Question

Please answer the following correctly!! Thanks so much!!

Answer 1

(1)

`f(x)=3((1)/(3))^x`

`g(x)=3((3)/(4))^x`

(2)

`(8x-9-2x)(15+5x-5)=30x^2+15x-90`

(3)

`(x-8)^2=52`

Explanation:

(1)

Calculation of f(x):

we can use exponential function formula

`f(x)=a(b)^x`

we can select any two points to find 'a' and 'b

At x=0 , y=3:

we can plug values

`f(0)=a(b)^0`

`3=a(b)^0`

`a=3`

now, we can plug it back

`f(x)=3(b)^x`

At x=-1 , y=9:

`f(-1)=3(b)^(-1)`

`9=3(b)^(-1)`

`b=(1)/(3)`

now, we can plug it back

`f(x)=3((1)/(3))^x`

Calculation of g(x):

we can use exponential function formula

`g(x)=a(b)^x`

we can select any two points to find 'a' and 'b

At x=0 , y=3:

we can plug values

`f(0)=a(b)^0`

`3=a(b)^0`

`a=3`

now, we can plug it back

`g(x)=3(b)^x`

At x=1 , y=4:

`g(1)=3(b)^(1)`

`4=3(b)^(-1)`

`b=(3)/(4)`

now, we can plug it back

`g(x)=3((3)/(4))^x`

(2)

we are given

`(8x-9-2x)(15+5x-5)`

we can combine like terms

`(8x-2x-9)(5x+15-5)`

`(6x-9)(5x+10)`

we can distribute it

`=6x\cdot \:5x+6x\cdot \:10+\left(-9\right)\cdot \:5x+\left(-9\right)\cdot \:10`

`=6\cdot \:5xx+6\cdot \:10x-9\cdot \:5x-9\cdot \:10`

`=30x^2+15x-90`

(3)

we are given

`x^2-16x+12=0`

Subtract both sides by 12

`x^2-16x+12-12=0-12`

`x^2-16x=-12`

We can complete square

`x^2-2* 8* x=-12`

we can add 8^2 both sides

`x^2-2* 8* x+8^2=-12+8^2`

`(x-8)^2=-12+8^2`

`(x-8)^2=-12+64`

`(x-8)^2=52`