Name: _____________________
Class: _________________
AU10: Notes & HW – Lesson 3
Date: _________________
1. If n is an odd integer, which equation can be used to find three consecutive odd integers
whose sum is -3? (RJu12#25 – AU7)
(1) n + (n + 1) + (n + 3) = -3
(3) n + (n + 2) + (n + 4) = -3
(2) n + (n + 1) + (n + 2) = -3
(4) n + (n + 2) + (n + 3) = -3
2. The length of the shortest side of a right triangle is 8 inches. The lengths of the other two
sides are represented by consecutive odd integers. Which equation could be used to find the
lengths of the other sides of the triangle? (SS4 – AU7/8)
(1) 8 2  x  1  x 2
(2) x 2  8 2   x  1
(3) 8 2  x  2  x 2
2
2
(4) x 2  8 2  x  2
2
3. Emma recently purchased a new car. She decided to keep track of how many gallons of gas
she used on five of her business trips. The results are shown in the table below.
Write the linear regression equation for this data where miles driven is the independent
variable. (Round all values to the nearest hundredth.) (FS 7 – AU3/5)
1
4. A model rocket is launched from a platform in a flat, level field and lands in the same field.
The height of the rocket follows the function, f x   16 x 2  150 x  5 , where f(x) is the
height, in feet, of the rocket and x is the time, in seconds, since the rocket is launched.
Determine the maximum height, to the nearest tenth of a foot, the rocket reaches.
Determine the length of time, to the nearest tenth of a second, from when the rocket is
launched until it hits the ground. [The use of the grid below is optional.] (GC 4 – AU2/9)
y
x
2
5. Solve for x in each of the equations/inequalities below. If appropriate write identity or no
solution. Name the property and/or properties used. (M1:EM#4 – AU1)
a)
3
x9
4
b) 10  5x  5x
c) a  x  b
d) cx  d
e)
1
xg m
2
f) q  5 x  5 x  q
g)
3
x  2  6x  12
4
h) 35  5x  5x
3
6. Suppose that Peculiar Purples and Outrageous Oranges are two different and unusual types of
bacteria. Both types multiply through a mechanism in which each single bacterial cell splits
into four. However, they split at different rates: Peculiar Purples split every 12 minutes,
while Outrageous Oranges split every 10 minutes. (M5:EM#4 – AU6)
a. If the multiplication rate remains constant throughout the hour and we start with three bacterial
cells of each, after one hour, how many bacterial cells will there be of each type? Show your
work and explain your answer.
b. If the multiplication rate remains constant for two hours, which type of bacteria is more
abundant? What is the difference between the numbers of the two bacterial types after two
hours?
c. Write a function to model the growth of Peculiar Purples and explain what the variable and
parameters represent in the context.
4
d. Use your model from part (c) to determine how many Peculiar Purples there will be after three
splits, i.e., at time 36 minutes. Do you believe your model has made an accurate prediction? Why
or why not?
e. Write an expression to represent a different type of bacterial growth with an unknown initial
quantity but in which each cell splits into 2 at each interval of time.
7. Consider the following system of equations with the solution x = 3, y = 4.
Equation A1: y  x  1
Equation A2: y  2 x  10
Write a unique system of two linear equations with the same solution set. This time make
both linear equations have positive slope. (M1:EM#11 – AU4)
Equation B1: ________________
Equation B2: ________________
5