Alandscaper makes a $2,000 profit in a week when he services 25 lawns. he makes a $600 profit in a week when he services 11 lawns. if his profit for the week is a linear function of the number of lawns serviced, how much profit would he receive in a week that he services 36 lawns?
$2,600
$2,880
$3,100
$3,600

The answer is $3,100.

Step-by-step explanation: Given that a landscaper makes a $2,000 profit in a week when he services 25 lawns. He makes a $600 profit in a week when he services 11 lawns.We are to calculate the profit that he will receive in a week that he services 36 lawns

Let 'x' represents the number of laws the landscaper serviced in a week in which he makes a profit of '$y'.

So, when x = 25, y = 2000 and when x = 11, y = 600.

Thus, A(25, 2000) and B(11, 600) are two points on the linear function that will be a straight line.

The equation of the line AB will be

Therefore, when he services 36 lawns, then x = 36. So,

Thus, the answer is (c) $3,100.

Hello there!

We know that the landscaper makes $2000 of profit when he services 25 lawns, and he makes $600 in profit when he services 11 lawns.

We also know that the relation between the profit and the number of lawns serviced is a linear relation, this means that the profit is of the form:

P(L) = K*L + b

where K is the slope, L is the number of lawns serviced and b is the y-intercept

Let's find the value of the slope, if we have two points (x1,y1) and (x2,y2)

the slope between them is:

in our case, the points are: (25, 2000) and (11, 600)

then the slope is:

now we have the function profit as:

P(L) = 100L + b

let's find the value of b.

we know that P(11) = 600 = 100*11 + b = 1100 + b

then b = 600 - 1100 = 500

and our profit function is:

P(L) = 100L - 500

now, if L = 36, we need to see

P(36) = 100*36 - 500 = 3100

this means that if he service 36 lawns, he makes $3100, then the right answer is the third one.

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

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step-by-step explanation: