Question

help!

Answer 1

@Michele_Laino

Ada and Steve spend a certain amount of money from their accounts each week at a pet shelter.

The table shows the relationship between the amount of money (y) remaining in Ada's account and the number of weeks (x):

Function 1:


Number of Weeks
(x) Amount Remaining (dollars)
(y)
1 40
2 36
3 32
4 28


The equation shows the relationship between the amount of money, y, remaining in Steve's account and the number of weeks, x:

Function 2:

y = –5x + 40

Which statement explains which function shows a greater rate of change?
Function 1, because Ada spends $4 each week and Steve spends –$5 each week
Function 1, because Ada spends $12 each week and Steve spends $35 each week
Function 2, because Steve spends $5 each week and Ada spends $4 each week
Function 2, because Steve spends $40 each week and Ada spends $12 each week

Answer 2

@Michele_Laino

Answer 3

we have to write the equation of function #1

Answer 4

in order to do that, we can start from this equation:
\[y = mx + n\]

Answer 5

next I substitute the coordinates of first ordered pair, so I get:
\[40 = m \cdot 1 + n\]

Answer 6

next I substitute the coordinates of the second ordered pair \((2,36)\):
\[36 = m \cdot 2 + n\]

Answer 7

so we got the subsequent linear system:
\[\left\{ \begin{gathered}
40 = m + n \hfill \\
36 = 2m + n \hfill \\
\end{gathered} \right.\]
please solve for \(m\) and \(n\)

Answer 8

i dont know how to solve those

Answer 9

I solve the first equation for \(m\), so I can write:
\[\left\{ \begin{gathered}
40 = m + n \hfill \\
36 = 2m + n \hfill \\
\end{gathered} \right. \Rightarrow \left\{ {\begin{array}{*{20}{c}}
{m = 40 - n} \\
{36 = 2m + n}
\end{array}} \right.\]

Answer 10

then I substitute such value of \(m\) into the second equation:
\[\left\{ \begin{gathered}
40 = m + n \hfill \\
36 = 2m + n \hfill \\
\end{gathered} \right. \Rightarrow \left\{ {\begin{array}{*{20}{c}}
{m = 40 - n} \\
{36 = 2m + n}
\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{c}}
{m = 40 - n} \\
{36 = 2\left( {40 - n} \right) + n}
\end{array}} \right.\]

Answer 11

please solve this equation for \(n\):
\[{36 = 2 \cdot \left( {40 - n} \right) + n}\]

Answer 12

um,
36=2* 40n +n

Answer 13

?????

Answer 14

hint:
we have these steps:
\[\begin{gathered}
36 = 2 \cdot \left( {40 - n} \right) + n \hfill \\
\hfill \\
36 = 80 - 2n + n \hfill \\
\hfill \\
36 = 80 - n \hfill \\
\hfill \\
n = 80 - 36 = ...? \hfill \\
\end{gathered} \]
please solve for \(n\)

Answer 15

what is \(80-36=...?\)

Answer 16

@Michele_Laino sorry, its 44

Answer 17

correct!

Answer 18

next I substitute such value into this equation:
\[m = 40 - n = 40 - 44 = ...?\]
please complete

Answer 19

4

Answer 20

are you sure?

Answer 21

oh sorry -4?

Answer 22

correct!
so the equation of the first function, namely Function #1, is:
\(y=-4x+44\)

Answer 23

ok...

Answer 24

whereas the equation of the second function is:
\(y=-5x+40\)

Answer 25

now, the rate, of such function, are given by the slopes of the corresponding lines, so we have:
\[\begin{gathered}
y = - 4x + 44 \Rightarrow rate = - 4 \hfill \\
y = - 5x + 40 \Rightarrow rate = - 5 \hfill \\
\end{gathered} \]

Answer 26

ok so is the answer C?

Answer 27

oh wait sorry A?

Answer 28

I think it is option C

Answer 29

oh ok!!!
next!

Answer 30

for function A, we have:
\[rat{e_A} = \frac{{16 - 14}}{{8 - 7}} = ...?\]

Answer 31

whereas, from the provided drawing, we have:
\[rat{e_B} = \frac{{8 - 4}}{{4 - 2}} = ...?\]

Answer 32

i solve rate A and b?

Answer 33

yes!

Answer 34

ok..

Answer 35

rate A= 2/1
rate b=4/2

Answer 36

and \(4/2=2\)
so what can you conclude?

Answer 37

A?

Answer 38

correct!