Name: _____________________
Class: _________________
M8-U10: Notes & HW #6
1.
The time between a flash of lightning and the sound of its thunder can be used to estimate
the distance from a lightning strike. The distance from the strike is the number of seconds
between seeing the flash and hearing the thunder divided by 5. Suppose you are 17 miles
from a lightning strike. Write and solve an equation to find how many seconds there
would be between the flash and thunder.
(Circle the correct answer.)
5
 d , so t is about 0.3 seconds
t
a)
b) t 
c) t  5  d , so t is about 22 seconds
2.
d)
d
, so t is about 3.4 seconds
5
t
 d , so t is about 85 seconds
5
Use the diagram to tell whether the angles MIB and BIH are complementary,
supplementary, or neither. Explain.
S
H
30º P
I
30º
________________________________
90º
________________________________
60º
B
M
________________________________
________________________________
1
3.
Point K below is reflected over the y-axis. How many units are between point K and its
reflection?
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
K
–5
(Circle the correct answer.)
4.
a) 3
b) 6
c) 4
d) 8
Simplify the expression:
a)
c)
x 8
. Express your answer using a positive exponent.
x19
1
x 27
b) x 11
1
d) x 27
x
 27
2
5.
The three different linear functions below are represented in three different ways, as
shown.
Which function has the greatest rate of change? Does any pair of functions have the same
rate of change? Justify your answer.
3
6.
Kimi and Jordan are each working during the summer to earn money in addition to their
weekly allowance, and they are saving all their money. Kimi earns $9 an hour at her job,
and her allowance is $8 per week. Jordan earns $7.50 an hour, and his allowance is $16
per week.
a. Complete the two tables shown below.
Number of hours worked in a week, h
Kimi's weekly total savings, K
0
1
2
3
4
5
6
7
Number of hours worked in a week, h
Jordan's weekly total savings, J
0
1
2
3
4
5
6
7
b. Write an equation that can be used to calculate the total of Kimi's allowance and job
earnings at the end of one week given the number of hours she works.
c. Write an equation that can be used to calculate the total of Jordan's allowance and job
earnings at the end of one week given the number of hours worked.
y
d. Sketch the graphs of your two equations on
one pair of axes.
100
90
80
70
e. Jordan wonders who will save more money in
a week if they both work the same number of
hours. Write an answer for him.
60
50
40
30
20
10
1
4
2
3
4
5
6
7
8
9
10
11
12
13
14
15
x
7.
The amount of money in both Sasha’s and Natalia’s bank account can be represented by a
linear function. Sasha started with $170, and after 10 weeks, she has $290. The graph
shows the amount of money in Natalia’s account.
Which statement is correct?
290  190
is
10  0
a) The rate of change of Natalia’s account balance is greater because
greater than
290  170
.
10  0
b) The rate of change of Natalia’s account balance is greater because
greater than
10  0
.
290  170
c) The rate of change of Sasha’s account balance is greater because
than
290  190
.
10  0
d) The rate of change of Sasha’s account balance is greater because
than
10  0
.
290  190
5
10  0
is
290  190
290  170
is greater
10  0
10  0
is greater
290  170
8.
9.
10.
A plant cell is 0.00001267 meter wide.
How is this number written in scientific notation?
a) 1.267  10 4
b) 1.267  10 5
c) 1.267  10 6
d) 1.267  10 8
7
1
3
1
Where do the lines modeled by the equations y   x  and y   x  intersect?
8
4
4
2
a.  4,2
b.  2,2
c. 2,2
d. 4,2
Look at figure PQRS below.
If figure PQRS is dilated using a scale factor of 0.5 with the center of dilation at (0, 0),
what are the coordinates of the points of the image P ' Q' R ' S ' ?
a. P' 1.5,1.5, Q' 2.5,1.5, R' 2.5,3.5, S ' 0.5,3.5
b. P' 2.5,2.5, Q' 6.5,4.5, R' 6.5,8.5, S ' 2.5,8.5
c. P' 4,4, Q' 12,8, R' 12,16, S ' 4,16
d. P' 1,1, Q' 3,2, R' 3,4, S ' 1,4
6
11.
Jeffrey and Fumi walk at different speeds. Fumi’s walking speed can be represented by
the equation y  85 x , where x is the time in minutes and y is the distance in meters. The
distance Jeffrey walked over time is shown in the graph below.
Which statement is true?
a. Jeffrey walks 5 meters per minute faster than Fumi.
b. Jeffrey walks 10 meters per minute faster than Fumi.
c. Jeffrey walks 5 meters per minute slower than Fumi.
d. Jeffrey walks 10 meters per minute slower than Fumi.
12.
When the points in a scatter plot are clustered closely around a line of best fit, what must
this imply about the correlation between the two variables?
a. There is a strong correlation.
b. There is a weak correlation.
c. There is a negative correlation.
d. There is a positive correlation.
7
13.
14.
Which equation has an infinite number of solutions?
a.  8x  8  0
b.
1
3x  12   1 x  3
4
4
c. 2x  8  2x  8
d.
1
6 x  10  3x  5
2
The figure below shows several rays that share a common endpoint.
What is the measure of QOR ?
a) 61
b) 59
c) 31
d) 26
8
15.
The table below lists the lengths of vines of different amounts of time after planting. The
line of best fit for the data is y  0.48 x  2.97 .
What is the meaning of the slope of the equation?
a. For every decrease in number of days by 1, the vine length decreases by 1 centimeter.
b. For every decrease in number of days by 1, the vine length decreases by 2.97
centimeter.
c. For every increase in number of days by 1, the vine length increases by 1 centimeter.
d. For every increase in number of days by 1, the vine length increases by 0.48
centimeter.
9
16.
Ingrid types faster than 50 words per minute.
Which graph represents the number of words Ingrid can type over time?
B
D
10
17.
Oven Fresh Bakery packages its chocolate cake in this container.
Part A
What is the volume of the container?
Show your work.
Answer _____________________ cubic inches
Part B
The bakery ordered new containers to hold their lemon cake. The container is 2 inches
shorter and has a radius 1 inch less than their chocolate cake containers. What is the
volume of the new container?
Show your work.
Answer _____________________ cubic inches
Part C
How much greater is the volume, in cubic inches, of the original container than the
volume of the new container?
Show your work.
Answer _____________________ cubic inches
11
18.
Amanda found the equation 10 x  5 y  20 in the “Linear Equations” chapter of her math
book.
Part A
What is an equation that can be written with Amanda’s equation to form a pair of linear
equations such that the system of equations has exactly one solution?
Show your work.
Equation _____________________
Part B
What is an equation that can be written with Amanda’s equation to form a pair of linear
equations such that the system of equations has infinitely many solutions?
Show your work.
Equation _____________________
12