Ahouse and a lot are appraised at $42. if the value of the lot 3/4 of the value of the house, how much is the lot alone worth?

Hello from MrBillDoesMath!

180000

Discussion:

Let H = house and L = lot. The Question tells us that H + L = 420000 and L = 3/4H. We are asked to solve for L

H        + L = 420000                => L = 3/4H implies that H =4/3L

(4/3)L + L = 420000               => (4/3) + 1 = 7/3

(7/3)L       = 420000               => multiply both sides by 3/7

(3/7)(7/3)L = (3/7)420000       => as (3/7)(7/3) = 1

L =  180000

Check:  

H + L                = 420000

H + 180000    = 420000

H                      = 420000 - 180000

H =                   =240000

Is L = 3/4H ?

Does     180000 = 3/4 ( 240000)   ?

Does     180000 = (3* 240000)/4 = 720000/4 = 180000  Yes! so the answers check!

Thank you,

MrB

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

it is ok do not worry about it my dude. have a good one