A piecewise function is a function that behaves differently in different intervals.
Here the piecewise function is:
f(x) = $2 if x < 5
f(x) = x - $3 if x ≥ 5
We know that:
"Fun park charges an entry fee of $2 for any family with less than 5 members."
"The park charges $3 less than the number of family members for the entry of any family with 5 or more members."
If we define x as the number of members of a family, the function of the price will be:
f(x) = $2 if x < 5 (the cost is $2 if the family has less than members)
f(x) = x - $3 if x ≥ 5 (the cost if the family has 5 members or more)
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Answer:

Step-by-step explanation:

Answer:
x = 9
Step-by-step explanation:
set a proportion: 8/12 = 6/x => 8x = 72 => x = 9
Answer:
The length of the hypotenuse is 2 square root of 13 ⇒ c
Step-by-step explanation:
The rule of the area of the right triangle is A =
× leg1 × leg2, where
leg1 and leg2 are the sides of the right angle
∵ The area of a right triangle is 12 in²
∵ The ratio of the length of its legs is 2: 3
→ Let leg1 = 2x and leg2 = 3x
∵ leg1 = 2x and leg2 = 3x
→ Substitute them in the rule of the area above
∴ 12 =
× 2x × 3x
∵ 2x × 3x = 6x²
∴ 12 =
× 6x²
∴ 12 = 3x²
→ Divide both sides by 3 to find x²
∴ 4 = x²
→ Take √ for both sides
∴ x = 2
→ Substitute x in the expressions of leg1 and leg2 to find them
∴ leg1 = 2(2) = 4 inches
∴ leg2 = 3(2) = 6 inches
∵ hypotenuse =
∴ hypotenuse = 
∵ The simplest form of
= 2
∴ The length of the hypotenuse = 2
inches