you see, the slope is not constant. So, the function is not linear.

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