Question

lesson 3.3 checkpoint
complete the previous problems, check your solutions, then complete the lesson checkpoint below.
complete the lesson reflection above by circling your current understanding of the learning goal(s).
evaluate the function when x = -2, 0, and 5.

1. v(x) = 12 - 2x - 5
2. the function d(t) = 300,000t represents the distance (in kilometers) that light travels in t seconds.

a) how far does light travel in 15 seconds?
b) how long does it take light to travel 12 million kilometers?

Explanation:

Problem 9: Evaluate \( v(x) = 12 - 2x - 5 \) at \( x = -2, 0, 5 \)

First, simplify the function \( v(x) \):

Step 1: Simplify \( v(x) \)

Combine like terms: \( 12 - 5 = 7 \), so \( v(x) = 7 - 2x \).

Step 2: Evaluate at \( x = -2 \)

Substitute \( x = -2 \) into \( v(x) \):
\( v(-2) = 7 - 2(-2) = 7 + 4 = 11 \).

Step 3: Evaluate at \( x = 0 \)

Substitute \( x = 0 \) into \( v(x) \):
\( v(0) = 7 - 2(0) = 7 - 0 = 7 \).

Step 4: Evaluate at \( x = 5 \)

Substitute \( x = 5 \) into \( v(x) \):
\( v(5) = 7 - 2(5) = 7 - 10 = -3 \).

The function is \( d(t) = 300,000t \), where \( t \) is time in seconds.

Step 1: Substitute \( t = 15 \)

Substitute \( t = 15 \) into \( d(t) \):
\( d(15) = 300,000 \times 15 \).

Step 2: Calculate the product

\( 300,000 \times 15 = 4,500,000 \).

We know \( d(t) = 300,000t \) and \( d(t) = 12,000,000 \) (12 million kilometers).

Step 1: Set up the equation

\( 300,000t = 12,000,000 \).

Step 2: Solve for \( t \)

Divide both sides by 300,000:
\( t = \frac{12,000,000}{300,000} \).

Step 3: Simplify the fraction

\( \frac{12,000,000}{300,000} = 40 \).

Answer:

• \( v(-2) = 11 \)
• \( v(0) = 7 \)
• \( v(5) = -3 \)

Problem 22a: Distance light travels in 15 seconds