Paula's Plumbing charges $100 for a house call, including up to one hour of work, and $35 per hour, pro-rated, thereafter. What are the domain and range of the function giving Paula's charge for a job lasting any particular number of hours? A x≥35;y≥135, B x≥0;y≥35, C x≥0;y≥0, D x≥0;y≥100

Step-by-step explanation:

Say the cost for plumbing services be y

and also the charges for any number of hours be x

we can model the cost as given that the flat rate is $100 and an additional $35 per hour

y=35x+100

From the expression above we can see that come what may Paula's earnings for a house call will be greater than $135 so long as Pauls spent an hour which will also give an amount greater than or equal to $35

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graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240