Question

1. an astronomical unit (au) is used to express great distances in space. it is based upon the distance from earth to the sun. a formula for converting any distance d in miles to au is:

\\( 93,000,000 \cdot au = d \\)

\\( \frac{93,000,000}{au} = d \\)

\\( au + 93,000,000 = d \\)

\\( au - 93,000,000 = d \\)

Explanation:

Identify the conversion relationship

Using the Astronomical Unit Conversion and Proportional Reasoning knowledge points

$$ 1\text{ AU} = 93,000,000\text{ miles} $$

Set up the conversion equation

Using the Proportional Reasoning knowledge point

$$ \text{AU} = \frac{d}{93,000,000} $$

Solve for the distance in miles

Using the Astronomical Unit Conversion knowledge point

$$ d = 93,000,000 \cdot \text{AU} $$

Answer:

• (A) \(93,000,000 \cdot \text{AU} = d\) (Correct answer)
• (B) \(\frac{93,000,000}{\text{AU}} = d\)
• (C) \(\text{AU} + 93,000,000 = d\)
• (D) \(\text{AU} - 93,000,000 = d\)