Answer:
Part 1) The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.
![x\leq 7.5\ pounds](https://tex.z-dn.net/?f=x%5Cleq%207.5%5C%20pounds)
Part 2) ![m+n=(0.76x-0.28)](https://tex.z-dn.net/?f=m%2Bn%3D%280.76x-0.28%29)
Step-by-step explanation:
Part 1)
Let
x-----> the number of pounds of regular coffee
we know that
The inequality that represent the situation is
![2x\leq 15](https://tex.z-dn.net/?f=2x%5Cleq%2015)
Solve for x
Divide by 2 both sides
![x\leq 15/2](https://tex.z-dn.net/?f=x%5Cleq%2015%2F2)
![x\leq 7.5\ pounds](https://tex.z-dn.net/?f=x%5Cleq%207.5%5C%20pounds)
The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.
The solution of the inequality is the interval ------> (-∞,7.5]
but the number of pounds cannot be a negative number
therefore
The solution is the interval -----> [0,7.5]
see the attached figure
Part 2) we have
![m=0.56x-0.25](https://tex.z-dn.net/?f=m%3D0.56x-0.25)
![m=0.20x-0.03](https://tex.z-dn.net/?f=m%3D0.20x-0.03)
Adds m and n
![m+n=(0.56x-0.25)+(0.20x-0.03)](https://tex.z-dn.net/?f=m%2Bn%3D%280.56x-0.25%29%2B%280.20x-0.03%29)
Group terms that contain the same variable
![m+n=(0.56x+0.20x)+(-0.25-0.03)](https://tex.z-dn.net/?f=m%2Bn%3D%280.56x%2B0.20x%29%2B%28-0.25-0.03%29)
Combine like terms
![m+n=(0.76x-0.28)](https://tex.z-dn.net/?f=m%2Bn%3D%280.76x-0.28%29)
9514 1404 393
Answer:
a) $2.40
b) $16.80
c) y = -2.40x +16.80
Step-by-step explanation:
a. Dylan's daily spending is the opposite of the slope of the line on the graph. That slope can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (4.8 -12)/(5 -2) = -7.2/3 = -2.4
Dylan spends $2.40 at lunch every day.
__
b. The y-intercept can be found from the formula ...
b = y1 -m(x1)
b = 12 -(-2.40)(2) = 16.80
Dylan's dad gives him $16.80 at the beginning of each week.
__
c. The slope-intercept equation is ...
y = mx + b
y = -2.40x +16.80
A1+(n-1)d
27-3(n-1)
n=4, 27-3(4-1)=27-9=18