Answer: the length of Maria's piece of string is 45 inches.
the length of Katy's piece of string is 39 inches
Step-by-step explanation:
Let x represent the length of Maria's piece of string.
Let y represent the length of Katy's piece of string.
When they put the two pieces of string together end to end, the total length is 84inches. This means that
x + y = 84 - - - - - - - - - - - -1
Maria's string is 6 inches longer than Katy's. This means that
x = y + 6
Substituting x = y + 6 into equation 1, it becomes
y + 6 + y = 84
2y + 6 = 84
2y = 84 - 6 = 78
y = 78/2 = 39
x = y + 6 = 39 + 6
x = 45
The formula for slope is y=mx+b
so if you re arrange the equation from 8y-16x=12
to 8y=16x+12
the slope will be the coefficient of x =16
Collect like terms and you'll get -2 - 3(a - b)
Based on the characteristics of <em>linear</em> and <em>piecewise</em> functions, the <em>piecewise</em> function
is shown in the graph attached herein. (Correct choice: A)
<h3>How to determine a piecewise function</h3>
In this question we have a graph formed by two different <em>linear</em> functions. <em>Linear</em> functions are polynomials with grade 1 and which are described by the following formula:
y = m · x + b (1)
Where:
- x - Independent variable.
- y - Dependent variable.
- m - Slope
- b - Intercept
By direct observation and by applying (1) we have the following <em>piecewise</em> function:

Based on the characteristics of <em>linear</em> and <em>piecewise</em> functions, the <em>piecewise</em> function
is shown in the graph attached herein. (Correct choice: A)
To learn more on piecewise functions: brainly.com/question/12561612
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