A pool is being filled with a large water hose. the height of the water in a pool is determined by 7g^2+3g-4. Previously the pool had been filled with a different hose. then the height was determined by 8g^2+2g-2. Enter an expression that determines the height of the water in the pool if both hoses are on the same time simplify the expression.

If both the hoses are on the same time then the height of the water in the pool is given by the expression  15g^2 + 5g - 6

Step-by-step explanation:

(7g^2 + 3g - 4) + (8g^2 + 2g - 2)

= (7g^2 + 8g^2) + ( 3g + 2g) + (-4 -2)

with the help of distribution law,

= (7 +8)g^2 + (3 + 2)g - (4 + 2)

= 15g^2 + 5g - 6

Therefore if both the hoses are on the same time then the height of the water in the pool is given by the expression  15g^2 + 5g - 6

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11 -1> 1 -1+ a

-12 > a