The piece-wise linear functions can be written as follows:
.
.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
For x less than 5, the y-intercept is of b = 3 and the function also gos through (2,2), hence the slope is:
m = (2 - 3)/(2 - 0) = -0.5.
Hence the rule is:
.
When x = 5, the function is constant at -5, hence:
For x less than 5, the function goes through points (6,3) and (7,2), hence the slope is:
m = (2 - 3)/(7 - 6) = -1.
Then:
y = -x + b
When x = 6, y = 3, hence the y-intercept is given as follows:
3 = -6 + b
b = 9.
Hence the rule is:
.
More can be learned about linear functions at brainly.com/question/25537936
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The answer is D. Hope this helps
The dot plot that corresponds to the given data is the second dot plot
The frequency and the percent frequency distribution are shown below
<h3>
Frequency distribution</h3>
The given data is
5.6 9.9 11.3 7.5 10.0 11.9 13.2 13.8 10.0 11.9
6.5 9.0 11.2 10.9 14.6 7.2 10.0 6.0 15.8 11.3
From the question, we are to construct a dot plot
Among the given options, the dot plot that corresponds to the given data is the second dot plot
b) We are to construct a frequency distribution
The frequency distribution table is shown below
Class Frequency
6.0 - 7.9 4
8.0 - 9.9 2
10.0 - 11.9 9
12.0 - 13.9 2
14.0 - 15.9 2
Total 19
b) We are to construct a percent frequency distribution
The percent frequency distribution table is shown below
Class Percent Frequency
6.0 - 7.9 21.1%
8.0 - 9.9 10.5%
10.0 - 11.9 47.4%
12.0 - 13.9 10.5%
14.0 - 15.9 10.5%
Total 100%
The frequency and the percent frequency distribution are shown above
Learn more on Frequency distribution here: brainly.com/question/1094036
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The answer would be positive if all 3 signs were the same. Yes, the product of two integers with the same sign will be positive, but that goes for any number of integers as long as they still have the same sign.
Distribute sum groups
x(x^2 + 4x - 2) - 5(x^2 + 4x - 2)
Distribute
x^3 + 4x^2 - 2x - 5(x^2 + 4x - 2)
Distribute
x^3 + 4x^2 - 2x - (5x^2 + 20x - 10)
Simplify brackets
x^3 + 4x^2 - 2x - 5x^2 - 20x + 10
Collect like terms
x^3 + (4x^2 - 5x^2) + (-2x - 20x) + 10
Simplify
<u>x^3 - x^2 - 22x + 10</u>
