Question

1. geometry a rectangle has side lengths of (3x + 6) inches and (2x - 4) inches. write an expression to represent the perimeter of the rectangle. then find the value of x if the perimeter is 94 inches.
2. cruise ships the table shows the number of cruise ships in a harbor on various days.

a. write an expression for the total number of cruise ships in the harbor on monday and tuesday.
b. write an expression for the total number of cruise ships in the harbor on all 5 days.

Explanation:

Step1: Find the perimeter formula for a rectangle

The perimeter \(P\) of a rectangle is given by \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Here, \(l=(3x + 6)\) and \(w=(2x-4)\).

$$P=2((3x + 6)+(2x - 4))$$

Step2: Simplify the expression inside the parentheses

Combine like - terms: \((3x+6)+(2x - 4)=3x+2x+6 - 4=5x + 2\)
So, \(P = 2(5x + 2)=10x+4\)

Step3: Solve for \(x\) when \(P = 94\)

Set up the equation \(10x+4 = 94\)
Subtract 4 from both sides: \(10x+4-4=94 - 4\), which gives \(10x=90\)
Divide both sides by 10: \(x=\frac{90}{10}=9\)

Answer:

The expression for the perimeter is \(10x + 4\) and the value of \(x\) is \(9\)