You are putting a rectangular hot tub on your back porch. it is 6 feet long, 5 feet wide, and 3 feet deep. a) how many cubic feet can the hot tub hold if it is completely full? b) how many gallons can it hold? (1 cubic foot = 7.418 gallons) c) how much will it cost to fill the hot tub if water costs $5 per 1000 gallons?

a) The hot tub can hold 90 cubic feet when completely full.

b) the Hot tub ca hold 667.62 gallons.

c) It will cost approximately $3.34 to fill the hot tub with water.

Step-by-step explanation:

Given:

Length of the tub = 6 feet

Width of the tub = 5 feet

Height of the tub = 3 feet.

a) We need to find how many cubic feet can the hot tub hold if it is completely full.

Now we will find the volume of the tub;

Now Volume of the tub is given by length times width times height.

framing in equation form we get;

Volume of the tub =

Hence The hot tub can hold 90 cubic feet when completely full.

b) Now we need to find how many gallons can it hold.

Given:

1 cubic foot = 7.418 gallons

90 cubic foot = number of gallons hot tub can hold.

By using Unitary method we get;

number of gallons hot tub can hold =

Hence the Hot tub ca hold 667.62 gallons.

c) Now we need to find how much will it cost to fill the hot tub if water costs $5 per 1000 gallons.

Now Given:

1000 gallons = $5

667.62 gallons = Cost to fill the hot tub with water.

By Using Unitary method we get;

Cost to fill the hot tub with water =

Hence It will cost approximately $3.34 to fill the hot tub with water.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.