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IMPACT Mathematics: Algebra and More, Course 2, Student Edition

McGraw-Hill

Chapter 4

Working with Signed Numbers - all with Video Answers

Educators

Chapter Questions

00:49

Problem 1

In Exercises 1-3, walk the number line to find each sum or difference. Describe your steps in words. Include the following in your descriptions:
• Where on the number line you start
• The direction the pointer is facing
• Whether you move forward or backward and how far you move
• The point on the number line at which you end (the answer)
• The complete addition or subtraction equation
$-8+5$

SM
Sara Mendoza
Numerade Educator
02:25

Problem 1

Compute each product or sum.
$-3 \times 52$

Vinnu M
Vinnu M
Numerade Educator
03:21

Problem 1

Plot these points on a coordinate plane. Label each point with its letter.
$$
A\left(3 \frac{2}{5}, 2\right) \quad B\left({ }^{-} 2,6\right) \quad C\left(0.4,{ }^{-4} 4\right) \quad D\left({ }^{-} 5,{ }^{-} 2\right)
$$

Raushan Kumar
Raushan Kumar
Numerade Educator
01:16

Problem 1

Four pirates are hunting for buried treasure on an island. They all start at the palm tree, which is at $(2,6)$ on their maps. All they know from their clues is that they must walk 10 paces either east or west, make a $90^{\circ}$ turn, and walk another 12 paces. So each pirate walks 10 paces, two heading east and two heading west. Then one pirate from each pair heads north another 12 paces, while the other heads south for 12 paces.
a. Where did each pirate end? Give the coordinates of each.
b. How far is each pirate from the palm tree, as the crow flies? ("As the crow flies" means "in a straight line from where you started.") Explain how you found your answers.

Tyler Moulton
Tyler Moulton
Numerade Educator

Problem 1

Find the length of the output if an 144-inch input is sent through each machine.
MACHINE CANT COPY

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00:49

Problem 2

Walk the number line to find each sum or difference. Describe your steps in words. Include the following in your descriptions:
• Where on the number line you start
• The direction the pointer is facing
• Whether you move forward or backward and how far you move
• The point on the number line at which you end (the answer)
• The complete addition or subtraction equation
$8+{ }^{-4}$

SM
Sara Mendoza
Numerade Educator
00:25

Problem 2

Compute each product or sum.
$6.2 \times{ }^{-5}$

James Kiss
James Kiss
Numerade Educator
01:15

Problem 2

Find the coordinates of Points $J$ through $O$.
GRAPH CANT COPY

James Kiss
James Kiss
Numerade Educator
02:01

Problem 2

For Exercises 2-6, use the Pythagorean Theorem to find the length of the segment.
GRAPH CANT COPY

Meredith Moody
Meredith Moody
Numerade Educator

Problem 2

Find the length of the output if an 144-inch input is sent through each machine.
MACHINE CANT COPY

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Problem 3

Walk the number line to find each sum or difference. Describe your steps in words. Include the following in your descriptions:
• Where on the number line you start
• The direction the pointer is facing
• Whether you move forward or backward and how far you move
• The point on the number line at which you end (the answer)
• The complete addition or subtraction equation
$3-{ }^{-5}$

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00:25

Problem 3

Compute each product or sum.
${ }^{-} 0.62 \times 5$

James Kiss
James Kiss
Numerade Educator
02:01

Problem 3

The graph of the Celsius-Kelvin conversion formula, $K=C+273$, is shown below.
GRAPH CANT COPY
Use the graph or the equation to answer the questions.
a. Are Kelvin and Celsius temperatures ever both positive? If so, for which Celsius temperatures? If this never happens, explain how you know.
b. Are Kelvin and Celsius temperatures ever both negative? If so, for which Celsius temperatures? If this never happens, explain how you know.
c. Are Kelvin temperatures ever positive when Celsius temperatures are negative? If so, for which Celsius temperatures? If this never happens, explain how you know.
d. Are Kelvin temperatures ever negative when Celsius temperatures are positive? If so, for which Celsius temperatures? If this never happens, explain how you know.

AG
Ankit Gupta
Numerade Educator
02:23

Problem 3

Use the Pythagorean Theorem to find the length of the segment.
GRAPH CANT COPY

Jennifer White
Jennifer White
Numerade Educator

Problem 3

Find the length of the output if an 144-inch input is sent through each machine.
MACHINE CANT COPY

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00:18

Problem 4

Walk the number line to compute each sum or difference.
$-6-3$

Heather Zimmers
Heather Zimmers
Numerade Educator
05:31

Problem 4

Compute each product or sum.
$-2 \times 4+3 \times-4$

JD
Josie Dalrymple
Numerade Educator
01:22

Problem 4

Without plotting each point, tell in which quadrant or on which axis it lies.
a. $(2,0)$
b. $(0,-24)$
c. $(35,-23)$
d. $(3,5)$
e. $(-2,-2)$
f. $(-52,5)$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:23

Problem 4

Use the Pythagorean Theorem to find the length of the segment.
GRAPH CANT COPY

Jennifer White
Jennifer White
Numerade Educator

Problem 4

If possible, find a single repeater machine that will do the same work as the given hookup.
MACHINE CANT COPY

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00:18

Problem 5

Walk the number line to compute each sum or difference.
$-2+-4$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:09

Problem 5

The product of two integers is -15 .
a. What could the integers be? List all the possibilities.
b. Find three more pairs of numbers-not necessarily integers-with a product of -15 .

Victor Salazar
Victor Salazar
Numerade Educator

Problem 5

In this problem, you will color a coordinate plane to show the signs of differences.
a. Create a coordinate plane in which you color a point $(c, d)$ red if $c-d$ is positive and blue if it is negative. If $c-d$ is 0 , color the point black. Shade the plane to show what it would look like if you colored every point red, blue, or black.
b. Now create a coordinate plane in which you color a point $(c, d)$ red if $d-c$ is positive and blue if it is negative. If $d-c$ is 0 , color the point black. Shade the plane to show what it would look like if you colored every point red, blue, or black.
c. How are the two coordinate planes similar? How are they different? Why are they similar and different in these ways?

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02:23

Problem 5

Use the Pythagorean Theorem to find the length of the segment.
GRAPH CANT COPY

Jennifer White
Jennifer White
Numerade Educator

Problem 5

If possible, find a single repeater machine that will do the same work as the given hookup.
MACHINE CANT COPY

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00:20

Problem 6

Walk the number line to compute each sum or difference.
$2+{ }^{-} 11$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:48

Problem 6

Solve $-3 x+4=-5$.

Matthew Biollo
Matthew Biollo
Numerade Educator
00:43

Problem 6

The average surface temperatures of the planets in our solar system are related to their average distances from the sun.
$$
\begin{aligned}
&\text { Planets in the Solar System }\\
&\begin{array}{|l|c|c|}
\hline \text { Planet } & \begin{array}{c}
\text { Distance from Sun } \\
\text { (millions of miles) }
\end{array} & \begin{array}{c}
\text { Surface } \\
\text { Temperature }\left({ }^{\circ} \mathbf{F}\right)
\end{array} \\
\hline \text { Mercury } & 36 & 662 \\
\text { Venus } & 67 & 860 \\
\text { Earth } & 93 & 68 \\
\text { Mars } & 142 & -9 \\
\text { Jupiter } & 483 & -184 \\
\text { Saturn } & 888 & -292 \\
\text { Uranus } & 1,784 & -346 \\
\text { Neptune } & 2,799 & -364 \\
\text { Pluto } & 3,674 & -382 \\
\hline
\end{array}
\end{aligned}
$$
a. Create a graph with distance from the sun on the $x$-axis and average surface temperature on the $y$-axis. Plot the nine points listed in the table.
b. Generally speaking, how does temperature change as you move farther from the sun?
c. Why do you think the relationship you noticed in Part b happens?
d. Which planet or planets don't fit the general pattern? Why might a planet not follow the pattern?

Victor Salazar
Victor Salazar
Numerade Educator
02:23

Problem 6

Use the Pythagorean Theorem to find the length of the segment.
GRAPH CANT COPY

Jennifer White
Jennifer White
Numerade Educator

Problem 6

If possible, find a single repeater machine that will do the same work as the given hookup.
MACHINE CANT COPY

Check back soon!
02:15

Problem 7

Walk the number line to compute each sum or difference.
$-9-{ }^{-5}$

Dana Mark
Dana Mark
Numerade Educator
01:24

Problem 7

Compute each product.
$-3 \cdot-32$

Joshua Fischbach
Joshua Fischbach
Numerade Educator
02:36

Problem 7

Think about straight lines on the coordinate plane. You might draw a coordinate plane and experiment with lines to answer these questions.
a. What is the greatest number of quadrants a straight line can go through? Explain.
b. What is the least number of quadrants a straight line can go through?

Eva R
Eva R
Numerade Educator
01:05

Problem 7

Use the distance formula to find the length of each segment.
$(4,2)$ to $(-5,-6)$

James Kiss
James Kiss
Numerade Educator

Problem 7

If possible, find a single repeater machine that will do the same work as the given hookup.
MACHINE CANT COPY

Check back soon!
01:22

Problem 8

Walk the number line to compute each sum or difference.
4 - 9

Dana Mark
Dana Mark
Numerade Educator
01:32

Problem 8

Compute each product.
$-\frac{1}{2} \cdot-35$

Dheeraj
Dheeraj
Numerade Educator
00:44

Problem 8

If you plotted all points for which the $y$-coordinate is the square of the $x$-coordinate, in which quadrants or on which axes would the points lie? Explain how you know your answer is correct.

Kristen Karbon
Kristen Karbon
Numerade Educator
02:34

Problem 8

Use the distance formula to find the length of each segment.
$(0,-3)$ to $(6,2)$

Leanna Crowe
Leanna Crowe
Numerade Educator
00:43

Problem 8

Describe a machine with a negative exponent that does the same work as the given machine.
MACHINE CANT COPY

K B
K B
Numerade Educator
00:56

Problem 9

Walk the number line to compute each sum or difference.
${ }^{-} 6+14$

SM
Sara Mendoza
Numerade Educator
00:34

Problem 9

Compute each product.
${ }^{-5} \cdot-0.7$

James Kiss
James Kiss
Numerade Educator
00:44

Problem 9

In this exercise, you will use the coordinate plane you colored for Problem Set $\mathrm{F}$ to help solve the inequality $x+5<0$.
a. Look at all the points on the coordinate plane you made in Problem Set $\mathrm{F}$ with a $y$-coordinate of 5 . Of these points, which are red? Which are blue? Which are black?
b. When is the sum of 5 and another number less than 0 ?
c. For which values of $x$ is $x+5<0$ ?

Allison Knapp
Allison Knapp
Numerade Educator
02:07

Problem 9

Use the distance formula to find the length of each segment.
$(-9,2)$ to $(-10,11)$

Christian Otero
Christian Otero
Numerade Educator
00:43

Problem 9

Describe a machine with a negative exponent that does the same work as the given machine.
MACHINE CANT COPY

K B
K B
Numerade Educator
01:34

Problem 10

Walk the number line to compute each sum or difference.
$-5-{ }^{-11}$

SM
Sara Mendoza
Numerade Educator
01:34

Problem 10

Compute each product.
$-2.5 \cdot-7$

Dheeraj
Dheeraj
Numerade Educator
02:23

Problem 10

In Problem Set E, you colored points on a coordinate plane to represent the sign of the products of coordinates. What about the quotients? Suppose you colored a coordinate plane so that point $(c, d)$ is red if $c \div d$ is positive, blue if $c \div d$ is negative, black if $c \div d$ is 0 , and green if it is impossible to calculate $c \div d$.
a. Shade a coordinate plane to show what it would look like if you colored every point red, blue, black, or green.
b. Compare your coordinate plane to the one you made in Problem 3 of Problem Set E. How are they similar and different? Why?

Ruth Wells
Ruth Wells
Numerade Educator
03:05

Problem 10

Use the distance formula to find the length of each segment.
$(6,1)$ to $(9,5)$

Savannah Langenstein
Savannah Langenstein
Numerade Educator
00:43

Problem 10

Describe a machine with a negative exponent that does the same work as the given machine.
MACHINE CANT COPY

K B
K B
Numerade Educator
00:56

Problem 11

Walk the number line to compute each sum or difference.
$-3.5-2.2$

SM
Sara Mendoza
Numerade Educator
00:38

Problem 11

Compute each product.
$-2^5 \cdot-3$

James Kiss
James Kiss
Numerade Educator
00:36

Problem 11

Evaluate each expression.
$4.5 \cdot 90.02$

Victor Salazar
Victor Salazar
Numerade Educator
02:05

Problem 11

Use the distance formula to order the segments below from shortest to longest. Give the length of each segment.
GRAPH CANT COPY

Sachit Kshatriya
Sachit Kshatriya
Numerade Educator
00:43

Problem 11

Describe a machine with a negative exponent that does the same work as the given machine.
MACHINE CANT COPY

K B
K B
Numerade Educator
01:30

Problem 12

Walk the number line to compute each sum or difference.
$2 \frac{1}{5}--3 \frac{2}{5}$

Willis James
Willis James
Numerade Educator
00:18

Problem 12

Compute each product.
$-3 \cdot-5^3$

Erika Bustos
Erika Bustos
Numerade Educator
01:00

Problem 12

Evaluate each expression.
$3.45 \div 0.5$

Joshua Fischbach
Joshua Fischbach
Numerade Educator
04:36

Problem 12

The grid shows the arrangement and length of mammal bones found embedded in a layer of the La Brea Tar Pits in California. (Assume the bones are lying flat in the tar pit, and are not tilted down into the pit.)
GRAPH CANT COPY
a. Which bone is the shortest? How long is it, if each unit on the grid represents 6 inches?
b. Which bone is the longest? How long is it?

Trizia Isaac
Trizia Isaac
Numerade Educator
00:43

Problem 12

Describe a machine with a negative exponent that does the same work as the given machine.
MACHINE CANT COPY

K B
K B
Numerade Educator
01:48

Problem 13

Walk the number line to compute each sum or difference.
$-8.25+1.75$

Dana Mark
Dana Mark
Numerade Educator
00:18

Problem 13

Compute each product.
$-3 \cdot(-5)^3$

Erika Bustos
Erika Bustos
Numerade Educator
00:50

Problem 13

Evaluate each expression.
$0.034 \cdot 3.2 \cdot \frac{1}{2}$

Ava Perkins
Ava Perkins
Numerade Educator
01:34

Problem 13

Use graph paper to help you think about this exercise. Draw a Point $A$ somewhere in the middle of the graph paper. Draw a new point labeled $B$ by moving from Point $A$, left 5 units and up 2 units.
a. From Point $A$, move left 2 units and up 5 units, and mark Point $C$. Is Segment $A C$ the same length as Segment $A B$ ? Why or why not?
b. From Point $A$, move up 2 units and left 5 units, and mark Point $D$. Is Segment $A D$ the same length as Segment $A B$ ? Why or why not?
c. Describe two ways you could move from Point $B$ back to Point $A$.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:43

Problem 13

Describe a machine with a negative exponent that does the same work as the given machine.
MACHINE CANT COPY

K B
K B
Numerade Educator
00:12

Problem 14

Walk the number line to compute each sum or difference.
$-\frac{13}{2}-\frac{13}{4}$

James Kiss
James Kiss
Numerade Educator
01:08

Problem 14

Compute each product.
$-3^2 \cdot(-3)^2$

Shahab Ullah
Shahab Ullah
Numerade Educator
01:59

Problem 14

Draw a flowchart for this rule: output $=2 n+4$. Use it to find the output for the input 8 .

Avery Chard
Avery Chard
Numerade Educator
05:19

Problem 14

Each grid unit on the map represents 15 miles. Suppose you are anchored at the point shown on White Sands Island.
MAP CANT COPY
a. If you can sail 100 miles per day, to which other islands could you travel in a day? You must travel to the harbors marked by the dots.
b. Is there a pair of islands to which you could travel in the same day? If so, which are they? (For example, starting from White Sands to Shell to Windy?) If not, why not?

Sheh Lit Chang
Sheh Lit Chang
University of Washington
00:25

Problem 14

Without calculating, figure out whether $4^{-3}$ or $4^{-4}$ is greater. Explain how you decided.

Maninder Singh
Maninder Singh
Numerade Educator
00:18

Problem 15

Walk the number line to compute each sum or difference.
$4.9-{ }^{-3.2}$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:38

Problem 15

Without calculating each product, determine whether it is less than 0 or greater than 0 .
$3 \times-2$

Ethan Somes
Ethan Somes
Numerade Educator
03:29

Problem 15

Draw a flowchart for this rule: output $=7 n+9$. Use it to find the output for the input 20 .

Kumareshwaran Rathinasabapathy
Kumareshwaran Rathinasabapathy
Numerade Educator
02:16

Problem 15

Make up a word problem to go with the graph at left. Design your problem so that you must use the distance formula to solve it.

Alaina Shelton
Alaina Shelton
Numerade Educator
00:16

Problem 15

Evaluate each expression.
$-343 \cdot 7^{-2}$

Julie Silva
Julie Silva
Numerade Educator
00:56

Problem 16

Walk the number line to compute each sum or difference, and record your steps by making a number-line drawing. Write the complete addition or subtraction equation next to the drawing.
$-2+-7$

SM
Sara Mendoza
Numerade Educator
00:38

Problem 16

Without calculating each product, determine whether it is less than 0 or greater than 0 .
$3 \times 2$

Ethan Somes
Ethan Somes
Numerade Educator
01:56

Problem 16

Draw a flowchart for this rule: output $=\frac{n-13}{12}$. Use it to find the output for the input 73 .

Lourence Gonhovi
Lourence Gonhovi
Numerade Educator
01:42

Problem 16

Find the value of the variable in each equation.
$6 b=15$

Sherrie Fenner
Sherrie Fenner
Numerade Educator
00:31

Problem 16

Evaluate each expression.
${ }^{-} 1,375 \cdot 5^{-3}$

Amy Jiang
Amy Jiang
Numerade Educator
00:48

Problem 17

Walk the number line to compute each sum or difference, and record your steps by making a number-line drawing. Write the complete addition or subtraction equation next to the drawing.
$6-{ }^{-2}$

Dana Mark
Dana Mark
Numerade Educator
00:38

Problem 17

Without calculating each product, determine whether it is less than 0 or greater than 0 .
$-3 \times 2$

Ethan Somes
Ethan Somes
Numerade Educator
01:50

Problem 17

Consider the triangle at left.
a. What is the area of the triangle?
b. Suppose you use this triangle as the base of a prism $1 \mathrm{~cm}$ high. What would the prism's volume be?
c. Draw another triangular base that would produce a 1-cm-high prism with this volume.
d. Suppose you use the triangle to make a prism $4 \mathrm{~cm}$ high. What would the prism's volume be?
e. Suppose you use the triangle to make a prism $h \mathrm{~cm}$ high. What would the prism's volume be?

James Kiss
James Kiss
Numerade Educator
01:53

Problem 17

Find the value of the variable in each equation.
$2 k-5=1.4$

Matthew Biollo
Matthew Biollo
Numerade Educator
03:36

Problem 17

Evaluate each expression.
$128 \cdot 2^{-5}$

Michael Cooper
Michael Cooper
Numerade Educator
00:56

Problem 18

Walk the number line to compute each sum or difference, and record your steps by making a number-line drawing. Write the complete addition or subtraction equation next to the drawing.
$5-7$

SM
Sara Mendoza
Numerade Educator
00:38

Problem 18

Without calculating each product, determine whether it is less than 0 or greater than 0 .
$-3 \times-2$

Ethan Somes
Ethan Somes
Numerade Educator
00:25

Problem 18

From the following list, find all the pairs of fractions with a sum of 1 .
$$
\begin{array}{llllllllll}
\frac{15}{21} & \frac{10}{25} & \frac{8}{14} & \frac{1}{6} & \frac{2}{7} & \frac{3}{7} & \frac{3}{6} & \frac{10}{12} & \frac{3}{5} & \frac{1}{2}
\end{array}
$$

Ashley Volpe
Ashley Volpe
Numerade Educator
02:24

Problem 18

Find the value of the variable in each equation.
$a=25 a$

Angela Hathaway
Angela Hathaway
Numerade Educator
00:54

Problem 18

Evaluate each expression.
$-72 \cdot 9^{-1}$

Joshua Fischbach
Joshua Fischbach
Numerade Educator
00:28

Problem 19

Walk the number line to compute each sum or difference, and record your steps by making a number-line drawing. Write the complete addition or subtraction equation next to the drawing.
$-3+11$

Marcial Vargas
Marcial Vargas
Numerade Educator
02:18

Problem 19

The product of two integers is 9 . What could the integers be? List all the possibilities.

Kayla Laughman
Kayla Laughman
Numerade Educator
00:34

Problem 19

At top speed, Chet the cheetah can run about $60 \mathrm{mph}$ for short distances. At this speed, how far can Chet run in 40 seconds?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:02

Problem 19

Find the value of the variable in each equation.
$3.5 m=7$

Kayleah Tsai
Kayleah Tsai
Numerade Educator
01:11

Problem 19

Evaluate each expression.
$48 \cdot 6^{-1}$

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
00:56

Problem 20

Walk the number line to compute each sum or difference, and record your steps by making a number-line drawing. Write the complete addition or subtraction equation next to the drawing.
$2.2-1.4$

SM
Sara Mendoza
Numerade Educator
00:34

Problem 20

Solve ${ }^{-5 y}+13=3$.

Ashly Sunny
Ashly Sunny
Numerade Educator
06:39

Problem 20

Diego surveyed the students in his English class about how many siblings (brothers or sisters) they had. The pictograph shows his results.
a. How many students did Diego survey?
b. What are the mean, median, and mode of Diego's data?
c. How many siblings do the students in Diego's English class have in all
d. If you choose a student at random from Diego's English class, what is the probability the student has exactly three siblings?
e. If you choose a student at random from Diego's English class, what is the probability the student has more than two siblings?
English Class Survey
SURVEY CANT COPY

Charles Carter
Charles Carter
Numerade Educator
01:09

Problem 20

Find the value of the variable in each equation.
$6-22 p=6$

Brandon Fox
Brandon Fox
Numerade Educator
00:53

Problem 20

Evaluate each expression.
$243 \cdot 3^{-4}$

Nick Johnson
Nick Johnson
Numerade Educator
00:38

Problem 21

Walk the number line to compute each sum or difference, and record your steps by making a number-line drawing. Write the complete addition or subtraction equation next to the drawing.
$-5 \frac{1}{3}+2 \frac{5}{6}$

SM
Sara Mendoza
Numerade Educator
00:41

Problem 21

Find each quotient.
$-3 \div 2.5$

Carson Merrill
Carson Merrill
Numerade Educator
00:49

Problem 21

Find the value of the variable in each equation.
$3 n \div 7=3$

Victor Salazar
Victor Salazar
Numerade Educator
00:27

Problem 21

Evaluate each expression.
$-9 \cdot 1^{-3}$

Julie Silva
Julie Silva
Numerade Educator
00:36

Problem 22

In Exercises 22-25, write the addition or subtraction equation represented by the drawing.
DRAWING CANT COPY

Jeyasree R T
Jeyasree R T
Numerade Educator
00:41

Problem 22

Find each quotient.
$-3 \div-25$

Carson Merrill
Carson Merrill
Numerade Educator
00:13

Problem 22

Rewrite each expression in exponential notation.
$c \cdot c \cdot c \cdot c$

Amy Jiang
Amy Jiang
Numerade Educator
00:57

Problem 22

Evaluate each expression.
$4,096 \cdot 8^{-2}$

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
00:41

Problem 23

Write the addition or subtraction equation represented by the drawing.
DRAWING CANT COPY

Amy Jiang
Amy Jiang
Numerade Educator
00:51

Problem 23

Find each quotient.
$45 \div-360$

Joshua Fischbach
Joshua Fischbach
Numerade Educator
00:08

Problem 23

Rewrite each expression in exponential notation.
$4 \cdot 4 \cdot 4$

James Kiss
James Kiss
Numerade Educator
00:21

Problem 23

Evaluate each expression.
${ }^{-} 11 \cdot 11^{-1}$

Erika Bustos
Erika Bustos
Numerade Educator
00:41

Problem 24

Write the addition or subtraction equation represented by the drawing.
DRAWING CANT COPY

Amy Jiang
Amy Jiang
Numerade Educator
01:46

Problem 24

Find each quotient.
$\frac{-45}{-90}$

Joshua Fischbach
Joshua Fischbach
Numerade Educator
00:18

Problem 24

Rewrite each number in standard notation.
$6 \times 10^2$

Amy Jiang
Amy Jiang
Numerade Educator
01:49

Problem 24

How could you rewrite Problem 22 as a division problem? As a multiplication problem using a positive exponent?

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
00:41

Problem 25

Write the addition or subtraction equation represented by the drawing.
DRAWING CANT COPY

Amy Jiang
Amy Jiang
Numerade Educator
00:29

Problem 25

One number divided by a negative number is 0.467 . What could the two numbers be? Think of three possibilities and write them as division equations.

Dale Sanford
Dale Sanford
Numerade Educator
00:19

Problem 25

Rewrite each number in standard notation.
$9 \times 10^5$

Amy Jiang
Amy Jiang
Numerade Educator
00:27

Problem 25

Decide whether each statement is true. If the statement is false, explain why.
$2^{-2} \cdot 2^{-1}=2^{-3}$

Leslie Deeb
Leslie Deeb
Numerade Educator
02:30

Problem 26

The sum of two numbers is -8 . What could the numbers be? Give three possibilities.

Aamir Mithaiwala
Aamir Mithaiwala
Numerade Educator
01:15

Problem 26

Solve each equation.
$\frac{x}{-3}+4=6$

Thomas Emment
Thomas Emment
Numerade Educator
01:02

Problem 26

Rewrite each number in scientific notation.
654,000

Liuxi Sun
Liuxi Sun
Numerade Educator
00:31

Problem 26

Decide whether each statement is true. If the statement is false, explain why.
$5^{-3} \cdot 5^{-1} \cdot 5^2=5^{-2}$

Brandon Fox
Brandon Fox
Numerade Educator
03:17

Problem 27

Write an addition equation and a subtraction equation that each numberline picture could describe. You might want to make a drawing.
DRAWING CANT COPY

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
00:44

Problem 27

Solve each equation.
$\frac{x}{8}-2.5=-3$

Elizabeth Xu
Elizabeth Xu
Numerade Educator
01:02

Problem 27

Rewrite each number in scientific notation.
$9,500,000,000$

Narayan Hari
Narayan Hari
Numerade Educator
00:34

Problem 27

Decide whether each statement is true. If the statement is false, explain why.
$3^{-1} \cdot 4^{-3}=12^{-4}$

Brandon Fox
Brandon Fox
Numerade Educator
03:17

Problem 28

Write an addition equation and a subtraction equation that each numberline picture could describe. You might want to make a drawing.
DRAWING CANT COPY

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
00:36

Problem 28

Solve each equation.
$-\frac{12}{x}+45=49$

Vicki Stebbins
Vicki Stebbins
Numerade Educator
01:43

Problem 28

Shayla has made a sketch of the garden she would like to plant in the spring. Each grid square has an area of 1 square foot.
SQUARE CANT COPY
a. How many more square feet will Shayla plant in corn than in pumpkins?
b. How many more squware yards will Shayla plant in corn than in pumpkins? (Be careful!)
c. What fraction of the total garden area will Shayla plant in squash?
d. What percentage of the total garden area will Shayla plant in lettuce?
e. Suppose Shayla adds more space to her garden in order to triple the size of the corn plot. What percentage of the total garden area will be planted in corn?

Rishi Kavikondala
Rishi Kavikondala
Numerade Educator
00:26

Problem 28

Decide whether each statement is true. If the statement is false, explain why.
$3^{-2} \cdot 3^{-3}=9^{-5}$

Brandon Fox
Brandon Fox
Numerade Educator
01:05

Problem 29

Compute each difference, and write your answer in the form of a subtraction equation. Then write an equivalent addition equation.
$25.2-{ }^{-3.4}$

Victor Salazar
Victor Salazar
Numerade Educator
01:51

Problem 29

As a parachutist descends into Death Valley, her elevation decreases 15 feet every second. Five seconds before she lands, she is at an elevation of -127 feet. What is the elevation of the place she lands?

Julie Silva
Julie Silva
Numerade Educator
02:24

Problem 29

Match each point on the graph to the coordinates given.
GRAPH CANT COPY
a. $(-2,0)$
b. $(1,-3)$
c. $(-2,3)$
d. $(-2,-4)$
e. $(2,1)$
f. $(3,4)$

AG
Ankit Gupta
Numerade Educator
00:36

Problem 29

Decide whether each statement is true. If the statement is false, explain why.
$x^{-5} \div x^7=x^{-12}$

Brandon Fox
Brandon Fox
Numerade Educator
00:27

Problem 30

Compute each difference, and write your answer in the form of a subtraction equation. Then write an equivalent addition equation.
$-43-18$

Patrick Burns
Patrick Burns
Numerade Educator
01:25

Problem 30

When it is cold outside and the wind is blowing, it feels colder than it would at the same temperature without any wind. Scientists call the temperature that it feels outside the windchill.
For example, if the temperature outside is $20^{\circ} \mathrm{F}$ and the wind speed is $20 \mathrm{mph}$, the equivalent windchill temperature is about ${ }^{-} 10^{\circ} \mathrm{F}$. That means that even though the thermometer reads $20^{\circ} \mathrm{F}$, it feels as cold as it would if you were in no wind at $-10^{\circ} \mathrm{F}$.
Here's how meteorologists calculate windchill. The variable $s$ represents wind speed in mph, and $t$ represents actual temperature in ${ }^{\circ} \mathrm{F}$.
$$
\text { windchill }=0.0817\left(3.71 \sqrt{s}+5.81-\frac{s}{4}\right)(t-91.4)+91.4
$$
This formula works when wind speeds are between $4 \mathrm{mph}$ and $45 \mathrm{mph}$.
a. If the wind blows at $20 \mathrm{mph}$ and the temperature is ${ }^{-} 5^{\circ} \mathrm{F}$, what is the windchill?
b. If the wind blows at $30 \mathrm{mph}$ and the temperature is ${ }^{-} 10^{\circ} \mathrm{F}$, what is the windchill?
c. Challenge If the wind blows at $25 \mathrm{mph}$ and the windchill is $-60^{\circ} \mathrm{F}$, what is the actual temperature?

Amy Jiang
Amy Jiang
Numerade Educator
00:36

Problem 30

Decide whether each statement is true. If the statement is false, explain why.
$k^{-2} \div k^{-5}=k^3$

Brandon Fox
Brandon Fox
Numerade Educator
01:12

Problem 31

Compute each sum, and write your answer in the form of an addition equation. Then write an equivalent subtraction equation.
$-6+-9$

Nicholas Bondra
Nicholas Bondra
Numerade Educator
00:48

Problem 31

Pedro said, "I'm thinking of a number. When I multiply my number by -2 and subtract 4 , I get -16 ." What is Pedro's number?

Carter Rogers
Carter Rogers
Numerade Educator
00:54

Problem 31

Decide whether each statement is true. If the statement is false, explain why.
$w^{-2} \div w^{-5}=w^{-7}$

Amy Jiang
Amy Jiang
Numerade Educator
01:29

Problem 32

Compute each sum, and write your answer in the form of an addition equation. Then write an equivalent subtraction equation.
$-21.8+17.4$

Noraney Ocampo
Noraney Ocampo
Numerade Educator
01:23

Problem 32

Without calculating, predict whether each product is less than 0 , equal to 0 , or greater than 0 .
$(-4)^3 \cdot(-2)^2$

Melissa Barry
Melissa Barry
Numerade Educator
00:54

Problem 32

Decide whether each statement is true. If the statement is false, explain why.
$b^{-8} \div g^{-4}=b g^{-2}$

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
00:59

Problem 33

At room temperature, mercury is a liquid. The freezing point of mercury - the point at which it turns from liquid to solid-is $-39^{\circ} \mathrm{C}$. What is the freezing point of mercury on the Kelvin scale?

Casey Evans
Casey Evans
Numerade Educator
00:38

Problem 33

Without calculating, predict whether each product is less than 0 , equal to 0 , or greater than 0 .
$(-3)^5 \cdot(-6)^3$

Ethan Somes
Ethan Somes
Numerade Educator
01:44

Problem 33

Without evaluating, tell whether each expression is greater or less than 1 .
$3^{-4} \times 3^5$

Priyanka Sadarangani
Priyanka Sadarangani
Numerade Educator
01:34

Problem 34

In this problem, you will solve this inequality: $-5-y<0$.
a. Find three positive values of $y$ that make the inequality true.
b. Find three negative values of $y$ that make the inequality true.
c. Describe all the values of $y$ that make the inequality true.

AG
Ankit Gupta
Numerade Educator

Problem 34

Without calculating, predict whether each product is less than 0 , equal to 0 , or greater than 0 .
$(-1)^5 \cdot 5^2$

Check back soon!
00:08

Problem 34

Without evaluating, tell whether each expression is greater or less than 1 .
$2^{-1} \times 2^{-3}$

Amy Jiang
Amy Jiang
Numerade Educator
01:30

Problem 35

If possible, give an example in which a negative number is subtracted from a positive number and the result is negative. If it is not possible, explain why.

Heather Zimmers
Heather Zimmers
Numerade Educator
01:29

Problem 35

Without calculating, predict whether each product is less than 0 , equal to 0 , or greater than 0 .
$(-2)^2 \cdot(-972)^{90}$

Wesley Hines
Wesley Hines
Numerade Educator
00:08

Problem 35

Without evaluating, tell whether each expression is greater or less than 1 .
$1^{-3} \div 2^{-3}$

Amy Jiang
Amy Jiang
Numerade Educator
00:17

Problem 36

The sum of two numbers is greater than 0 .
a. Could both numbers be negative? If so, give an example. If not, explain why not.
b. Could both numbers be positive? If so, give an example. If not, explain why not.
c. Could one number be negative and one positive? If so, give an example. If not, explain why not.

Tiffany Tran
Tiffany Tran
Numerade Educator

Problem 36

Without calculating, predict whether each product is less than 0 , equal to 0 , or greater than 0 .
$-45^2 \cdot(-35)^5$

Check back soon!
00:14

Problem 36

Without evaluating, tell whether each expression is greater or less than 1 .
$10^{-5} \div 10^3$

Amy Jiang
Amy Jiang
Numerade Educator
00:29

Problem 37

The difference between two numbers is less than 0 .
a. Could both numbers be positive? If so, give an example. If not, explain why not.
b. Could both numbers be negative? If so, give an example. If not, explain why not.
c. Could one number be negative and one positive? If so, give an example. If not, explain why not.

Julie Silva
Julie Silva
Numerade Educator
01:04

Problem 37

Without calculating, predict whether each product is less than 0 , equal to 0 , or greater than 0 .
$(-2)^8 \cdot(-5)^8$

Dheeraj
Dheeraj
Numerade Educator
01:51

Problem 37

Evaluate each expression.
$-4^{-2}$

Michael Cooper
Michael Cooper
Numerade Educator
01:30

Problem 38

Do each computation by walking the number line. Explain each step you take.
$3+-4+-2-5$

Willis James
Willis James
Numerade Educator
00:20

Problem 38

If possible, solve each equation. If it is not possible, explain why.
$y^3=-8$

Lily An
Lily An
Numerade Educator
00:14

Problem 38

Evaluate each expression.
$(-5)^{-1}$

Erika Bustos
Erika Bustos
Numerade Educator
02:13

Problem 39

Do each computation by walking the number line. Explain each step you take.
$-2-9+2-4--15$

Raushan Kumar
Raushan Kumar
Numerade Educator
01:47

Problem 39

If possible, solve each equation. If it is not possible, explain why.
$x^2=-9$

Yujie Wang
Yujie Wang
College of San Mateo
00:13

Problem 39

Evaluate each expression.
$-2^3$

Amy Jiang
Amy Jiang
Numerade Educator
01:15

Problem 40

The chart shows the high temperature, in degrees Fahrenheit, for the first 10 days of the year in a small Alaskan town. What is the average of these temperatures?
$$
\begin{aligned}
&\text { Daily High Temperatures }\\
&\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|}
\hline \text { Date } & 1 / 1 & 1 / 2 & 1 / 3 & 1 / 4 & 1 / 5 & 1 / 6 & 1 / 7 & 1 / 8 & 1 / 9 & 1 / 10 \\
\hline \text { Temp }\left({ }^{\circ} \mathbf{F}\right) & 3 & 1 & 13 & 5 & 2 & 2 & -4 & -7 & -2 & -2 \\
\hline
\end{array}
\end{aligned}
$$

Erika Bustos
Erika Bustos
Numerade Educator
00:35

Problem 40

Describe the values of $b$ that make each inequality true.
$3 b<0$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:26

Problem 40

Evaluate each expression.
$(-10)^4$

Amy Jiang
Amy Jiang
Numerade Educator
02:01

Problem 41

Luis said, "If you add -3 to my sister's age, you will get my age." Luis is 12. How old is his sister?

Patrick Burns
Patrick Burns
Numerade Educator
00:35

Problem 41

Describe the values of $b$ that make each inequality true.
$3(b-2)<0$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:19

Problem 41

Rewrite each expression using a single base and a single exponent.
$\frac{1}{2^{-2}} \times 4^{-2}$

Amy Jiang
Amy Jiang
Numerade Educator
01:17

Problem 42

Without calculating each sum or difference, figure out whether it is less than 0 , greater than 0 , or equal to 0 .
$-8-9$

Christopher Stanley
Christopher Stanley
Numerade Educator
04:42

Problem 42

Without calculating, determine whether the quotient in Exercises $42-44$ is less than ${ }^{-} 1$, between ${ }^{-1}$ and 0 , between 0 and 1 , or greater than 1 .
FIGURE CANT COPY
$1 \div-\frac{3}{5}$

Alexandra Embry
Alexandra Embry
Numerade Educator
00:25

Problem 42

Rewrite each expression using a single base and a single exponent.
$100^{-20} \div-25^{-20}$

Amy Jiang
Amy Jiang
Numerade Educator
01:05

Problem 43

Without calculating each sum or difference, figure out whether it is less than 0 , greater than 0 , or equal to 0 .
${ }^{-3}-{ }^{-} \pi$

Jeyasree R T
Jeyasree R T
Numerade Educator
06:11

Problem 43

Without calculating, determine whether the quotient in Exercises $42-44$ is less than ${ }^{-} 1$, between ${ }^{-1}$ and 0 , between 0 and 1 , or greater than 1 .
FIGURE CANT COPY
$\frac{-555.233}{-5,552}$

Noah Duncan
Noah Duncan
Numerade Educator
01:01

Problem 43

Rewrite each expression using a single base and a single exponent.
$-3^{100} \times-\frac{5}{6^{100}} \times 10^{100}$

Joseph Lentino
Joseph Lentino
Numerade Educator
01:17

Problem 44

Without calculating each sum or difference, figure out whether it is less than 0 , greater than 0 , or equal to 0 .
$-78+2^6$

Christopher Stanley
Christopher Stanley
Numerade Educator
06:11

Problem 44

Without calculating, determine whether the quotient in Exercises $42-44$ is less than ${ }^{-} 1$, between ${ }^{-1}$ and 0 , between 0 and 1 , or greater than 1 .
FIGURE CANT COPY
$78.3636 \div-25.33$

Noah Duncan
Noah Duncan
Numerade Educator
00:20

Problem 44

Rewrite each expression using a single base and a single exponent.
$\left(\frac{1}{3}\right)^{-a} \times\left(\frac{1}{5}\right)^{-a}$

Amy Jiang
Amy Jiang
Numerade Educator
02:04

Problem 45

Copy and complete the flowchart.
FLOWCHART CANT COPY

Zach Steedman
Zach Steedman
Numerade Educator
01:28

Problem 45

The average of 10 temperatures is $-21^{\circ} \mathrm{F}$. What could the temperatures be?

Teresa Fuston
Teresa Fuston
Numerade Educator
00:48

Problem 45

Rewrite each expression using a single base and a single exponent.
$-1,000^0 \div 3^0$

Amy Jiang
Amy Jiang
Numerade Educator
02:43

Problem 46

Integers are whole numbers and their opposites: . . , $-3,-2,-1,0$, $1,2,3, \ldots$ The sum of two negative integers is ${ }^{-} 6$.
a. What could the integers be? List all the possibilities.
b. Find two more pairs of negative numbers (not integers) whose sum is ${ }^{-} 6$.

Rylie Howey
Rylie Howey
Numerade Educator
00:47

Problem 46

The average of 5 temperatures is $-21^{\circ} \mathrm{F}$. What could the temperatures be?

Sophie S
Sophie S
Numerade Educator
00:20

Problem 46

Rewrite each expression using a single base and a single exponent.
$15^{-5} \times\left(\frac{1}{5}\right)^{-5}$

Amy Jiang
Amy Jiang
Numerade Educator
00:34

Problem 47

Use the distributive property to rewrite each expression as simply as you can.
$6 x--2 x$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:10

Problem 47

Solve each equation. Be careful: Each equation has two solutions.
$\left(\frac{1}{y}\right)^2=\frac{1}{9}$

Jake Zanazzi
Jake Zanazzi
Numerade Educator
01:25

Problem 47

Find the value of $n$ in each equation.
$7.24 \cdot 10^n=0.00724$

Kristof Mueller
Kristof Mueller
Numerade Educator
01:17

Problem 48

Use the distributive property to rewrite each expression as simply as you can.
$3 z-5 z$

Kristof Mueller
Kristof Mueller
Numerade Educator
00:23

Problem 48

Solve each equation. Be careful: Each equation has two solutions.
$y^2=\frac{1}{9}$

James Kiss
James Kiss
Numerade Educator
00:36

Problem 48

Find the value of $n$ in each equation.
$5 \cdot 10^n=0.5$

Victor Salazar
Victor Salazar
Numerade Educator
00:55

Problem 49

Use the distributive property to rewrite each expression as simply as you can.
$7 x+{ }^{-2} 2 x$

Arin Asawa
Arin Asawa
Numerade Educator
00:36

Problem 49

Solve each equation.
$\left(\frac{1}{z}\right)^2=16$

Jake Zanazzi
Jake Zanazzi
Numerade Educator
01:14

Problem 49

Find the value of $n$ in each equation.
$n \cdot 10^{-4}=0.000104$

Kristof Mueller
Kristof Mueller
Numerade Educator
00:27

Problem 50

Maya thinks that for all values of $x$ and $y$, this equation is true:
$$
|x+y|=|x|+|y|
$$
For example, if $x$ is ${ }^{-5}$ and $y$ is ${ }^{-} 6$, the two sides of the equation become
$$
|x+y|=\left|{ }^{-} 5+{ }^{-} 6\right|=\left|{ }^{-} 11\right|=11
$$
and
$$
|x|+|y|=|-5|+|-6|=5+6=11
$$
Is Maya right? If so, explain why. If not, give an example of values for $x$ and $y$ such that $|x+y| \neq|x|+|y|$.

Matt Gibson
Matt Gibson
Numerade Educator
01:49

Problem 50

Solve each equation.
$-\frac{5}{x}+4=2$

Peter Winans
Peter Winans
Numerade Educator
00:31

Problem 50

Find the value of $n$ in each equation.
$9.2 \cdot n=0.0092$

James Kiss
James Kiss
Numerade Educator
00:37

Problem 51

Choose a number, and write down both the number and its opposite.
a. What happens when you add the two numbers?
b. Will the same thing happen when you add any number to its opposite? Explain why or why not.

AG
Ankit Gupta
Numerade Educator
01:09

Problem 51

Evaluate each expression.
$0.125 \cdot 0.3$

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
00:37

Problem 51

A mile is $1.609 \times 10^5$ centimeters. How many miles is a centimeter? Express your answer in scientific notation.

Rishabh Mittal
Rishabh Mittal
Numerade Educator
00:45

Problem 52

Solve each equation by using backtracking or another method.
$x+{ }^{-9}=1.5$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:28

Problem 52

Evaluate each expression.
$0.125 \cdot 0.5$

Julie Silva
Julie Silva
Numerade Educator
00:34

Problem 52

There is $7.8125 \times 10^{-3}$ gallon in an ounce. How many ounces are in a gallon? Express your answer in scientific notation.

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:29

Problem 53

Solve each equation by using backtracking or another method.
$y-3=-0.5$

Julie Silva
Julie Silva
Numerade Educator
00:28

Problem 53

Evaluate each expression.
$0.125 \cdot 0.04$

Julie Silva
Julie Silva
Numerade Educator
01:03

Problem 53

Simplify each expression.
$-6 a^{-2} \div 4 a^{-4}$

Lourence Gonhovi
Lourence Gonhovi
Numerade Educator
01:19

Problem 54

Solve each equation by using backtracking or another method.
$3-x=8.4$

Eva R
Eva R
Numerade Educator
01:17

Problem 54

Evaluate each expression.
$0.125 \cdot 0.004$

Nick Johnson
Nick Johnson
Numerade Educator
00:33

Problem 54

Simplify each expression.
$-\frac{1}{2} x^{-3} \times x^4$

Amy Jiang
Amy Jiang
Numerade Educator
00:48

Problem 55

What values of $y$ make each inequality true?
a. $2+y<0$
b. $-10<2+y$
c. $-10<2+y$ and $2+y<0$

Yujie Wang
Yujie Wang
College of San Mateo
00:28

Problem 55

Evaluate each expression.
$0.125 \cdot 2$

Julie Silva
Julie Silva
Numerade Educator
01:34

Problem 55

Simplify each expression.
$z^2 \times 2 z^{-3} \div-6 z^{-2}$

Amy Jiang
Amy Jiang
Numerade Educator
00:29

Problem 56

Copy each problem, and fill in the blank with a number that gives a sum between $-1 \frac{1}{2}$ and $-\frac{1}{2}$.
a. $10+$
b. ${ }^{-} 1.2+$
c. $-2+$
d. $-84+$
e. In Parts a-d, what did you need to do to make the answer be between $-1 \frac{1}{2}$ and $-\frac{1}{2}$ ?

AG
Ankit Gupta
Numerade Educator
00:28

Problem 56

Evaluate each expression.
$0.125 \cdot 200$

Julie Silva
Julie Silva
Numerade Educator
01:03

Problem 56

Simplify each expression.
$9 b^4 \times 9 b^{-8}$

Prashansha Kaushik
Prashansha Kaushik
Numerade Educator
01:13

Problem 57

Without solving each equation, determine whether the value of $x$ is less than 0 , equal to 0 , or greater than 0 .
$x-3=-5$

Carson Merrill
Carson Merrill
Numerade Educator
05:50

Problem 57

Tama drew the following flowcharts. For each flowchart, tell what equation Tama was trying to solve. Then, copy and complete the flowchart.
FLOWCHART CANT COPY

Wayne Loutet
Wayne Loutet
Numerade Educator
00:43

Problem 57

Describe a machine that has a negative exponent and that does the same work as the machine shown at right.
MACHINE CANT COPY

K B
K B
Numerade Educator
01:13

Problem 58

Without solving each equation, determine whether the value of $x$ is less than 0 , equal to 0 , or greater than 0 .
${ }^{-} x+3=5$

Carson Merrill
Carson Merrill
Numerade Educator
05:50

Problem 58

Tama drew the following flowcharts. For each flowchart, tell what equation Tama was trying to solve. Then, copy and complete the flowchart.
FLOWCHART CANT COPY

Wayne Loutet
Wayne Loutet
Numerade Educator

Problem 58

Find the length of the output if a meterstick is sent through each hookup.
MACHINE CANT COPY

Check back soon!
00:59

Problem 59

Without solving each equation, determine whether the value of $x$ is less than 0 , equal to 0 , or greater than 0 .
$4-x=9$

Sherrie Fenner
Sherrie Fenner
Numerade Educator
05:50

Problem 59

Tama drew the following flowcharts. For each flowchart, tell what equation Tama was trying to solve. Then, copy and complete the flowchart.
FLOWCHART CANT COPY

Wayne Loutet
Wayne Loutet
Numerade Educator

Problem 59

Find the length of the output if a meterstick is sent through each hookup.
MACHINE CANT COPY

Check back soon!
01:09

Problem 60

Without solving each equation, determine whether the value of $x$ is less than 0 , equal to 0 , or greater than 0 .
$x-3=12$

Carson Merrill
Carson Merrill
Numerade Educator
01:30

Problem 60

Find the value for $\frac{1}{2} k^2$ for each value of $k$.
a. 0
b. $\frac{1}{2}$
c. 1.2
d. 4

David Mccaslin
David Mccaslin
Numerade Educator

Problem 60

Find the length of the output if a meterstick is sent through each hookup.
MACHINE CANT COPY

Check back soon!
02:00

Problem 61

In this exercise, you will investigate the possible results for the sum of two positive numbers and a negative number.
a. Choose two positive numbers and one negative number. Is their sum positive, negative, or 0 ?
b. Suppose you repeat Part a with different numbers. Will the sum be always positive; always negative, or sometimes positive, sometimes negative, and sometimes 0 ? How do you know?

Heather Zimmers
Heather Zimmers
Numerade Educator
02:00

Problem 61

Find the value for $10 m^2$ for each value of $m$.
a. 0
b. $\frac{1}{2}$
c. 1.2
d. 4

Grace Muhihu
Grace Muhihu
Numerade Educator

Problem 61

Find the length of the output if a meterstick is sent through each hookup.
MACHINE CANT COPY

Check back soon!
00:35

Problem 62

If possible, rewrite each expression using the laws of exponents.
$y^2 \times y^6$

Prashansha Kaushik
Prashansha Kaushik
Numerade Educator
05:09

Problem 62

Find the value for $3 p^2+10$ for each value of $p$.
a. 0
b. $\frac{1}{2}$
c. 1.2
d. 4

Brian Austin
Brian Austin
Numerade Educator
00:31

Problem 62

A 1-inch stick of gum went into each machine. Complete the chart.
CHART CANT COPY

Charles Carter
Charles Carter
Numerade Educator
View

Problem 63

If possible, rewrite each expression using the laws of exponents.
$a^n \times a^n$

Suzanne W.
Suzanne W.
Numerade Educator
00:43

Problem 63

A calculator costs $$\$ 14$$ and requires three batteries that are not included in the price of the calculator.
a. Suppose each battery costs $b$ dollars. Write an expression for the total cost of the calculator and batteries.
b. What is the total cost if each battery is $$\$ .89$$ ?

Nick Johnson
Nick Johnson
Numerade Educator
03:36

Problem 63

A strand of wire is sent through this hookup. It emerges 2 inches long. What was the starting length?
MACHINE CANT COPY

Vishal Gupta
Vishal Gupta
Numerade Educator
01:18

Problem 64

If possible, rewrite each expression using the laws of exponents.
$2 b \times 3 b^2$

Sherrie Fenner
Sherrie Fenner
Numerade Educator
00:58

Problem 64

Consider this cylinder.
a. Find the volume of the cylinder.
b. Find the volume of a cylinder with a radius twice the length of this cylinder's radius.
c. Find the volume of a cylinder that is twice as high as this cylinder.

Andrew Bassila
Andrew Bassila
Numerade Educator
02:13

Problem 64

Without calculating, figure out whether each expression is positive or negative and explain how you decided.
$\left({ }^{-4}\right)^{-1}$

Paul Mcinerney
Paul Mcinerney
Numerade Educator
00:17

Problem 65

If possible, rewrite each expression using the laws of exponents.
$4^5 \times 9^5$

Brandon Fox
Brandon Fox
Numerade Educator
02:16

Problem 65

Sherina bought two dozen superballs to give out at her birthday party, and she put them in a bag. A third of the superballs were blue, $25 \%$ were striped, an eighth were hot pink, and the rest were made to glow in the dark.
a. Antonie arrived first, and Sherina asked him to reach into the bag without looking and take a ball. What is the probability that Antonie's ball will glow in the dark?
b. Antonie picked a blue ball. Lucita arrived next and said she hoped to pick hot pink. What is the probability she will get her wish?
c. Lucita didn't get what she'd wanted, but Emilio, who picked next, did get hot pink. What was the probability of this happening?
d. Emilio traded with Lucita for her striped superball. Miki picked next, hoping for a glow-in-the-dark ball. What is the probability of her choosing one?

Anna Jones
Anna Jones
Numerade Educator
02:13

Problem 65

Without calculating, figure out whether each expression is positive or negative and explain how you decided.
$\left({ }^{-4}\right)^{-2}$

Paul Mcinerney
Paul Mcinerney
Numerade Educator
00:57

Problem 66

If possible, rewrite each expression using the laws of exponents.
$5 a^4 \times 5 a^4$

Coach Rye
Coach Rye
Numerade Educator
02:13

Problem 66

Without calculating, figure out whether each expression is positive or negative and explain how you decided.
$(-4)^{-3}$

Paul Mcinerney
Paul Mcinerney
Numerade Educator
00:19

Problem 67

If possible, rewrite each expression using the laws of exponents.
$a^{100} \times b^{100}$

Sherrie Fenner
Sherrie Fenner
Numerade Educator
02:13

Problem 67

Without calculating, figure out whether each expression is positive or negative and explain how you decided.
$(-4)^{-4}$

Paul Mcinerney
Paul Mcinerney
Numerade Educator
00:47

Problem 68

If possible, rewrite each expression using the laws of exponents.
$\left(1.1^2\right)^4$

Amy Jiang
Amy Jiang
Numerade Educator
00:42

Problem 68

Without calculating, figure out whether each expression is positive or negative and explain how you decided.
$(-2)^{-3}$

Nick Johnson
Nick Johnson
Numerade Educator
00:36

Problem 69

If possible, rewrite each expression using the laws of exponents.
$\left(0.9^4\right)^3$

Amy Jiang
Amy Jiang
Numerade Educator
00:42

Problem 69

Without calculating, figure out whether each expression is positive or negative and explain how you decided.
$(-2)^{-2}$

Nick Johnson
Nick Johnson
Numerade Educator
00:36

Problem 70

If possible, rewrite each expression using the laws of exponents.
$\left(a^3\right)^4$

Amy Jiang
Amy Jiang
Numerade Educator
00:36

Problem 70

Without calculating, figure out whether each expression is positive or negative and explain how you decided.
$(-5)^{-1}$

Jeyasree R T
Jeyasree R T
Numerade Educator
00:36

Problem 71

If possible, rewrite each expression using the laws of exponents.
$\left(a^4\right)^0$

Brandon Fox
Brandon Fox
Numerade Educator
00:41

Problem 71

Without calculating, figure out whether each expression is positive or negative and explain how you decided.
$(-10)^{-6}$

Nick Johnson
Nick Johnson
Numerade Educator
00:10

Problem 72

If possible, rewrite each expression using the laws of exponents.
$\left(x^2\right)^3$

Coach Rye
Coach Rye
Numerade Educator
01:01

Problem 72

It is true that $\left(\frac{1}{2}\right)^{-1}=\left(2^{-1}\right)^{-1}=2^1=2$. In Parts a-c, you will explain each step in this calculation.
a. Why does $\left(\frac{1}{2}\right)^{-1}=\left(2^{-1}\right)^{-1}$ ?
b. Why does $\left(2^{-1}\right)^{-1}=2^1$ ?
c. Why does $2^1=2$ ?

Matt Gibson
Matt Gibson
Numerade Educator
View

Problem 73

If possible, rewrite each expression using the laws of exponents.
$\left(3^n\right)^m$

Suzanne W.
Suzanne W.
Numerade Educator
03:13

Problem 73

Protons, neutrons, and electrons are stable particles-they can exist for a very long time. But many other particles exist for only very short periods of time. A muon, for example, has an average life of 0.000002197 second.
a. Write this length of time in scientific notation.
b. A particular muon existed for half the average life of this type of particle. How long did it exist?
c. Another muon existed for three times the average life of this type of particle. How long did it exist?

Guilherme Barros
Guilherme Barros
Numerade Educator
00:57

Problem 74

Find each product.
$6 \times \frac{1}{10^2}$

Yujie Wang
Yujie Wang
College of San Mateo
00:26

Problem 74

Evaluate.
$11 \cdot 33$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:31

Problem 75

Find each product.
$35,900 \times \frac{1}{10^3}$

Brandon Fox
Brandon Fox
Numerade Educator

Problem 75

Evaluate.
$11 \cdot 44$

Check back soon!
02:01

Problem 76

Find each product.
$564,890 \times \frac{1}{10^2}$

Brooke Bussoletti
Brooke Bussoletti
Numerade Educator

Problem 76

Evaluate.
$11 \cdot 55$

Check back soon!
02:01

Problem 77

Find each product.
$90,500 \times 10^4$

Brooke Bussoletti
Brooke Bussoletti
Numerade Educator
00:42

Problem 77

Evaluate.
$3.5+0.251$

Karly Williams
Karly Williams
Numerade Educator
02:04

Problem 78

Copy and complete each flowchart.
FLOWCHART CANT COPY

Zach Steedman
Zach Steedman
Numerade Educator
01:07

Problem 78

Evaluate.
$3.54+0.754$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
02:04

Problem 79

Copy and complete each flowchart.
FLOWCHART CANT COPY

Zach Steedman
Zach Steedman
Numerade Educator
00:42

Problem 79

Evaluate.
$3.5-1.6$

Karly Williams
Karly Williams
Numerade Educator
01:37

Problem 80

On the first Saturday of her new weekend exercise plan, Jen bikes 2 miles to the park, 5 miles around the park on Perimeter Path, and then 2 miles back home. She plans to gradually build her workout by adding one loop on Perimeter Path each Saturday.
a. On which Saturday will Jen ride more than 25 miles?
b. After the first month on her new plan (four Saturdays), what average distance will Jen have ridden each Saturday? Show how you found your answer.
c. How many more miles will Jen ride on the sixth Saturday than on the first Saturday?
d. Jen doesn't want to ride more than 50 miles in a day. After which Saturday will she stop increasing the distance she rides? What will be the distance she rides on that Saturday?

Ashley High
Ashley High
Numerade Educator
00:57

Problem 80

Draw a flowchart to represent the expression $\frac{4 x+8}{2}$. Then use backtracking to find the solution to the equation $\frac{4 x+8}{2}=10$.

Ernest Castorena
Ernest Castorena
Numerade Educator
02:04

Problem 81

Complete each table.
$$
\begin{array}{|l|l|l|l|l|l|l|l|}
\hline \boldsymbol{m} & 0 & 1 & 2 & 3 & 4 & 40 & \\
\hline \mathbf{3 m + 1 0} & & & & & & & 109 \\
\hline
\end{array}
$$

Shaza Hammoud
Shaza Hammoud
Numerade Educator
01:47

Problem 81

Complete each table, and write another expression that gives the same values.
$$
\begin{array}{|l|l|l|l|l|l|l|}
\hline n & 1 & 2 & 3 & 4 & 5 & 100 \\
\hline \frac{n-1}{2} & & \frac{1}{2} & & & & \\
\hline
\end{array}
$$

Yujie Wang
Yujie Wang
College of San Mateo
01:53

Problem 82

Complete each table.
$$
\begin{array}{|l|l|l|l|l|l|l|l|}
\hline \boldsymbol{t} & 1 & 2 & 4 & 8 & 11 & & \\
\hline \mathbf{4} \boldsymbol{t} \mathbf{- 4} & & & & & & 96 & 120 \\
\hline
\end{array}
$$

Julie Silva
Julie Silva
Numerade Educator
00:48

Problem 82

Complete each table, and write another expression that gives the same values.
$$
\begin{array}{|l|l|l|l|l|l|l|}
\hline q & 0 & 1 & 2 & 3 & 4 & 100 \\
\hline \frac{q+8}{2} & & & & & & \\
\hline
\end{array}
$$

Ashley Volpe
Ashley Volpe
Numerade Educator
00:44

Problem 83

Use a protractor to measure the angles on the figure at left. Give your answers to the nearest $5^{\circ}$.

Victor Salazar
Victor Salazar
Numerade Educator
02:40

Problem 84

In June 2002, you could have received about 48.984 Indian rupees for 1 U.S. dollar.
a. How many dollars could you have received in exchange for 100 Indian rupees?
b. How many Indian rupees could you have received in exchange for 100 U.S. dollars?

Debasish Das
Debasish Das
Numerade Educator
02:14

Problem 85

The table shows how long a person born in the given year was expected to live, on average. For example, a boy born in 1950 was expected to live 65.6 years.
TABLE CANT COPY
a. By how many years did the life expectancy of a baby girl rise from 1900 to 2000 ? By how many years did the life expectancy of a baby boy rise in that time?
b. By what percentage did the life expectancy of a baby girl rise from 1900 to 1990 ? By what percentage did the life expectancy of a baby boy rise in that time?
c. What might have contributed to the dramatic rise in life expectancy between 1900 and 2000?
d. Estimate the life expectancies of a baby boy and a baby girl in the year 2010 .

Kristen Karbon
Kristen Karbon
Numerade Educator