12-14 please in detail

Step-by-step explanation:

12) looking at the right angle triangle,

x = hypotenuse

y = adjacent side

Opposite side = 4

To determine x, we would apply

the sine trigonometric ratio.

Sin θ, = opposite side/hypotenuse. Therefore,

Sin 30 = 4/x

x = 4/sin30 = 4/0.5

x = 8

To determine y, we would apply

the Cosine trigonometric ratio.

Cos θ, = adjacent side/hypotenuse. Therefore,

Cos 30 = y/8

y = 8Cos30 = 8 × 0.866

y = 6.93

14) looking at the right angle triangle,

hypotenuse = 22

y = opposite side

x = adjacent side

To determine y, we would apply

the sine trigonometric ratio.

Therefore,

Sin 45 = y/22

y = 22Sin45 = 22 × 0.7071

y = 15.6

x = y = 15.6 because the triangle is an isosceles triangle.

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)

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