Question

Can you help with did pretty please I'm stuck help just a, c ,d thanks luv.

Answer 1

Answer:

a) The slope of the function is 3.

c) The equation is represented by $n(t) = 3\cdot t + 35$.

d) The y-intercept of the function is 35.

Step-by-step explanation:

a) According to the statement, we must assume that number of pieces of mail that must be hand-sorted (dependent variable) is represented by a linear function in terms of time (independent variable). That is:

$n(t) = m\cdot t + n_{o}$ (1)

Where:

$m$ - Slope, measured in number of pieces per minute.

$t$ - Time, measured in minutes.

$n_{o}$ - Initial number of pieces of mail that must be hand-sorted (y-intercept), measured in pieces.

$n$ - Current number of pieces of mail that must be hand-sorted, measured in pieces.

From Geometry, we know that a line can be formed by know two distinct points. If we know that $n(15\,min) = 80\,p$ and $n(45\,min) = 170\,p$, then the following system of linear equations is formed:

$15\cdot m + n_{o} = 80$ (2)

$45\cdot m + n_{o} = 170$ (3)

The solution of the system of equations is:

$m = 3$ and $n_{o} = 35$

The slope of the function is 3.

c) By (1) and using results from a) we conclude that the equation function is:

$n(t) = 3\cdot t + 35$ (4)

d) The y-intercept of the function is 35.