Eight hot dogs and seven hot dog rolls cost $\$13.60$. Seven hot dogs and eight hot dog rolls cost $\$13.40$. How much, in dollars, does a hot dog and a hot dog roll cost combined?

$1.80

Step-by-step explanation:

Let the cost of a hot dog = x

The cost of a hot dog roll = y

Eight hot dogs and seven hot dog rolls cost $\$13.60$.

8x + 7x = $13.60 Equation 1

Seven hot dogs and eight hot dog rolls cost $\$13.40$.

7x + 8x = $13.40 Equation 2

Combining both Equation

8x + 7x = $13.60 Equation 1

7x + 8x = $13.40 Equation 2

Eliminating x

Multiply 1 by 7

Multiply 2 by 8

56x + 49y = 95.2 Equation 3

56x + 64y = 107.2 Equation 4

Subtracting 4 from 3

-15y = -12

y = -12/-15

y = 0.8

Cost of one hot dog roll = $0.8

Solving for x

8x + 7x = $13.60

8x + 7(0.8) = 13.60

8x + 5.6 = 13.60

8x = 13.60 - 5.60

8x = 8.0

x = 8.0/8

x = 1.

Cost of one hot dog = $1.0

The cost in dollars of a hot dog and a hot dog roll cost combined is

x + y

= $1 + $0.8

= $1.80

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