Homework 1 #4 Integrated Mathematics I / Math I AIR Practice 2016 (Robertson)
Student Name/ID: 1. Answer each question below.
8
y
8
Figure A
6
6
4
4
2 -8
-6
-4
-2
2
x 2
-2
4
6
8
y
-8
-6
-4
-4
-2
-2
x 2
4
6
8
-4
-6
-6
Figure B
-8
Figure D
-8
Figure C
Are Figure A and Figure B congruent? Yes No
Are Figure C and Figure D congruent? Yes No
Which transformation will map Figure A onto Figure B exactly?
Which transformation will map Figure C onto Figure D exactly?
Translate Figure A to the right 4 units
4 units Reflect Figure A over the x -axis Reflect Figure A over the y -axis Rotate Figure A clockwise 90 ° about the Translate Figure A up
origin
Rotate Figure A counterclockwise about the origin None of these
180 °
Translate Figure C to the left 6 units Translate Figure C down
6 units
Reflect Figure C over the x -axis Reflect Figure C over the y -axis Rotate Figure C clockwise origin
180 °
Rotate Figure C counterclockwise about the origin None of these
about the
90 °
2. The function f is defined by the following rule.
f x =3x −5 Complete the function table.
x
f x
−3 0 2 4 5
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3. Shown below are the scatter plots for four different data sets. Answer the questions that follow. The same response may be the correct answer for more than one question. 11 10 9 8 7 6 5 4 3 2 1 0
y
x
11 10 9 8 7 6 5 4 3 2 1
1 2 3 4 5 6 7 8 9 10 11
0
y
x 1 2 3 4 5 6 7 8 9 10 11
Figure 1
11 10 9 8 7 6 5 4 3 2 1 0
Figure 2
y
x
11 10 9 8 7 6 5 4 3 2 1
1 2 3 4 5 6 7 8 9 10 11
0
y
x 1 2 3 4 5 6 7 8 9 10 11
Figure 3
Figure 4
1. For which data set is the correlation coefficient r closest to - The data set in Figure 1 - The data set in Figure 2 - The data set in Figure 3 - The data set in Figure 4
1?
2. Which data set indicates the strongest negative linear relationship between its two variables? - The data set in Figure 1 - The data set in Figure 2 - The data set in Figure 3 - The data set in Figure 4 3. For which data set is the correlation coefficient r closest to - The data set in Figure 1 - The data set in Figure 2 - The data set in Figure 3 - The data set in Figure 4
0?
4. Kevin bought n packs of pencils. Each pack has 10 pencils. Write an equation to represent the total number of pencils p that Kevin bought.
5. A cyclist rides his bike at a rate of 12 miles per hour. What is this rate in miles per minute? How many miles will the cyclist travel in
5 minutes? Do not round your answers.
6. An arithmetic sequence is given below.
18 , 15 , 12 , 9 , ... Write an explicit formula for the
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n th term a n .
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7. Yoko has been withdrawing the same amount of money from her bank account every month. The table below shows the amount of money in her account after different amounts of time. Time (months)
6
8
10
12
Money (dollars)
640
570
500
430
Answer the following questions. (a) Choose the statement that best describes how the time and amount of money in her account are related. Then give the value requested. As time increases, the amount of money in her account decreases. At what rate is the amount of money in her account decreasing? ______ dollars per month As time increases, the amount of money in her account increases. At what rate is the amount of money in her account increasing? ______ dollars per month (b) How much money was in her account before Yoko starting withdrawing money? ______ dollars
8. Each day, Joe earns a fixed wage plus extra money for every hour of overtime he works. The graph shows his total pay (in dollars) versus the amount of overtime (in hours) that he works. y 250 225 200 175 150
Total pay 125 (dollars) 100 75 50 25 x 0
1
2
3
4
5
6
7
8
9
Overtime (hours)
Answer the following questions. (a) What is Joe's total pay with
0 hours of overtime?
$ ______ (b) Choose the statement that best describes how the amount of overtime and total pay are related. Then give the value requested. As the amount of overtime increases, the total pay decreases. At what rate is the total pay decreasing?
$ ______ per hour As the amount of overtime increases, the total pay increases. At what rate is the total pay increasing?
$ ______ per hour
9. A textbook store sold a combined total of 423 biology and math textbooks in a week. The number of math textbooks sold was 51 less than the number of biology textbooks sold. How many textbooks of each type were sold?
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10. Graph the line.
y = −2 x y 8 6 4 2 x -8
-6
-4
-2
2
4
6
8
-2 -4 -6 -8
11. Consider the line
y=
3 x. 4
What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line?
12. Goran is going for a run. He runs at a speed of 4.8 miles per hour for
3 hours. For how many miles does he run?
13. Graph the line.
y = −5 x + 5 y 8 6 4 2 x -8
-6
-4
-2
2
4
6
8
-2 -4 -6 -8
14. Solve for y .
y −8 =c
15. A plant is already 41 centimeters tall, and it will grow one centimeter every month. Let H be the plant's height (in centimeters) after Write an equation relating Equation: Plant's height after
38
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M months.
H to M. Then use this equation to find the plant's height after 38
months.
months: ______ centimeters
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16. The figure below shows a circular courtyard. Its radius is 44
m.
44 m
(a)
Use the calculator to find the circumference and area of the courtyard.
Use 3.14 for π in your calculations, and do not round your answers. Make sure to include the correct units.
Circumference: Area: (b)
A chain will surround the courtyard. Which measure would be used in finding the amount of chain needed?
- Circumference - Area (c)
The courtyard will be paved. Which measure would be used in finding the amount of pavement needed?
- Circumference - Area
17. Determine whether a triangle with the given vertices is a scalene, isosceles, or equilateral triangle. Check all that apply. Scalene triangle
J 1 , −2
,
D 7, 0
E −1 , 6
,
A −2 , 0
,
K 0 , −6 ,
B −2 , 2
18. The equation
,
Isosceles triangle
Equilateral triangle
L 6 , −6
F −1 , −4 ,
C 3, 1
6 y − 1 = −18
is solved in several steps below.
For each step, choose the reason that best justifies it. Step
Reason
6 y − 1 = −18 6 y −1 −18 = 6 6
Given equation - Addition Property of Equality - Subtraction Property of Equality - Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property - Addition Property of Equality - Subtraction Property of Equality - Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property
y − 1 = −3
- Addition Property of Equality
y − 1 + 1 = −3 + 1
- Subtraction Property of Equality - Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property
y = −2
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−3 , 3
4, 3
- Addition Property of Equality - Subtraction Property of Equality - Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property
4, − 7
−3 , − 7
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19. Find the area and perimeter of the rectangle with vertices
−3 , 3
,
4, 3
4, − 7
,
, and
−3 , − 7
.
3
7
Note that you can draw in the Scratch Area below, but it is not part of the answer.
8
y
7 6 5 4 3 2 1 -8
-7
-6
-5
-4
-3
-2
-1
-1
x 1
2
4
5
6
8
-2 -3 -4 -5 -6 -7 -8
Area: _____ square units Perimeter: _____ units
20. Kaitlin is a software saleswoman. Her monthly salary is
$ 2100
plus an additional
$ 110
for every copy of History is Fun she sells.
Let S represent her total salary this month (in dollars), and let N represent the number of copies of History is Fun she sells. Write an equation relating equation using the axes below. 3000
S
to
N , and then graph your
S
2750 2500 2250 2000 1750 1500 1250 1000 750 500 250
N 1
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2
3
4
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5
6
7
23
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21. The scatter plot shows the time spent watching TV, x , and the time spent doing homework, y , by each of 23 students last week. 32
y
28 24 Time spent
20
doing homework
16
in hours
12 8 4 x 0
4
8
12
16
20
24
28
32
36
Time spent watching TV in hours
Use the equation of the line of best fit, y = −0.76 x + 26.04 , to answer the questions below. Give exact answers, not rounded approximations. (a) What is the predicted time spent doing homework for a student who doesn't spend any time watching TV? (b) What is the predicted time spent doing homework for a student who spends 12 hours watching TV?
(c) For an increase of one hour in the time spent watching TV, what is the predicted decrease in the time spent doing homework?
_____hours
_____hours
_____hours
22. Owners of a recreation area are filling a small pond with water. Let y represent the total amount of water in the pond (in liters). Let x represent the total number of minutes that water has been added. Suppose that x and
y are related by the equation y = 500 + 34 x .
Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What was the starting amount of water in the pond? ________ liters What is the change per minute in the amount of water in the pond? ________ liters
23. Solve for x .
z =3x −7y
−8
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+3 = 32
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24. The equation
−8 u + 3 = 32
is solved in several steps below.
For each step, choose the reason that best justifies it. Step
Reason
−8 u + 3 =32
Given equation - Addition Property of Equality - Subtraction Property of Equality - Multiplication Property of Equality - Division Property of Equality
−8 u − 24 =32
- Simplifying - Distributive Property - Addition Property of Equality - Subtraction Property of Equality
−8 u − 24 + 24 = 32 + 24
- Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property - Addition Property of Equality - Subtraction Property of Equality
−8 u =56
- Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property - Addition Property of Equality
−8 u 56 = −8 −8
- Subtraction Property of Equality - Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property - Addition Property of Equality
u = −7
- Subtraction Property of Equality - Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property
25. Leila will choose between two restaurants to purchase pizzas for her party. The first restaurant charges a delivery fee of $ 4 for the entire purchase and second restaurant has no delivery fee and charges $ 12 per pizza.
$ 10
per pizza. The
Let x be the number of pizzas purchased. (a) For each restaurant, write an expression for the total charge of purchasing
x pizzas (with delivery).
Total charge from the first restaurant (in dollars) = __
Total charge from the second restaurant (in dollars) = __ (b) Write an equation to show that the total charge (with delivery) from the two restaurants is the same. __
26. For each ordered pair, determine whether it is a solution to
x, y
5 x − 4 y = 17 .
Is it a solution? Yes
No
−3 , − 8
−6 , 2
1, − 3
2, 9
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27. Solve the equation by graphing.
0 =2x +2
y 8 6 4 2 x -8
-6
-4
-2
2
4
6
8
-2 -4 -6 -8
28. One month Michael rented 8 movies and each movie and each video game.
4 video games for a total of $ 41 . The next month he rented 3 movies and 2 video games for a total of $ 18 . Find the rental cost for
29. The owners of a recreation area filled a small pond with water in liters) in the pond versus time (in minutes).
120
minutes. The pond already had some water at the beginning. The graph shows the amount of water (in
Find the range and the domain of the function shown. 1500
y
1350 1200 1050
Amount of water (liters)
900 750 600 450 300 150 0
x 20
40
60
80
100 120 140 160 180
Time (minutes)
Write your answers as inequalities, using
x or y as appropriate.
range: domain:
30. The Sugar Sweet Company is going to transport its sugar to market. It will cost $ 6500 to rent trucks, and it will cost an additional $ 125 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating to transport 11 tons of sugar.
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C to S . Then use this equation to find the total cost
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31. Each part below contains one triangle and one figure that can be adjusted to make a triangle. The markings indicate congruence. (a) Adjust the figure on the right to explore the different triangles that can be formed. Then answer the question. Note that the figure will not be graded.
Which of the following is true? The two triangles must be congruent. Reason:
'Side-Angle-Side (SAS) Congruence Property' , 'Angle-Side-Angle (ASA) Congruence Property' , 'Side-Side-Side (SSS) Congruence Property' , 'Angle-Angle-Side (AAS) Congruence Property'
The two triangles do not have to be congruent. (b) Adjust the figure on the right to explore the different triangles that can be formed. Then answer the question. Note that the figure will not be graded.
Which of the following is true? The two triangles must be congruent. Reason:
'Side-Angle-Side (SAS) Congruence Property' , 'Angle-Side-Angle (ASA) Congruence Property' , 'Side-Side-Side (SSS) Congruence Property' , 'Angle-Angle-Side (AAS) Congruence Property'
The two triangles do not have to be congruent.
32. A construction crew is lengthening a road. Let L be the total length of the road (in miles). Let D be the number of days the crew has worked. Suppose that L = 3 D + 400 gives L as a function of D. The crew can work for at most 90 days.
Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values. Domain Description of Values length of the road (in miles) number of days the crew has worked Set of Values the set of all real numbers from 400 to 670 the set of all real numbers from 3 to 400 the set of all real numbers from 0 to 90 {90, 91, 92, 93, ...} {0, 1, 2, 3, ..., 400} {3, 6, 9, 12, ...} Range Description of Values length of the road (in miles) number of days the crew has worked Set of Values the set of all real numbers from 400 to 670 the set of all real numbers from 3 to 400 the set of all real numbers from 0 to 90 {90, 91, 92, 93, ...} {0, 1, 2, 3, ..., 400} {3, 6, 9, 12, ...}
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17.92
7
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33. A construction crew has just built a new road. They built 17.92 kilometers of road at a rate of 7 kilometers per week. How many weeks did it take them? 34. For each graph below, state whether it represents a function. y 8 6 4 2 -8
-6
-4
-2
x 2
-2
4
6
8
-4
Function?: Yes No
-6 -8
y 4
2
-2
x
Function?: Yes No
x
Function?: Yes No
2 -2
-4 y 4 2
-4
-2
2
4
-2 -4
2
y
1
x -2
-1
1
2
-1
Function?: Yes No
-2
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y 4
Function?: Yes No
2 x -4
-2
2 -2
4
y
4 -4 2
Function?: Yes No
x -4
-2
2
4
-2 -4
35. Ahmad has 13 shirts to fold. Let N be the number of shirts he would have left to fold after folding Write an equation relating
F of them.
N to F. Then graph your equation using the axes below.
N 18 16 14 12 10 8 6 4 2 F 2
4
6
8
10
12
14
16
18
36. Below is the table of values of a function. Write the output when the input is n . input
6
8
9
output
1
3
4
n
37. Write an inequality for the following statement.
c is greater than or equal to 6
38. Solve for y .
7 y − 1 − 1 = −3 −7 y + 4 − 2 y Simplify your answer as much as possible.
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39. The figure below shows a rectangular window. 38 in
66 in
(a)
Use the calculator to find the perimeter and area of the window. Make sure to include the correct units.
Perimeter: Area: (b)
The window's glass will be replaced. Which measure would be used in finding the amount of glass needed?
- Perimeter - Area (c)
A silver wire will be placed around the window. Which measure would be used in finding the amount of wire needed?
- Perimeter - Area
40. Linda had
m
dollars to begin with. She just spent 29 dollars. Using
m , write an expression for the number of dollars she has left.
41. Answer the questions below. 1. A financial magazine conducted a survey. It showed that a person with more years of education tends to have a higher salary. What is likely true? There is no correlation between years of education and salary. There is a correlation between years of education and salary. There may or may not be causation. Further studies would have to be done to determine this. There is a correlation between years of education and salary. There is probably also causation. This is because there is an increase in salary with an increase in the years of education. 2. A grocery store collected sales data. It found that a change in price does not imply that people will buy more or less milk. What can we determine from this information? There is no correlation between price and amount of milk bought. There is a correlation between price and amount of milk bought. However, there is no causation. This is because there is likely a decrease in the amount of milk bought with an increase in the price. There is a correlation between price and amount of milk bought. There may or may not be causation. Further studies would have to be done to determine this. 3. Mr. Nelson studied his students' geography test scores and TV habits. He found that students who watched less TV tended to earn higher scores on the test. What conclusion should he make? There is no correlation between test score and amount of TV watched. There is a correlation between test score and amount of TV watched. There is probably also causation. This is because there is an increase in a student's test score with a decrease in the amount of TV watched. There is a correlation between test score and amount of TV watched. There may or may not be causation. Further studies would have to be done to determine this.
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42. For each relation, decide whether or not it is a function.
Relation 1
Relation 2
Domain
Range
t
g
g
w
w
t
s
s
z
z
Domain
Range
-2
sky
-7
star
1
sky
-1
desk
3
star
1
desk
Function
Function
Not a Function
Not a Function
Relation 3
Relation 4
(6, -1), (8, -1), (6, 6), (8, 6)
(-6, r), (-9, n), (-9, y), (-6, g)
Function
Function
Not a Function
Not a Function
43. Translate this sentence into an equation. The product of 3 and Mai's age is 39 . Use the variable
m
to represent Mai's age.
44. The first three terms of an arithmetic sequence are as follows.
−9 , −4 , 1 Find the next two terms of this sequence.
45. Graph the inequality.
2 x − 5 y < 10 y 10 8 6 4 2 -10
-8
-6
-4
-2
-2
x 2
4
6
8
10
-4 -6 -8 -10
46. Find the slope of the line passing through the points
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−7 , 2
and
9, 6
.
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47. Graph the inequality.
y < −x − 5 y 8 6 4 2 x -8
-6
-4
-2
2
4
6
8
-2 -4 -6 -8
48. An engineer estimated the weight of a steel beam to be
150
pounds. The actual weight of the beam was 143 pounds.
Find the absolute error and the percent error of the engineer's estimate. If necessary, round your answers to the nearest tenth.
49. Which pairs of figures below are congruent?
Congruent?
Yes
No
Yes
No
Congruent?
Yes
No
Yes
No
50. Rita bought some books for
$ 4 each and received a discount of $ 5 off of her total purchase. She spent $ 71
after the discount. How many books did she buy?
(a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 4 , 5 , and represent the number of books. ___b + ___
=
___
___b − ___
=
___
71 . Let b
(b) Solve the equation in part (a) to find the number of books.
b=
______
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51. Below is the table of values of a function. Write the output when the input is n . input
1
3
9
output
3
9
27
n
52. Henry is printing extra flyers to distribute. The flyers are printed at a constant rate. The table below shows the number of flyers he has after different amounts of time. Time (minutes)
10
15
20
25
Flyers
87
112
137
162
Answer the following questions. (a) How many flyers did Henry already have when he started printing? ______ flyers (b) Choose the statement that best describes how the time and number of flyers Henry has are related. Then give the value requested. As time increases, the number of flyers decreases. At what rate is the number of flyers decreasing? ______ flyers per minute As time increases, the number of flyers increases. At what rate is the number of flyers increasing? ______ flyers per minute
53. Find the slope of the line graphed below. y 5 4 3 2 1 x -5
-4
-3
-2
-1
1
2
3
4
5
-1 -2 -3 -4 -5
54. The sequences below are either arithmetic or geometric. For each sequence, determine whether it is arithmetic or geometric, and write the formula for the
n th term a n of that
sequence. Sequence
8 , 16 , 32 , ... 13 , 16 , 19 , ...
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Type Arithmetic Geometric Arithmetic Geometric
nth term formula
a n = ____ a n = ____
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55. The function
g is defined as follows for the domain given.
g x = 2 x + 1,
= −5 , −1 , 2 , 3
domain
Write the range of g using set notation. Then graph
g.
range = _______________ y
9 8 7 6 5 4 3 2 1
x
-9 -8 -7 -6 -5 -4 -3 -2 -1-1 -2
1
2
3
4
5
6
7
8
9
-3 -4 -5 -6 -7 -8 -9
56. The first three terms of a geometric sequence are as follows.
2 , −8 , 32 Find the next two terms of this sequence. Give exact values (not decimal approximations).
57. Melissa has 12 cars available to rent. Let C be the number of cars she would have left after renting Write an equation relating
R
of them.
C to R . Then graph your equation using the axes below.
C 18 16 14 12 10 8 6 4 2 R 2
4
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6
8
10
12
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14
16
18
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Homework 1 #4 Answers for class Math I AIR Practice 2016 1. 8
y
8
Figure A
6
6
4
4
2 -8
-6
-4
-2
-2
2
x 2
4
6
8
-8
-6
-4
-4
-2
-2
x 2
4
6
8
-4
-6 -8
y
-6
Figure B
Figure D
-8
Figure C
Are Figure A and Figure B congruent? Yes No
Are Figure C and Figure D congruent? Yes No
Which transformation will map Figure A onto Figure B exactly?
Which transformation will map Figure C onto Figure D exactly?
Translate Figure A to the right 4 units
4 units Reflect Figure A over the x -axis Reflect Figure A over the y -axis Rotate Figure A clockwise 90 ° about the Translate Figure A up
origin
Rotate Figure A counterclockwise about the origin None of these
180 °
Translate Figure C to the left 6 units Translate Figure C down
6 units
Reflect Figure C over the x -axis Reflect Figure C over the y -axis Rotate Figure C clockwise origin
180 °
Rotate Figure C counterclockwise about the origin None of these
about the
90 °
2. x
f x
−3
−14
0
−5
2
1
4
7
5
10
3. 1. For which data set is the correlation coefficient r closest to - The data set in Figure 1 - The data set in Figure 2 - The data set in Figure 3 - The data set in Figure 4
1?
2. Which data set indicates the strongest negative linear relationship between its two variables? - The data set in Figure 1 - The data set in Figure 2 - The data set in Figure 3 - The data set in Figure 4 3. For which data set is the correlation coefficient r closest to - The data set in Figure 1 - The data set in Figure 2 - The data set in Figure 3 - The data set in Figure 4
0?
4. p = 10 n 5. Rate: 0.2
mi min
Distance traveled in 6. a
n
5 minutes: 1 mi
= −3 n + 21
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7. (a) Choose the statement that best describes how the time and amount of money in her account are related. Then give the value requested. As time increases, the amount of money in her account decreases. At what rate is the amount of money in her account decreasing?
35
dollars per month
As time increases, the amount of money in her account increases. At what rate is the amount of money in her account increasing? ______ dollars per month (b) How much money was in her account before Yoko starting withdrawing money?
850
dollars
8. (a) What is Joe's total pay with
0 hours of overtime?
$ 125 (b) Choose the statement that best describes how the amount of overtime and total pay are related. Then give the value requested. As the amount of overtime increases, the total pay decreases. At what rate is the total pay decreasing?
$ ______ per hour As the amount of overtime increases, the total pay increases. At what rate is the total pay increasing?
$ 25
per hour
9. Number of biology textbooks sold: 237 Number of math textbooks sold: 186
10. y 8 6 4 2
-8
-6
-4
x
(0, 0)
-2
2
-2 -4
4
6
8
(1, -2) (2, -4)
-6 -8
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© 2016 M c G r aw - H i l l Educ ati on. Al l R i ghts R es er v ed.
11. Slope of a perpendicular line:
−
Slope of a parallel line:
3 4
4 3
12. 14.4 miles 13. y 8 6
(0, 5)
4 2
-8
-6
-4
(1, 0)
-2
2
x 4
6
8
-2 -4
(2, -5)
-6 -8
14. y = c + 8 15. Equation: H = 41 Plant's height after
38
+M
months: 79 centimeters
16. (a)
Use the calculator to find the circumference and area of the courtyard.
Use 3.14 for π in your calculations, and do not round your answers. Make sure to include the correct units.
Circumference: 276.32 Area: 6079.04 (b)
m
m
A chain will surround the courtyard. Which measure would be used in finding the amount of chain needed?
- Circumference (c)
The courtyard will be paved. Which measure would be used in finding the amount of pavement needed?
- Area
17. Scalene triangle
J 1 , −2
,
D 7, 0
E −1 , 6
,
A −2 , 0
,
K 0 , −6 ,
B −2 , 2
H om ew or k 1 #4
,
Isosceles triangle
Equilateral triangle
L 6 , −6
F −1 , −4 ,
C 3, 1
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© 2016 M c G r aw - H i l l Educ ati on. Al l R i ghts R es er v ed.
18. Step
Reason
6 y − 1 = −18
Given equation - Addition Property of Equality
6 y −1 −18 = 6 6
- Subtraction Property of Equality - Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property - Addition Property of Equality - Subtraction Property of Equality
y − 1 = −3
- Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property
y − 1 + 1 = −3 + 1
- Addition Property of Equality - Subtraction Property of Equality - Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property - Addition Property of Equality - Subtraction Property of Equality
y = −2
- Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property
19. Area: 70 square units Perimeter: 34 units
20. S 3000
S
= 2100 + 110 N
2750 2500 2250 2000 1750 1500 1250 1000 750 500 250
N 1
2
3
4
5
6
7
21. (a) What is the predicted time spent doing homework for a student who doesn't spend any time watching TV? (b) What is the predicted time spent doing homework for a student who
26.04 hours
(c) For an increase of one hour in the time spent watching TV, what is the predicted decrease in the time spent doing homework?
0.76 hours
spends 12 hours watching TV?
16.92 hours
22. What was the starting amount of water in the pond?
500
liters
What is the change per minute in the amount of water in the pond?
34
23. x =
liters
z +7y 3
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© 2016 M c G r aw - H i l l Educ ati on. Al l R i ghts R es er v ed.
24. Step
Reason
−8 u + 3 =32
−8 u − 24 =32
Given equation - Addition Property of Equality - Subtraction Property of Equality - Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property - Addition Property of Equality - Subtraction Property of Equality
−8 u − 24 + 24 = 32 + 24
- Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property
−8 u =56
- Addition Property of Equality - Subtraction Property of Equality - Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property - Addition Property of Equality
−8 u 56 = −8 −8
- Subtraction Property of Equality - Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property - Addition Property of Equality - Subtraction Property of Equality
u = −7
- Multiplication Property of Equality - Division Property of Equality - Simplifying - Distributive Property
25. (a) For each restaurant, write an expression for the total charge of purchasing
x pizzas (with delivery).
Total charge from the first restaurant (in dollars) = 4 + 10 x Total charge from the second restaurant (in dollars) =12 x
(b) Write an equation to show that the total charge (with delivery) from the two restaurants is the same.
4 + 10 x = 12 x
26. x, y
Is it a solution? Yes
No
−3 , − 8
−6 , 2
1, − 3
2, 9
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© 2016 M c G r aw - H i l l Educ ati on. Al l R i ghts R es er v ed.
27. y 8 6 4 2
− 1, 0 -8
-6
-4
-2
2
x 4
6
8
-2 -4 -6 -8
Solution: x = −1 28. Rental cost for each movie: $ 2.50
Rental cost for each video game: $ 5.25 29. range: 600
≤ y ≤ 1500
domain: 0 ≤ x ≤ 120 30. Equation: C = 6500
+ 125 S
Total cost to transport 11 tons of sugar: $ 7875 31. (a) Adjust the figure on the right to explore the different triangles that can be formed. Then answer the question. Note that the figure will not be graded.
Which of the following is true? The two triangles must be congruent. Reason:
Angle-Side-Angle (ASA) Congruence Property
The two triangles do not have to be congruent. (b) Adjust the figure on the right to explore the different triangles that can be formed. Then answer the question. Note that the figure will not be graded.
Which of the following is true? The two triangles must be congruent. Reason:
Side-Angle-Side (SAS) Congruence Property
The two triangles do not have to be congruent.
H om ew or k 1 #4
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© 2016 M c G r aw - H i l l Educ ati on. Al l R i ghts R es er v ed.
32. Domain Description of Values length of the road (in miles) number of days the crew has worked Set of Values the set of all real numbers from 400 to 670 the set of all real numbers from 3 to 400 the set of all real numbers from 0 to 90 {90, 91, 92, 93, ...} {0, 1, 2, 3, ..., 400} {3, 6, 9, 12, ...} Range Description of Values length of the road (in miles) number of days the crew has worked Set of Values the set of all real numbers from 400 to 670 the set of all real numbers from 3 to 400 the set of all real numbers from 0 to 90 {90, 91, 92, 93, ...} {0, 1, 2, 3, ..., 400} {3, 6, 9, 12, ...}
33. 2.56 weeks 34. 8
y
4
y
y 4
6 4
2
2 -8
-6 -4
-2
2
x 2
-2
4
6
x
8
-2
2
-4
x -4
-2
No 2
-4
-4
Yes
Function?
Yes
y
No 4
1
Yes y 4
2
-1
1
2
2 x
-4
-2
2
Yes
N
x -4
-2
No
Yes
2
4
-2 -4
-4
-2
35. Equation: N = 13
4
-2
-1
Function?
No
y
x -2
4
-2
-2
-6 -8
2
No
Yes
No
−F
18 16 14 12 10 8 6 4 2 F 2
4
6
H om ew or k 1 #4
8
10
12
14
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18
© 2016 M c G r aw - H i l l Educ ati on. Al l R i ghts R es er v ed.
36. input
6
8
9
n
output
1
3
4
n −5
37. c ≥ 6 38. y =
1 3
39. (a)
Use the calculator to find the perimeter and area of the window. Make sure to include the correct units.
Perimeter: 208 Area: 2508 (b)
in
2
in
The window's glass will be replaced. Which measure would be used in finding the amount of glass needed?
Area (c)
A silver wire will be placed around the window. Which measure would be used in finding the amount of wire needed?
Perimeter
40. m
− 29
41. 1. A financial magazine conducted a survey. It showed that a person with more years of education tends to have a higher salary. What is likely true? There is no correlation between years of education and salary. There is a correlation between years of education and salary. There may or may not be causation. Further studies would have to be done to determine this. There is a correlation between years of education and salary. There is probably also causation. This is because there is an increase in salary with an increase in the years of education. 2. A grocery store collected sales data. It found that a change in price does not imply that people will buy more or less milk. What can we determine from this information? There is no correlation between price and amount of milk bought. There is a correlation between price and amount of milk bought. However, there is no causation. This is because there is likely a decrease in the amount of milk bought with an increase in the price. There is a correlation between price and amount of milk bought. There may or may not be causation. Further studies would have to be done to determine this. 3. Mr. Nelson studied his students' geography test scores and TV habits. He found that students who watched less TV tended to earn higher scores on the test. What conclusion should he make? There is no correlation between test score and amount of TV watched. There is a correlation between test score and amount of TV watched. There is probably also causation. This is because there is an increase in a student's test score with a decrease in the amount of TV watched. There is a correlation between test score and amount of TV watched. There may or may not be causation. Further studies would have to be done to determine this.
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© 2016 M c G r aw - H i l l Educ ati on. Al l R i ghts R es er v ed.
42. Relation 1
Domain
Range
t
g
g
w
w
t
s
s
z
z
Domain
Range
-2
sky
-7
star
1
sky
-1
desk
3
star
1
desk
Function
Function
Not a Function
Not a Function
Relation 3
Relation 4
(6, -1), (8, -1), (6, 6), (8, 6)
(-6, r), (-9, n), (-9, y), (-6, g)
Function
Function
Not a Function
Not a Function
43. 3 m 44.
Relation 2
= 39
−9 , −4 , 1 , 6 , 11
45. 10
y
8 6 4 2 -10
-8
-6
-4
-2
x 2
-2
4
6
8
10
-4 -6 -8 -10
1 4
46. 47.
y 8 6 4 2 -8
-6
-4
-2
-2
x 2
4
6
8
-4 -6 -8
48. absolute error percent error
= 7 pounds = 4.9 %
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© 2016 M c G r aw - H i l l Educ ati on. Al l R i ghts R es er v ed.
49.
Congruent?
Yes
No
Yes
No
Congruent?
Yes
No
Yes
No
50. (a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 4 , 5 , and the number of books. ___b + ___
=
71 . Let b represent
___
4 b − 5 = 71 (b) Solve the equation in part (a) to find the number of books.
b = 19
51. input
1
3
9
output
3
9
27
n
3
×
n
52. (a) How many flyers did Henry already have when he started printing?
37
flyers
(b) Choose the statement that best describes how the time and number of flyers Henry has are related. Then give the value requested. As time increases, the number of flyers decreases. At what rate is the number of flyers decreasing? ______ flyers per minute As time increases, the number of flyers increases. At what rate is the number of flyers increasing?
5 flyers per minute
53.
−
5 6
H om ew or k 1 #4
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© 2016 M c G r aw - H i l l Educ ati on. Al l R i ghts R es er v ed.
54. Sequence
Type
nth term formula
Arithmetic
8 , 16 , 32 , ...
a n = 8 ·2
Geometric Arithmetic
13 , 16 , 19 , ...
n −1
a n = 3 n + 10
Geometric
55. range
= −9 , −1 , 5 , 7 y
9 8 7 6 5 4 3 2 1
x
-9 -8 -7 -6 -5 -4 -3 -2 -1-1
1
2
3
4
5
6
7
8
9
-2 -3 -4 -5 -6 -7 -8 -9
56. 2 ,
−8 , 32 , −128 , 512
57. Equation: C = 12 C
−R
18 16 14 12 10 8 6 4 2 R 2
4
6
H om ew or k 1 #4
8
10
12
14
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16
18
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