True or false

Question

5. The first time Mya competed in a 500 meter free style race, her time was 15 minutes flat. Each subsequent race, Mya's time was reduced by 10 seconds.

Complete the statement.

(2 points)
The context is best represented by
a linear function
and the domain is
continuous

Answer 1

True.

The context of Mya's swimming times can be represented by a linear function because her time decreases by a constant amount (10 seconds) in each race, resulting in a straight-line equation when graphed over time or the number of races.

Regarding the domain, it is not strictly continuous in the mathematical sense, as Mya can only compete in whole races (discrete values). However, if you are considering the continuous aspect of time or the idea that she could potentially swim an infinite number of races, the statement that the domain is "continuous" may imply a broader interpretation.

Thus, a more precise completion would be: The context is best represented by a linear function, and the domain is discrete (if considering individual races) or could be seen as continuous (in a theoretical sense regarding time).

Answer 2

4. The 3rd term of an arithmetic sequence is 32
. The common difference is 12
. Complete the statement.(2 points)

Answer 3

To find the first term of an arithmetic sequence (denoted as \( a_1 \)), we can use the information provided. The \( n \)-th term of an arithmetic sequence can be expressed as:

\[ a_n = a_1 + (n - 1) \cdot d \]

where \( d \) is the common difference.

Given that:

• The 3rd term (\( a_3 \)) is 32.
• The common difference (\( d \)) is 12.

Substituting these values into the formula for the 3rd term:

\[ a_3 = a_1 + (3 - 1) \cdot d \]

This simplifies to:

\[ 32 = a_1 + 2 \cdot 12 \]

\[ 32 = a_1 + 24 \]

Now, solving for \( a_1 \):

\[ a_1 = 32 - 24 \]

\[ a_1 = 8 \]

Now we can complete the statement:

The first term of the arithmetic sequence is 8.