Answer:
Step-by-step explanation:
We are given that The monthly charge for a waste collection service is 1830 dollars for 100 kg of waste
So, 
We are also given that The monthly charge for a waste collection service is 2460 dollars for 135 kg of waste.
So, 
We are supposed to find a linear model for the cost, C, of waste collection as a function of the number of kilograms, w.
So, we will use two point slope form :
Formula : 
Substitute the values
y denotes the cost
x denotes the weight
So, Replace y with C and x with w
So, a linear model for the cost, C, of waste collection as a function of the number of kilograms, w is
Answer:
Dimensions of the rug = 13 ft × 26 ft
Step-by-step explanation:
Dimensions of the room = 21 ft × 34 ft
Area of the room = 21 × 34 = 714 ft²
Cynthia wants to leave a uniform strip of floor around the rug.
Let the width of the rug = x ft
Then the dimensions of the rug will be = (21- 2x)ft × (34 - 2x)ft
Area of the rug = (21 - 2x)×(34 - 2x) square feet
338 = (21 - 2x)×(34 - 2x)
338 = 714 - 68x - 42x + 4x²
4x² - 110x + 714 - 338 = 0
4x² - 110x + 376 = 0
2x² - 55x + 188 = 0
2x² - 47x - 8x + 188 = 0
x(2x - 47) - 8(x - 47) = 0
(x - 4)(2x - 47) = 0
x = 4, 
For x = 23.5 area of the rug will be negative.
Therefore, x = 4 ft will be the width of the rug.
Dimensions of the rug will be 13 ft × 26 ft.
To get the coordinates of C we shall proceed as follows:
AB:BC=1:4
B-A=[(-3--7),(-5--8)]=(4,3)
4(4,3)=(16,12)
thus the coordinates of C will be:
(16-3,-5+12)
=(13,7)
