A rectangular garden measuring 10 feet by 5 feet is to have a sidewalk that is x feet wide installed all the way around it, increasing the total area to 150 square feet. What is the width, x, of the sidewalk?

Width of sidewalk = 2.5 feet

Step-by-step explanation:

If a sidewalk that is x feet wide installed all the way around the rectangular garden, then the total length of the garden and the side walk would be (10 + 2x) feet while the total width of the garden and the side walk would be (5 + 2x) feet

The formula for determining the area of a rectangle is expressed as

Area = length × width

If the total area increased to 150 square feet, then

(10 + 2x)(5 + 2x) = 150

50 + 20x + 10x + 4x² = 150

4x² + 30x + 50 - 150 = 0

4x² + 30x - 100 = 0

4x² + 40x - 10x - 100 = 0

4x(x + 10) - 10(x + 10) = 0

4x - 10 = 0 or x + 10 = 0

x = 10/4 or x = - 10

Since the width of the sidewalk cannot be negative, then

x = 10/4 = 2.5 feet

true

explanation:

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