Find two numbers if their sum 16 and their ratio is 5:7

6.666  or 6 2/3   and  9. 333  or 9 1/3

Step-by-step explanation:

5+7 = 12 so 1 part is 1

16/12 = 1.333.. = 1 1/3   1 part is changed when the total is higher

5 x 1  1/3 = 6.666  6 2/3

7 x 1  1/3 = 9. 333  = 9 1/3

Step-by-step explanation:

Let A and B stand for the two numbers.

A + B = 16

A/B = 5/7

Rearrange the first and substitute:

A = 16-B

(16-B)/B = 5/7

(16-B) = 5B/7

5B/7 = (16-B)

5B = 7(16-B)

5B = 112 - 7B

12B = 112

B = 9.3333 or 9 1/3

A = (16 - 9.333) or (16 - 9 1/3)

A = 6.6667 or 6 2/3

A + B = 16?

9 1/3 + 6 2/3 = 16  YES

A/B = 5/7 ?

(6 2/3)/(9 1/3) = (20/3)/(28/3) = (20/3)*(3/28)

= (20/28) = 5/7  YES

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