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

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt