### All Algebra II Resources

## Example Questions

### Example Question #14 : Variable Relationships

What is the next number in this sequence: 8, 27, 64, 125 ?

**Possible Answers:**

**Correct answer:**

Find the pattern of the sequence:

This pattern is so the next number in the sequence would be

### Example Question #15 : Variable Relationships

Find the next 2 numbers in this sequence: 33, 46, 72, 111

**Possible Answers:**

**Correct answer:**

Find the pattern in this sequence of numbers:

In this case, the pattern is adding 13n to the previous number where n= how many numbers came before the current number.

so the first number we are looking for would be:

the second number we are looking for would be:

### Example Question #16 : Variable Relationships

The amount of water inside of a leaky boat is measured periodically after the boat has been in the water in different periods of time and are found to have a linear relationship. The results are given in the following chart:

Time in water (mins) | Amount of water in the boat (gal) |

0 | 0 |

6 | 4.8 |

19 | 15.2 |

28 | 22.4 |

Using the method of linear extrapolation based on the data from the table, how much water would you expect to be in the boat after 53 minutes?

**Possible Answers:**

**Correct answer:**

To extrapolate the results of the study out to 53 minutes, first we have to determine an equation representing the relationship between time passed and amount of water; we can write our equation in *slope-intercept form*:

Where our y-axis represents amount of water and the x-axis represents time. We can pick 2 points and label them *Point 1* and *Point 2*; looking back at the table:

Time in water (mins) | Amount of water in the boat (gal) |

0 | 0 |

6 | 4.8 |

19 | 15.2 |

28 | 22.4 |

We label *Point 1* as and *Point 2* as ; we plug these points into the slope formula as follows:

So, the slope of our line that describes how much water is in the boat is ; to find our term, the y-intercept, we need to pick a point on the graph and plug in our slope to solve for y-intercept. Let's once again choose the point :

Simplify the expression and we find that b=0, so our *slope-intercept* equation is:

Plugging in a value of 53 for , we find that:

So the answer is 42.4 gallons of water in the boat after 53 minutes.