Unit 7 Practice Problems Lesson 1 Problem 1 Write each expression using an exponent: 1. 2. 3. 4. The number of coins Jada will have on the eighth day, if Jada starts with one coin and the number of coins doubles every day. (She has two coins on the first day of the doubling.) Solution 1. 2. 3. 4. Problem 2 Evaluate each expression: Solution 1. 32 2. 27 3. 64 4. 36 5. 1 7 7 7 7 7 ⋅⋅⋅⋅⋅ 1 ( ) ( ) ( ) ( ) ( ) ⋅ 4 5 ⋅ 4 5 ⋅ 4 5 ⋅ 4 5 ⋅ 4 5 1 (9.3) (9.3) (9.3) (9.3) (9.3) (9.3) (9.3) (9.3) ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 7 5 ( 4 5 ) 5 (9.3) 8 2 8 1. 2. 3. 2 5 3 3 4 3 4. 5. 6. 6 2 ( ) 1 2 4 ( ) 1 3 2 1 16 1
Transcript
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Unit 7 PracticeProblems
Lesson 1Problem 1Write each expression using an exponent:
1.
2.
3.
4. The number of coins Jada will have on the eighth day, if Jada starts withone coin and the number of coins doubles every day. (She has two coins onthe first day of the doubling.)
Problem 3Clare made $160 babysitting last summer. She put the money in a savingsaccount that pays 3% interest per year. If Clare doesn’t touch the money in heraccount, she can find the amount she’ll have the next year by multiplying hercurrent amount by 1.03.
1. How much money will Clare have in her account after 1 year? After 2years?
2. How much money will Clare have in her account after 5 years? Explain yourreasoning.
3. Write an expression for the amount of money Clare would have after 30years if she never withdraws money from the account.
Problem 4(from Unit 3, Lesson 1)The equation gives the number of feet, , in miles. What does thenumber 5,280 represent in this relationship?
SolutionThere are 5,280 feet in every mile. For example, each additional mile thatsomeone travels is equivalent to traveling an additional 5,280 feet.
Problem 5(from Unit 3, Lesson 5)The points and lie on a line. What is the slope of the line?
A. 2
B. 1
C.
D.
SolutionD
Problem 6(from Unit 2, Lesson 6)The diagrams shows a pair of similar figures, one contained in the other. Name apoint and a scale factor for a dilation that moves the larger figure to the smallerone.
19
160 ⋅ 1.035
160 ⋅ 1.0330
y = 5,280x y x
(2, 4) (6, 7)
43
34
SolutionCenter: , scale factor:
Lesson 2Problem 1Write each expression with a single exponent:
Solution1.
2.
3.
4.
5.
6.
Problem 2A large rectangular swimming pool is 1,000 feet long, 100 feet wide, and 10 feetdeep. The pool is filled to the top with water.
1. What is the area of the surface of the water in the pool?
2. How much water does the pool hold?
3. Express your answers to the previous two questions as powers of 10.
Solution1. 100,000 square feet
2. 1,000,000 cubic feet
3. square feet, cubic feet
Problem 3(from Unit 2, Lesson 7)Here is triangle .
A 13
1.
2.
3.
103 ⋅ 109
10 ⋅ 104
1010 ⋅ 107
4.
5.
6.
103 ⋅ 103
105 ⋅ 1012
106 ⋅ 106 ⋅ 106
1012
105
1017
109
1017
1018
105 106
ABC
Solution and (The scale factor is , so each side length is half the
corresponding side length of .)
Problem 4(from Unit 3, Lesson 3)Elena and Jada distribute flyers for different advertising companies. Elena getspaid 65 cents for every 10 flyers she distributes, and Jada gets paid 75 cents forevery 12 flyers she distributes.
Draw graphs on the coordinate plane representing the total amount each of themearned, , after distributing flyers. Use the graph to decide who got paid moreafter distributing 14 flyers.
Solution
Triangle is similarto triangle , andthe length of is 5cm. What are thelengths of sides and , incentimeters?
DEFABCEF
DEDF
DE = 3 DF = 4 12
ABC
y x
Elena is paid more money after distributing 14 flyers because her graph issteeper than Jada's. For any number of flyer, the point on Jada’s graph is higherthan the point on Elena’s graph.
Lesson 3Problem 1Write each expression with a single exponent:
1.
2.
3.
4.
5.
6.
Solution1.
2.
3.
4.
5.
6.
Problem 2You have 1,000,000 number cubes, each measuring one inch on a side.
1. If you stacked the cubes on top of one another to make an enormous tower,how high would they reach? Explain your reasoning.
2. If you arranged the cubes on the floor to make a square, would the square
(107)2
(109)3
(106)3
(102)3
(103)2
(105)7
1014
1027
1018
106
106
1035
fit in your classroom? What would its dimensions be? Explain yourreasoning.
3. If you layered the cubes to make one big cube, what would be thedimensions of the big cube? Explain your reasoning.
Solution1. The height of the tower would be 1,000,000 inches. That is about 83,333
feet ( ), which is almost 16 miles ().
2. The square would be 1,000 inches on a side, because . 1,000 inches is about 83 feet. This probably
wouldn’t fit in a classroom.
3. The cube would be 100 inches on a side because . This is feet.
Problem 3(from Unit 7, Lesson 1)An amoeba divides to form two amoebas after one hour. One hour later, each ofthe two amoebas divides to form two more. Every hour, each amoeba divides toform two more.
1. How many amoebas are there after 1 hour?
2. How many amoebas are there after 2 hours?
3. Write an expression for the number of amoebas after 6 hours.
4. Write an expression for the number of amoebas after 24 hours.
5. Why might exponential notation be preferable to answer these questions?
Solution1. 2
2. 4
3. (or 64)
4. (or 16,777,216)
5. Exponential notation is simpler to write than very large or small numbers,and the expression visibly includes the information that the amoebashave divided 24 times.
Problem 4(from Unit 4, Lesson 15)Elena noticed that, nine years ago, her cousin Katie was twice as old as Elenawas then. Then Elena said, “In four years, I’ll be as old as Katie is now!” If Elenais currently years old and Katie is years old, which system of equationsmatches the story?
A.
B.
C.
1,000,000 ÷ 12 ≈ 83,33383,333 ÷ 5,280 ≈ 15.78
1,000 1,000 = 1,000,000⋅
100 100 100 = 1,000,000⋅ ⋅ 8 13
26
224
224
e k
{ k − 9 = 2ee + 4 = k
{ 2k = e − 9e = k + 4
{ k = 2e − 9e + 4 = k + 4
{
D.
SolutionD
Lesson 4Problem 1Evaluate:
1.
2.
3.
Solution1. 1
2. 1
3. 111
Problem 2Write each expression as a single power of 10.
1.
2.
3.
4.
5.
Solution1.
2.
3.
4.
5.
Problem 3The Sun is roughly times as wide as the Earth. The star KW Sagittarii isroughly times as wide as the Earth. About how many times as wide as theSun is KW Sagittarii? Explain how you know.
Solution (or 1,000). This can be determined by calculating , since both the Sun
and KG Sagittarii’s widths can be compared to the width of the Earth.
{ k − 9 = 2(e − 9)e + 4 = k
100
103
103
+ +102 101 100
103⋅104
105
( )104 ⋅ 1012
107
( 105
103 )4
104⋅105⋅106
103⋅107
(105 )2
(102 )3
102
109
108
105
104
102
105
103 105
102
Problem 4(from Unit 5, Lesson 3)Bananas cost $1.50 per pound, and guavas cost $3.00 per pound. Kiranspends $12 on fruit to for a breakfast his family is hosting. Let be the number ofpounds of bananas Kiran buys and be the number of pounds of guavas hebuys.
1. Write an equation relating the two variables.
2. Rearrange the equation so is the independent variable.
3. Rearrange the equation so is the independent variable.
Solution1.
2.
3.
Problem 5(from Unit 3, Lesson 1)Lin’s mom bikes at a constant speed of 12 miles per hour. Lin walks at a constantspeed of the speed her mom bikes. Sketch a graph of both of theserelationships.
Solution
bg
b
g
1.5b + 3g = 12
g = 4 − b12
b = 8 − 2g
13
Lesson 5Problem 1Write with a single exponent: (ex: )
1.
2.
3.
4.
5.
Solution1.
2.
3.
4.
5.
Problem 2Write each expression as a single power of 10.
1.
2.
3.
4.
5.
6.
Solution1.
2.
3.
4.
5.
6.
Problem 3Select all of the following that are equivalent to :
A. B. C.
=110 ⋅ 1
10 10-2
110 ⋅ 1
10 ⋅ 110
110 ⋅ 1
10 ⋅ 110 ⋅ 1
10 ⋅ 110 ⋅ 1
10 ⋅ 110
( 110 ⋅ 1
10 ⋅ 110 ⋅ 1
10 )2
( 110 ⋅ 1
10 ⋅ 110 )3
(10 10 10⋅ ⋅ )-2
10-3
10-7
10-8
10-9
10-6
10-3 ⋅ 10-2
104 ⋅ 10-1
105
107
(10-4)5
10-3 ⋅ 102
10-9
105
10-5
10-3
10-2
10-20
10-1
10-14
110,000
(10,000)-1
(-10,000)(100)-2
(10 -4
D. E.
SolutionA, C, D
Problem 4(from Unit 3, Lesson 2)Match each equation to the situation it describes. Explain what the constant ofproportionality means in each equation.
SolutionExplanations vary. Sample responses:
A. Situation 2. For each cup of salt, there are 3 cups of water.
B. Situation 4. For every cookie I bake, my students get half.
C. Situation 1. The dump truck hauls 3.5 square feet of dirt in each load.
D. Situation 3. Each hat costs $2.50.
Problem 5(from Unit 2, Lesson 8)
1. Explain why triangle is similar to .
2. Find the missing side lengths.
Solution1. Explanations vary. Sample explanation: Both triangles contain a right angle,
and angles and are vertical angles. The triangles are similarbecause two pairs of corresponding angles are congruent.
2. Side measures 24, and side measures 15. (The scale factor is or 1.5.)
Lesson 6
(100)(10)-4
(-10)2
Equations:
A.
B.
C.
D.
y = 3x
x = y12
y = 3.5x
y = x52
Situations:
1. A dump truck is hauling loads of dirt to a construction site.After 20 loads, there are 70 square feet of dirt.
2. I am making a water and salt mixture that has 2 cups of saltfor every 6 cups of water.
3. A store has a “4 for $10” sale on hats.
4. For every 48 cookies I bake, my students get 24.
ABC EDC
ACB ECD
BC DE 3926
Problem 1Priya says “I can figure out by looking at other powers of 5. is 125, is 25,then is 5.”
1. What pattern do you notice?
2. If this pattern continues, what should be the value of ? Explain how youknow.
3. If this pattern continues, what should be the value of ? Explain how youknow.
Solution1. When the power of 5 drops by one, the value is divided by 5.
2. 1. The value of should be the value of divided by 5.
3. . The value of should be the value of divided by 5.
Problem 2Select all the expressions that are equivalent to .
A. -12B. C. D. E. 12F. G.
SolutionB, C, D
Problem 3Write each expression using a single exponent.
1.
2.
3.
4.
5.
Solution1.
2.
3.
4.
5.
Problem 4
50 53 52
51
50
5-1
50 51
15 5-1 50
4-3
2-6
143
( ) ( ) ( )14 ⋅ 1
4 ⋅ 14
(-4) (-4) (-4)⋅ ⋅8-1
22
53
56
(143)6
83 ⋅ 86
166
163
(213)-6
5-3
1418
89
163
21-18
(from Unit 5, Lesson 6)Andre sets up a rain gauge to measure rainfall in his back yard. On Tuesday, itrains off and on all day.
He starts at 10 a.m. with an empty gauge when it starts to rain.Two hours later, he checks, and the gauge has 2 cm of water in it.It starts raining even harder, and at 4 p.m., the rain stops, so Andre checksthe rain gauge and finds it has 10 cm of water in it.While checking it, he accidentally knocks the rain gauge over and spillsmost of the water, leaving only 3 cm of water in the rain gauge.When he checks for the last time at 5 p.m., there is no change.
1. Which of the two graphs could represent Andre’s story? Explain yourreasoning.
2. Label the axes of the correct graph with appropriate units.
3. Use the graph to determine how much total rain fell on Tuesday.
Solution1. Graph A
2.
3. 10 cm of rain fell in total on Tuesday. No rain fell after Andre spilled the raingauge.
Lesson 7Problem 1Write with a single exponent:
1.
2.
3.
Graph A Graph B
76
72
(114)5
42 ⋅ 46
6 8
4.
5.
6.
7.
8.
9.
Solution1.
2.
3.
4.
5.
6.
7.
8.
9.
Problem 2Noah says that . Tyler says that .
1. Do you agree with Noah? Explain or show your reasoning.
2. Do you agree with Tyler? Explain or show your reasoning.
Solution1. Agree. Reasoning varies. Sample reasoning: , but
is much bigger than 144.
2. Disagree. Reasoning varies. Sample reasoning: and , so should equal or .
Lesson 8Problem 1Select all the true statements:
A.
B.
C.
D.
SolutionA, B
6 ⋅ 68
(122)7
310
3
(0.173 (0.173)9 ⋅ )2
0.875
0.873
( 52 )8
( 52 )6
74
1120
48
69
1214
39
0.17311
0.872
( 52 )2
=24 ⋅ 32 66 =24 ⋅ 42 162
= 16 9 = 14424 ⋅ 32 ⋅66
= 1624 = 1642
24 ⋅ 42 16 16⋅ 162
=28 ⋅ 29 217
=82 ⋅ 92 722
=82 ⋅ 92 724
=28 ⋅ 29 417
Problem 2Find , , and if .
Solution, ,
Problem 3Han found a way to compute complicated expressions more easily. Since
, he looks for pairings of 2s and 5s that he knows equal 10. Forexample,
UseHan's technique to compute the following:
1.
2.
Solution1. 270,000
2. 180,000
Problem 4(from Unit 5, Lesson 8)The cost of cheese at three stores is a function of the weight of the cheese. Thecheese is not prepackaged, so a customer can buy any amount of cheese.
Store A sells the cheese for dollars per pound.
Store B sells the same cheese for dollars per pound and a customer hasa coupon for $5 off the total purchase at that store.
Store C is an online store, selling the same cheese at dollar per pound,but with a $10 delivery fee.
This graph shows the price functions for stores A, B, and C.
1. Match Stores A, B, and C with Graphs , , and .
2. How much does each store charge for the cheese per pound?
3. How many pounds of cheese does the coupon for Store B pay for?
4. Which store has the lowest price for a half a pound of cheese?
5. If a customer wants to buy 5 pounds of cheese for a party, which store hasthe lowest price?
x y z (3 5 (2 3 (2 5 =⋅ )4 ⋅ ⋅ )5 ⋅ ⋅ )7 2x ⋅ 3y ⋅ 5z
6. How many pounds would a customer need to order to make Store C a goodoption?
Solution1. Store A: Graph
Store B: Graph Store C: Graph
2. Store A charges $4 per pound, Store B changes $5 per pound, and Store Ccharges $3 per pound.
3. 1 pound of cheese.
4. Store B
5. Store A or Store B would both charge the same amount for 5 lbs of cheese.
6. If a customer orders more than 10 pounds of cheese, Store C has thelowest price.
Lesson 9Problem 1Match each number to its name.
SolutionA. 5
B. 1
C. 6
D. 3
E. 2
F. 4
Problem 2Write each expression as a multiple of a power of 10:
1. 42,300
2. 2,000
3. 9,200,000
4. Four thousand
5. 80 million
6. 32 billion
Solution1. Answers vary. Sample responses: ,
ℓkj
A. 1,000,000B. 0.01C. 1,000,000,000D. 0.000001E. 0.001F. 10,000
1. One hundredth2. One thousandth3. One millionth4. Ten thousand5. One million6. One billion
423 ⋅ 102 4.23 ⋅ 104
2 3
2. Answers vary. Sample response:
3. Answers vary. Sample responses: ,
4. Answers vary. Sample response:
5. Answers vary. Sample response:
6. Answers vary. Sample responses: ,
Problem 3Each statement contains a quantity. Rewrite each quantity using a power of 10.
1. There are about 37 trillion cells in an average human body.
2. The Milky Way contains about 300 billion stars.
3. A sharp knife is 23 millionths of a meter thick at its tip.
4. The wall of a certain cell in the human body is 4 nanometers thick. (Ananometer is one billionth of a meter.)
Solution1. (or equivalent)
2. (or equivalent)
3. (or equivalent)
4. (or equivalent)
Problem 4(from Unit 5, Lesson 20)A fully inflated basketball has a radius of 12 cm. Your basketball is only inflatedhalfway. How many more cubic centimeters of air does your ball need to fullyinflate? Express your answer in terms of . Then estimate how many cubiccentimeters this is by using 3.14 to approximate .
Solution cubic cm, 3,617.28 cubic cm
Problem 5(from Unit 4, Lesson 5)Solve each of these equations. Explain or show your reasoning.
Solution1. . Responses vary. Sample response: Divide each side by 2, then
subtract 3 from each side, then divide each side by -2.
2. . Responses vary. Sample response: Add 2 to each side, then add to each side, then divide each side by 9.
3. . Responses vary. Sample response: Distribute 5 on the right side,add 10 to each side, then divide each side by 5.
Problem 6(from Unit 3, Lesson 10)
2 ⋅ 103
92 ⋅ 105 9.2 ⋅ 106
4 ⋅ 103
8 ⋅ 107
32 ⋅ 109 3.2 ⋅ 1010
37 ⋅ 1012
300 ⋅ 109
23 ⋅ 10-6
4 ⋅ 10-9
ππ
1,152π
2(3 − 2c) = 30 3x − 2 = 7 − 6x 31 = 5(b − 2)
c = -6
x = 1 6x
b = 415
-2
Graph the line going through with a slope of and write its equation.
Solution
Lesson 10Problem 1Find three different ways to write the number 437,000 using powers of 10.
SolutionAnswers vary. Possible answers: , ,
Problem 2For each pair of numbers below, circle the number that is greater. Estimate howmany times greater.
(-6, 1) -23
y = x − 3-23
4.37 ⋅ 105 43.7 ⋅ 104 437 ⋅ 103
or 17 ⋅ 108 4 ⋅ 108 or 2 ⋅ 106 7.839 ⋅ 106 or 42 ⋅ 107 8.5 ⋅ 108
Solution1. , about 4 times larger
2. , about 4 times larger
3. , about 2 times larger
Problem 3What number is represented by point ? Explain or show how you know.
SolutionAnswers vary. Sample response: . Point lies between and
. It is because it is four tick marks from .
Problem 4(from Unit 6, Lesson 7)Here is a scatter plot that shows the number of points and assists by a set ofhockey players. Select all the following that describe the association in thescatter plot:
SolutionA, C
Problem 5(from Unit 5, Lesson 5)Here is the graph of days and the predicted number of hours of sunlight, , onthe -th day of the year.
17 ⋅ 108
7.839 ⋅ 106
8.5 ⋅ 108
A
7.4 ⋅ 1011 A 7 ⋅ 1011
8 ⋅ 1011 7.4 ⋅ 1011 7.0 ⋅ 1011
A. Linear association
B. Non-linear association
C. Positive association
D. Negative association
E. No association
hd
1. Is hours of sunlight a function of days of the year? Explain how you know.
2. For what days of the year is the number of hours of sunlight increasing? Forwhat days of the year is the number of hours of sunlight decreasing?
3. Which day of the year has the greatest number of hours of sunlight?
Solution1. is a function of . For every there is one and only one value of .
2. From day 0 to day 180, the hours of sunlight are increasing. From day 180to day 365, the hours of sunlight are decreasing.
3. The day with the greatest number of hours of sunlight is day 180.
Lesson 11Problem 1Select all the expressions that are equal to :
A.
B.
C.
D.
E.
F.
SolutionA, C, E
Problem 2Write each expression as a multiple of a power of 10:
1. 0.04
2. 0.072
3. 0.0000325
4. Three thousandths
5. 23 hundredths
h d d h
4 ⋅ 10-3
4 ( ) ( ) ( )⋅ 110 ⋅ 1
10 ⋅ 110
4 (-10) (-10) (-10)⋅ ⋅ ⋅4 0.001⋅4 0.0001⋅0.004
0.0004
6. 729 thousandths
7. 41 millionths
Solution1. Answers vary. Sample response:
2. Answers vary. Sample response: ,
3. Answers vary. Sample responses: ,
4. Answers vary. Sample response:
5. Answers vary. Sample responses: ,
6. Answers vary. Sample responses: ,
7. Answers vary. Sample responses: ,
Problem 3(from Unit 3, Lesson 9)A family sets out on a road trip to visit their cousins. They travel at a steady rate.The graph shows the distance remaining to their cousins' house for each hour ofthe trip.
Solution1. 60 miles per hour
2. Negative. Explanations vary. Sample explanation: The slope is negativebecause the line moves down toward the right. It shows the change inremaining miles for each hour. There are 60 fewer miles remaining eachhour, which means the car is traveling at a steady rate of 60 miles eachhour.
3. 480 miles and 8 hours. Explanations vary. Sample explanation: The trip is
4 ⋅ 10-2
7.2 ⋅ 10-2 72 ⋅ 10-3
3.25 ⋅ 10-5 325 ⋅ 10-7
3 ⋅ 10-3
2.3 ⋅ 10-1 23 ⋅ 10-2
7.29 ⋅ 10-1 729 ⋅ 10-3
4.1 ⋅ 10-5 41 ⋅ 10-6
1. How fast are they traveling?
2. Is the slope positive or negative?Explain how you know and whythat fits the situation.
3. How far is the trip and how longdid it take? Explain how youknow.
480 miles because the remaining distance was 480 miles when they startedout (after 0 hours). The trip took 8 hours because after 8 hours, there were0 miles remaining.
Lesson 12Problem 1Which is larger: the number of meters across the Milky Way, or the number ofcells in all humans? Explain or show your reasoning.
Some useful information:
The Milky Way is about 100,000 light years across.There are about 37 trillion cells in a human body.One light year is about meters.The world population is about 7 billion.
SolutionThere are more human cells than there are meters across the Milky Way. Since100,000 is , it is about or meters across the Milky Way.Notice that 37 trillion is and 7 billion is , so the total number ofcells of all humans is . This gives human cells.This is about 260 times larger than , the approximate number of metersacross the Milky Way. Using more precise values for population and the numberof meters in a light year will yield slightly different results.
Problem 2(from Unit 6, Lesson 5)Ecologists measure the body length and wingspan of 127 butterfly specimenscaught in a single field.
SolutionAnswers vary. Sample response:
1.
2.
3. For every 4 millimeters the length of the wingspan increases, the bodylength increases 1 millimeter.
Problem 3
1016
105 105 ⋅ 1016 1021
(3.7) ⋅ 1013 7 ⋅ 109
(3.7) 7⋅ 1013 ⋅ ⋅ 109 (25.9) ⋅ 1022
1021
1. Draw a line that you think is agood fit for the data.
2. Write an equation for the line.
3. What does the slope of the linetell you about the wingspans andlengths of these butterflies?
y = x + 514
(from Unit 4, Lesson 5)Diego was solving an equation, but when he checked his answer, he saw hissolution was incorrect. He knows he made a mistake, but he can’t find it. Whereis Diego’s mistake and what is the solution to the equation?
SolutionDiego’s mistake occurred in the transition from the first line to the second line.The distributive property with should give . The correctsolution is .
Problem 4(from Unit 2, Lesson 7)The two triangles are similar. Find .
Solution (The obtuse angle in both triangles measures because they are
similar. The sum of the three angles in a triangle is .)
Lesson 13Problem 1Write each number in scientific notation.
1. 14,700
2. 0.00083
3. 760,000,000
4. 0.038
5. 0.38
6. 3.8
7. 3,800,000,000,000
8. 0.0000000009
Solution1.
-4(7 − 2x) = 3(x + 4)-28 − 8x = 3x + 12
-28 = 11x + 12-40 = 11x
= x -4011
-4(7 − 2x) -28 + 8xx = 8
x
x = 28 106∘180∘
1.47 × 104
8.3 × -4
2.
3.
4.
5.
6.
7.
8.
Problem 2Perform the following calculations. Express your answers in scientific notation.
1.
2.
3.
4.
5.
Solution1.
2.
3.
4.
5.
Problem 3Jada is making a scale model of the solar system. The distance from Earth to themoon is about miles. The distance from Earth to the sun is about
miles. She decides to put Earth on one corner of her dresser andthe moon on another corner, about a foot away. Where should she put the sun?
On a windowsill in the same room?In her kitchen, which is down the hallway?A city block away?
Explain your reasoning.
SolutionThe model sun should go down the block. Explanations vary. The distance fromEarth to the sun is about or 400 times the distance from the Earth to themoon. Since Jada’s dresser is about a foot long, this means that her model sunshould be about 400 feet away from the dresser. Jada’s house or apartment isprobably not 400 feet long; a block away is about right.
Problem 4(from Unit 4, Lesson 12)Here is the graph for one equation in a system of equations.
8.3 × 10-4
7.6 × 108
3.8 × 10-2
3.8 × 10-1
3.8 × 100
3.8 × 1012
9 × 10-10
(2 × ) + (6 × )105 105
(4.1 × ) 2107 ⋅(1.5 × ) 31011 ⋅(3 × 103)2
(9 × ) (3 × )106 ⋅ 106
8 × 105
8.2 × 107
4.5 × 1011
9 × 106
2.7 × 1013
2.389 × 105
9.296 × 107
4 × 102
1. Write a second equation for the system so it has infinitely many solutions.
2. Write a second equation whose graph goes through so that thesystem has no solutions.
3. Write a second equation whose graph goes through so that thesystem has one solution at .
Solution1.
2.
3.
Lesson 14Problem 1Evaluate each expression. Use scientific notation to express your answer.
1.
2.
3.
4.
Solution1.
2.
3.
4.
Problem 2How many bucketloads would it take to bucket out the world’s oceans? Writeyour answer in scientific notation.
Some useful information:
The world’s oceans hold roughly cubic kilometers of water.A typical bucket holds roughly 20,000 cubic centimeters of water.There are cubic centimeters in a cubic kilometer.
(0, 2)
(2, 2)(4, 3)
y = x − 332
y = x + 232
y = x + 112
(1.5 × )(5 × )102 1010
4.8×10-8
3×10-3
(5 × )(4 × )108 103
(7.2 × ) ÷ (1.2 × )103 105
7.5 × 1012
1.6 × 10-5
2 × 1012
6 × 10-2
1.4 × 109
1015
Solution. The world’s oceans hold cubic centimeters of water, found
by multiplying by . Then divide by to get . Inscientific notation, this quotient is .
Problem 3(from Unit 5, Lesson 5)The graph represents the closing price per share of stock for a company eachday for 28 days.
1. What variable is represented on the horizontal axis?
2. In the first week, was the stock price generally increasing or decreasing?
3. During which period did the closing price of the stock decrease for at least 3days in a row?
Solution1. The day
2. Increasing
3. Days 7 to 10
Problem 4(from Unit 3, Lesson 11)Write an equation for the line that passes through and .
Solution
Problem 5(from Unit 2, Lesson 6)Explain why triangle is similar to triangle .
7 × 1019 1.4 × 1024
1.4 × 109 1015 2 × 104 0.7 × 1020
7 × 1019
(-8.5, 11) (5, -2.5)
y = -x + 2.5
ABC CFE
SolutionAnswers vary. Sample responses:
Translate to , and then dilate with center by a factor of .
Dilate with center by a factor of 2, then translate to .
Lesson 15Problem 1Evaluate each expression, giving the answer in scientific notation:
1.
2.
3.
4.
Solution1.
2.
3.
4.
Problem 2(from Unit 5, Lesson 10)
1. Write a scenario that describes what is happening in the graph.
2. What is happening at 5 minutes?
3. What does the slope of the line between 6 and 8 minutes mean?
C A A 12
A A C
5.3 × + 4.7 ×104 104
3.7 × − 3.3 ×106 106
4.8 × + 6.3 ×10-3 10-3
6.6 × − 6.1 ×10-5 10-5
1 × 105
4 × 105
1.11 × 10-2
5 × 10-6
Solution1. Answers vary. Sample response: A person is driving. The distance
measures distance away from their house.
2. Answers vary. Sample response: The person is stopped 4 km from home.
3. Answers vary. Sample response: The slope between 6 and 8 minutesindicates the speed the person is driving (1 km per minute), which is fasterthan any of their speeds between 0 and 6 minutes.
Problem 3(from Unit 4, Lesson 10)Apples cost $1 each. Oranges cost $2 each. You have $10 and want to buy 8pieces of fruit. One graph shows combinations of apples and oranges that total to$10. The other graph shows combinations of apples and oranges that total to 8pieces of fruit.
1. Name one combination of 8 fruits shown on the graph that whose cost doesnot total to $10.
2. Name one combination of fruits shown on the graph whose cost totals to$10 that are not 8 fruits all together.
3. How many apples and oranges would you need to have 8 fruits that cost$10 at the same time?
