Question

mixed review
4)**evaluate: $9\frac{4}{5}\times3\frac{1}{4}$
answer:________

1. which of the expressions below can be used to find the distance between -8 and -23?

a) $| - 23| - | - 8|$
b) $| - 8| - | - 23|$
c) $| - 23 - 8|$
d) $-23 - 8$
6)* on monday, the temperature was $-8^{circ}f$. on tuesday, the temperature was 9 degrees warmer than it was on monday. on wednesday, the temperature was 31 degrees colder than it had been on tuesday. what was the temperature on wednesday?
expression:________
answer:________

1. evaluate: $| - 5 + 4| - |6|$

a. 7
b. -7
c. -5
d. 3
8)* patricia went skydiving for her birthday. she descended 504 feet in 12 minutes. what was her mean change in elevation in feet per minute?
answer:________

Explanation:

4)

Step1: Convert mixed numbers to improper fractions

$9\frac{4}{5}=\frac{9\times5 + 4}{5}=\frac{49}{5}$, $3\frac{1}{4}=\frac{3\times4+1}{4}=\frac{13}{4}$

Step2: Multiply the two fractions

$\frac{49}{5}\times\frac{13}{4}=\frac{49\times13}{5\times4}=\frac{637}{20}=31\frac{17}{20}$

5)

The distance between two numbers \(a\) and \(b\) on the number - line is \(|a - b|\). Here \(a=-23\) and \(b = - 8\), so the distance is \(|-23-(-8)|=|-23 + 8|=|-(23 - 8)|=| - 15|=15\). Also, \(|-23-(-8)|=|-23 + 8|=| - 15|=15\) and \(|-23-(-8)|=| - 23+8|=|-(23 - 8)|=| - 15|=15\).
If we use the formula \(|a - b|\) with \(a=-23\) and \(b=-8\), we can also rewrite it as \(|(-23)-(-8)|=| - 23 + 8|=|-(23 - 8)|=| - 15|=15\). Another way to think about it is that the distance between two numbers \(x\) and \(y\) is \(|x - y|\). So for \(x=-23\) and \(y=-8\), the expression is \(|-23-(-8)|=|-23 + 8|=| - 15|=15\).
Let's check each option:

• Option a: \(|-23|-|-8|=23 - 8=15\)
• Option b: \(|-8|-|-23|=8 - 23=-15\) (distance can't be negative)
• Option c: \(|-23 - 8|=|-31|=31\)
• Option d: \(-23-8=-31\) (distance can't be negative)

6)

Step1: Find the temperature on Tuesday

The temperature on Monday is \(-8^{\circ}F\). The temperature on Tuesday is \(9\) degrees warmer than Monday. So the temperature on Tuesday is \(-8 + 9=1^{\circ}F\)

Step2: Find the temperature on Wednesday

The temperature on Wednesday is \(31\) degrees colder than Tuesday. So the temperature on Wednesday is \(1-31=-30^{\circ}F\)
The expression is \((-8 + 9)-31\)

7)

Step1: Simplify inside the absolute - value

First, simplify \(|-5 + 4|\): \(-5+4=-1\), so \(|-5 + 4|=|-1| = 1\)
Second, \(|6| = 6\)

Step2: Subtract

\(|-5 + 4|-|6|=1-6=-5\)

8)

Step1: Use the formula for mean change

The mean change in elevation is \(\frac{\text{total change in elevation}}{\text{time}}\). She descended \(504\) feet (a change of \(-504\) feet) in \(12\) minutes.
The formula is \(\frac{-504}{12}\)

Step2: Divide

\(\frac{-504}{12}=-42\) feet per minute

Answer:

1. \(31\frac{17}{20}\)
2. a) \(|-23|-|-8|\)
3. Expression: \((-8 + 9)-31\); Answer: \(-30^{\circ}F\)
4. c. \(-5\)
5. \(-42\) feet per minute