Question

the temperature dropped 3° per hour. how much did the temperature drop in:
a 2 hours
b 4 hours
c 7 hours
d 5 hours
e 8 hours

evaluate each expression:
a. 2·(-4)·5
b. 2·(-4)·(-5)
c. (-2)·(-4)·(-5.2)

(another problem with similar temperature drop context and expression evaluation: \create an equation: the temperature drops 3° per hour. how much did the temperature drop in...\ and \what is the value of each expression? 8(-4) (-3)^3 |-4|\)

Explanation:

Part 1: Temperature Drop (Assuming 3°F per hour, let's solve for each option)

Step 1: Understand the formula

The temperature drop \( T \) is given by the rate \( r = 3^\circ\text{F per hour} \) multiplied by time \( t \), so \( T = r \times t = 3t \).

Step 2: Solve for each option

• A. 2 hours: \( T = 3 \times 2 = 6^\circ\text{F} \)
• B. 4 hours: \( T = 3 \times 4 = 12^\circ\text{F} \)
• C. 7 hours: \( T = 3 \times 7 = 21^\circ\text{F} \)
• D. 5 hours: \( T = 3 \times 5 = 15^\circ\text{F} \)
• E. \( x \) hours: \( T = 3x^\circ\text{F} \) (general formula)

Part 2: Evaluate Expressions

a. \( 2 \times (-4) \times 5 \)

Step 1: Multiply left to right

First, \( 2 \times (-4) = -8 \)

Step 2: Multiply by 5

\( -8 \times 5 = -40 \)

b. \( 2 \times (-4) \times (-5) \)

Step 1: Multiply first two numbers

\( 2 \times (-4) = -8 \)

Step 2: Multiply by -5

\( -8 \times (-5) = 40 \) (negative times negative is positive)

c. \( (-2) \times (-4) \times (-5.2) \)

Step 1: Multiply first two numbers

\( (-2) \times (-4) = 8 \) (negative times negative is positive)

Step 2: Multiply by -5.2

\( 8 \times (-5.2) = -41.6 \) (positive times negative is negative)

Other Expressions (assuming typo, let's evaluate \( 8(-4) \), \( (-3)^3 \), \( |-4| \))

• \( 8(-4) = 8 \times (-4) = -32 \)
• \( (-3)^3 = (-3) \times (-3) \times (-3) = 9 \times (-3) = -27 \)
• \( |-4| = 4 \) (absolute value)

Answer:

s:

Temperature Drop:

• A. 2 hours: \( 6^\circ\text{F} \)
• B. 4 hours: \( 12^\circ\text{F} \)
• C. 7 hours: \( 21^\circ\text{F} \)
• D. 5 hours: \( 15^\circ\text{F} \)
• E. \( x \) hours: \( 3x^\circ\text{F} \)

Expression Evaluation:

• a. \( 2 \times (-4) \times 5 = -40 \)
• b. \( 2 \times (-4) \times (-5) = 40 \)
• c. \( (-2) \times (-4) \times (-5.2) = -41.6 \)
• \( 8(-4) = -32 \)
• \( (-3)^3 = -27 \)
• \( |-4| = 4 \)