A plumber charges $50 to visit a house plus $40 for every
hour of work. Define a variable and write an expression to represent
the total cost of hiring a plumber.

Step-by-step explanation:

Regardless of how many hours the plumber works, you have to pay $50 for him to even walk into your house.  That's non-negotiable.  If he charges $40 per hour, then the amount you pay him obviously depends upon the number of hours he works.  The variable is x and it represents the number of hours the plumber works.  The cost function for hiring this plumber is

y = 40x + 50

That means that $50 is paid even if the plumber does no work at all.  If he does an hour's worth of work, x will be replaced by 1, and the fee he will charge is 40 + 50 = 90.  If he works 2 hours, x will be replaced by 2, the fee he will charge is 80 + 50 = 130.  Etc.  Above is the cost function you need to answer this question.

345

step-by-step explanation:

(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