Lin’s mother has a car that she uses for work, shopping, and trips. About how many times does one tire on her car revolve in a year? Explain or show your reasoning.

Some useful information:

• The diameter of her tire is 27 inches.
• She drives about 10,000 miles in one year.
• There are 5,280 feet in one mile.
• There are 12 inches in one foot.

Ecologists measure the body length and wingspan of 127 butterfly specimens caught in a single field.

1. Draw a line that you think is a good fit for the data.
2. Write an equation for the line.
   
3. What does the slope of the line tell you about the wingspans and lengths of these butterflies?

Diego was solving an equation, but when he checked his answer, he saw his solution was incorrect. He knows he made an error, but he can’t find it. Where is Diego’s error and what is the solution to the equation?

\(\displaystyle \begin{align} \text-4(7-2x)=3(x+4)\\ \text-28-8x=3x+12\\ \text-28=11x+12\\ \text-40=11x\\ \text{-}\frac {40}{11}=x\ \end{align}\)

 

The two triangles are similar. Find \(x\).