Algebra 1
Attach this cover sheet to your work. Be sure to completely answer each of the following questions. You
should also state any assumptions you make while answering a question. I highly recommend reading all of
the questions before answering any of them since often questions relate to each other.
1) Recall we have discussed several ways to show if expressions are equivalent or not. Show the following
expressions are not equivalent in two different ways: 12 + x and
€
144 + x
2
.
2) The cost of printing a brochure to advertise your lawn – care business is a flat rate of $10 with an additional
charge of 8 cents per copy.
a. If yo u have budgeted $500 to spend on advertising, how many copies can you have printed for that
amount?
b. Create a table of data for at least 6 different values for the number of copies.
c. Create a graph of the data in part c. Label your axes and include your scales with units.
d. If you have not already done so, translate the given verbal rule to a symbolic rule for this scenario. Be
sure to define your variable.
3) The construction company E. Noether and Sons is reviewing a collection of recent jobs and analyzing th eir
costs. Below is a table showing highway lengths and costs for recent jobs.
Length (miles) 12 19 26 33 41 48 52 59 73
Cost (hundreds of thousands of dollars) 147 135 223 275 359 417 409 451 611
a. Do the points represented by the data set all lie on exactly the same line? Carefully explain your
answer (hint: it’s enough to look at the first three pairs).
b. Use a linear regression equation to answer the following questions:
i. Predict the cost of building 80 miles of highway.
ii. Given a budget of 44 million dollars, estimate the number of miles of highway they can build.
iii. What is the error between the actual cost of building 48 miles of highway and the cost given by
the linear regression
c. Use your graphing calculator to simultaneously graph the data and the regression line. How many of
the data points lie below the line?
4) A linear equation with a single solution is called consistent. If a linear equation is not consistent it is either
an identity or a contradiction.
a. Define identity and contradiction in terms of linear equations .
b. Determine if each equation is an identity, contradiction or consistent. Provide sufficient support for
each conclusion.
i. 5t + 3 = 2(t + 6) ii.
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7( 4 + 2 x )
(28+ 14x )
= 3
iii. 3(2w – 7) = 2(3w + 5) – 31 iv.
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21+ 3(b − 4 ) = 4 (b + 5) − b 1 +
12
b
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5) A couple of this weeks MathXL questions from activity 2.10 asked if two expressions appeared to be
equivalent based on tables of input/output values. We know from our class discussion that tables are great
tools to obtaining a hunch about equivalent expressions but the only way to prove equivalency is
symbolically (which would be next to impossible to devise a way to grade in MathXL). Let’s finish off two
of the MathXL problems in which we used tables to obtain a hunch. Symbolically show the following pa irs
of expressions are equivalent.
a. x
2
– 6 and (- x )
2
– 6
b. 5 x
2
– 10 and 5( x
2
– 2)
6) A company purchases a computer system for $11,500. The depreciation of this system over a five- year
period is given by the following ordered pairs: (0, 11500), (1, 5500), (2, 2500), (3, 1000),
(4, 250), and (5, 0)
a. Construct a table to display this information.
b. What are the input and output variables? Be sure to include units.
c. Plot the given points. Be sure to label and scale your axis.
d. What would the computer system be worth after the fifth year? What about after the sixth year?
Explain your thoughts.
e. Would it be reasonable for this data to be modeled by a linear regression line? If so, give the linear
regression equation that best fits this data. If not, explain wh y.
7) In 2006, Kyle bought a new house in a rapidly expanding real estate market. The market value of his home
can be approximated using equation
€
V = 15⋅ 2.5
(− x
2
+ 2 x −1)
+ 7 . Here x is the number of years since 2006 and
v is the market value of his home in tens of thousands of dollars. The amount Kyle owes on his mortgage
can be approximated using the equation
€
P = 13⋅ 0.95
x
. Again x is the number of years since 2006, while P
is the remaining principal on his loan in tens of thousands of dollars.
a. Use your calculator to find values of V and P when x =0. Explain the practical significance of these
particular values for x , V , and P .
b. Use your calculator to sketch a graph of these equations in the following window:
Xmin = 0 Xmax = 5 Xscl = 1 Ymin = 0 Ymax = 30 Yscl =5
c. Explain why the intersection point on the graph is a solution to the equation
€
15⋅ 2.5
(− x
2
+ 2 x −1 )
+ 7 = 13⋅ 0.95
x
d. Use your graphing calculator to estimate solutions to the above equation. Recall Appendix D
discusses keystrokes f o r a TI – 83/T I 84; particular helpful topics include “Functions and Graphs with
the TI – 83/TI- 84” and “Solving Equations Graphically Using the TI – 83/TI- 84” (A – 28 to A- 34). Also
note that V will appear as follows when typed into your calculator: 15*2.5^(- x
2
+2x – 1) + 7.
Note that since the functions (V and P ) and view window were given for this function, you do not
have to restate these when providing supportive work for this problem. If only part c. and d. were
given, then you would need to state your functions (y
1
, y
2
, etc.) and your view window (Xmin, Xmax,
Xscl, Ymin, and Ymax) as well as sketch a graph to provide complete work for the problem.
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