Question

1. alberto drops a stone from a cliff 115 feet above the water. the stone lands 16 feet below the water. use an integer to describe the distance that the stone traveled.
2. add: (-12) + (-12) + (+48)
3. evaluate: |11 - 30|
4. find the area of a rectangle whose length is 3.2 feet and whose width is 1.7 feet. write your answer in square feet.

Explanation:

Step1: Calculate the sum of \((-12)+(-12)\)

Using the rule for adding two negative numbers \(a + b\) (where \(a=-12\), \(b = - 12\)), \((-12)+(-12)=-(12 + 12)=-24\)

Step2: Calculate \(-24+(+48)\)

Using the rule for adding a negative and a positive number \(a + b\) (where \(a=-24\), \(b = 48\)), \(48-24 = 24\)

Step3: Calculate \(|11 - 30|\)

First, find \(11-30=-19\). Then, by the definition of absolute value \(|x|=

$$\begin{cases}x, & x\geq0\\-x, & x<0\end{cases}$$

\), for \(x=-19\), \(| - 19|=19\)

Step4: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\), where \(l = 3.2\) and \(w=1.7\). \(3.2\times1.7=(3 + 0.2)\times1.7=3\times1.7+0.2\times1.7 = 5.1+0.34=5.44\)

Answer:

1. \(24\)
2. \(19\)
3. \(5.44\) square feet