TASK 2: Lodge Profits After a long day on the slopes, the skiers/snowboarders like to relax in the lodge with some food and a beverage. Help the Slopey Mountain Lodge manager calculate some scenarios 1) In order to make deliciously warm cappuccinos, the lodge must purchase a cappuccino machine for $500. If the lodge charges $5 for a cappuccino a) Write a linear equation to represent the lodge’s profit (P) for “x” number of cappuccinos.. b) Graph the linear equation that would represent the lodge’s profit for “x” number of cappuccinos. What do the numbers on the x-axis represent? What do the numbers on the y-axis represent? According to your graph, after how many cappuccinos does the lodge break even (reach $0)? c) Use your equation to calculate the lodges profit after selling 300 cappuccinos? d) Use your equation to calculate how many cappuccinos the lodge must sell to make a profit of $1,650

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)

(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