The area of the numbered triangle on a shuffle board court is 27 ft2.Its height is 3 feet more than the length of the base. Find the length of the base and the height. Base ft Height ft

Base = 6ft

Height =9ft

Step-by-step explanation:

Area of a triangle: 1/2 x base length x height

Base = b

Height = b+3

27 = 1/2 x b x (b+3)

27/(1/2) = b (b+3)

54= b^2 +3b

0=b^2 +3b -54

For: ax2+ bx + c  

a=1 ; b=3 ; c =-54

x =[ -b ± √b²-4ac] /2a  

Replacing with the values given:  

x =[ -3 ± √(3)²-4(1)-54] /2(1)  

x = [ -3± √9 +216] /2  

x = [-3 ± √225] /2  

x = [ -3 ± 15] /2  

Positive:  

x = [ -3 + 15] /2 =12/2 = 6  

b= 6 ft (base length)

Height =b+3 = 6+3 = 9 ft

Feel free to ask for more if needed or if you did not understand something.  

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