Hector collects rainwater in a barrel that weighs 15 pounds when there are 10 gallons of water in the barrel, the total water of the barrel and the water is 98.4 pounds. when there are 20 gallons of water, the total weight is 181.8 pounds

"the total water of the barrel and the water is 98.4 pounds" should, I think read "the total weight of the barrel and the water is 98.4 pounds."

What are you expected to do here?

Perhaps finding the weight of the barrel is your goal.

In that case, set up a system of linear equations, using b for the weight of the barrel and w for the weight of the water in the barrel.

Then:

1b + 10g = 98.4 lb

1b + 20g = 181.8 lb

Solve for b and g by elimination. Mult. the 1st eqn by -2: -2b - 20g = 196.8

Add that result to the second equation:

-2b - 20g = -196.8

1b + 20g = 181.8 lb

Then -b = -15 lb. Thus, the weight of the barrel is 15 lb.

What is g, the weight of 1 gallon of water?

Subst. 15 lb for b in the equation 1b + 20g = 181.8 lb

becomes: 15lb + 20g = 181.8 lb

g = 9.09 lb

Thus, the barrel weights 15 lb and each gallono of water weights 9.09 lb.

"if it is my birthday, then it is snowing"

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph