Answer:
A) 32, 40, 48, 56, 64, 72, 80
B) y-axis goes 4, 8, 12
x-axis goes 4, 8, 12, 16, 20
4(5x + 12) simplified = 20x + 48
Answer:
A. ![y=-1.2x+59](https://tex.z-dn.net/?f=y%3D-1.2x%2B59)
B. 42.2 million
Step-by-step explanation:
Part A:
Given:
Newspapers circulated in year 2004, ![y_{1}=59\textrm{ million}](https://tex.z-dn.net/?f=y_%7B1%7D%3D59%5Ctextrm%7B%20million%7D)
Newspapers circulated in year 2014, ![y_{2}=47\textrm{ million}](https://tex.z-dn.net/?f=y_%7B2%7D%3D47%5Ctextrm%7B%20million%7D)
Let the time
start at the year 2004. So, ![x_{1}=0](https://tex.z-dn.net/?f=x_%7B1%7D%3D0)
For the year 2014, ![x_{2}=2014-2004=10](https://tex.z-dn.net/?f=x_%7B2%7D%3D2014-2004%3D10)
Therefore, linear relationship between newspapers circulated and time passed since 2004 is given as:
![y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})\\y-59=\frac{47-59}{10-0}(x-0)\\y-59=-\frac{12}{10}x\\y=-1.2x+59](https://tex.z-dn.net/?f=y-y_%7B1%7D%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D%28x-x_%7B1%7D%29%5C%5Cy-59%3D%5Cfrac%7B47-59%7D%7B10-0%7D%28x-0%29%5C%5Cy-59%3D-%5Cfrac%7B12%7D%7B10%7Dx%5C%5Cy%3D-1.2x%2B59)
Therefore, the equation describing the relationship is: ![y=-1.2x+59](https://tex.z-dn.net/?f=y%3D-1.2x%2B59)
Part B:
For the year 2018, ![x=2018-2004=14](https://tex.z-dn.net/?f=x%3D2018-2004%3D14)
Plug in 14 for
in the above equation and solve for
. This gives,
![y=-1.2(14)+59\\y=-16.8+59\\y=42.2](https://tex.z-dn.net/?f=y%3D-1.2%2814%29%2B59%5C%5Cy%3D-16.8%2B59%5C%5Cy%3D42.2)
Therefore, in the year 2018, the newspaper circulation will be 42.2 million.
Answer:
a) 32
b) ![7+(n-1)\times 5](https://tex.z-dn.net/?f=%207%2B%28n-1%29%5Ctimes%205)
Step-by-step Explanation:
Initial pattern has 7 sticks.
Second one has 7+5 sticks.
Third has 7+5+5 sticks.
.
.
.
Sixth has 7+5+5+5+5+5=32 sticks.
$n^{th}$ has $7+ 5(n-1)$ sticks.