8th Grade Packet #3 April 22-May 6 Days 21-30 · 44 Lesson 5 Scientic Notation Curriculum Associates, LLC Copying is not permitted. Guided Practice Practice Lesson 5 Study the example

8th Grade Packet #3

April 22-May 6

Days 21-30

Notes for Exponents & Scientific Notation (p. 1-2)

Day 21- Exponents Review (p. 3-4)

Day 22- I-Ready

Day 23- Lesson 5 (p.5-8)

Day 24- Lesson 6 (p.9-12)

Day 25- Exponents & Scientific Notation Review #1 (p.13-15)

Day 26- Exponents & Scientific Notation Review # 2 (p.16-17)

Day 27- I-Ready

Day 28- Quiz (p.18-20)

Day 29- Notes & Geometry Review #1 (p.21-30)

Day 30- Geometry Review #2 (p.31-36)

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Rules of Exponents

©2017 Lindsay Perro. All rights reserved. www.beyondtheworksheet.com

Product Rule : When multiplying

exponents with the same base, keep the

base and add the powers.

Quotient Rule : When dividing exponents with the same base, keep the base and subtract the

powers.

Power of a Power Rule : To raise a power to a power, multiply the

exponents.

Power of a Product Rule : Each base is raised to the

same power.

Negative Exponent Rule :

A negative exponent causes the number to

be re-written as the reciprocal of the

original number and the exponent

becomes positive.

Zero Exponent Rule :Any number raised to the zero power is equal to one.

xn i xm = xn+mxn

xm= xn−m

(xn )m = xnm

x−n = 1xn(xy)m = xmym

n0 = 1

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Scientific Notation


All About Scientific Notation :

• When a number is written in scientific notation, there is only one non-zero number in front of the decimal. That number is multiplied by an exponent with a base of ten. • If a number written in scientific

notation has a negative exponent, it means the number is less than one but greater than zero. • If a number written in scientific

notation has a positive exponent, it means the number is greater than one.

Multiply & Divide :You can multiply and divide two numbers written in scientific notation. 1. Split the expressions into

constants and powers of ten. 2. Multiply the constants. 3. Multiply the powers of ten

(using the product rule). 4. Write your answer in scientific

notation.

Add & Subtract :You can add and subtract two expressions written in scientific notation. 1. Raise all powers of 10 to

the same exponent by moving the decimal point left or right (changing the power of ten). Move left if you are increasing an exponent and right if you are decreasing it.

2. Add or subtract the constants.

Writing in Scientific Notation :

• Move the decimal the left or right until there is a single digit (not zero) in front of the decimal.

• Count the number of places the decimal was moved. This becomes your exponent.

• If you moved the decimal to the right, the exponent will be negative.

• If you moved the decimal to the left, the exponent will be positive.

• Write the number as x.xx � 10#

(6.4 � 105) (3.2 � 108)

(6.4 � 3.2) (105 � 108)

(20.48) � 1013

20.48 � 1013

2.048 � 1014

6.4 � 105 + 3.2 � 108

0.0064 � 108 + 3.2 � 108

(0.0064 + 3.2) � 108

3.2064 � 108

8WB8-32

2014 University of Utah Middle School Math Project in partnership with the

Utah State Office of Education. Licensed under Creative Commons, cc-by.

8.1f Homework: Properties of Exponents Mixed Practice

Directions: Simplify each expression. Assume that no denominator is equal to zero.

1.

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©Curriculum Associates, LLC Copying is not permitted.44 Lesson 5 Scientific Notation

Guided Practice

Practice

Lesson 5

Study the example below. Then solve problems 19–21.

Example

Write 0.0000408306 in scientific notation.

Look at how you could solve this problem.

In scientific notation, the solution will look like n • 10a. n must be greater than or equal to 1 and less than 10. a must be an integer.

To write 0.0000408306 in scientific notation, first move the decimal point 5 places to the right. Then multiply that number by a power of 10. The exponent in that power of 10 will be 25, which is found by counting the number of places the decimal is moved to the right.

Solution

19 Earth is about 5,974,000,000,000,000,000,000,000 kg. Write this number in scientific notation.

Show your work.

Solution

Pair/ShareWhat is another method you could use to write the number in scientific notation?

Pair/ShareExplain why the procedure used to write a number in scientific notation works.

0.0000408306 5 4.08306 3 1025

The student moved the decimal point the number of places necessary to get a number greater than or equal to 1 and less than 10.

Do you move the decimal point to the right or to the left to write the number in scientific notation?

Writing and Comparing Numbers in Scientific Notation

Day 23

©Curriculum Associates, LLC Copying is not permitted. 45Lesson 5 Scientific Notation

20 Use the information in the table to solve the problem.

Orbiting Body Approximate Distance from the Sun (in miles)

Mercury 36,300,000

Mars 142,000,000

Neptune 2,800,000,000

Pluto 3,670,000,000

Show your work.

Write each distance in scientific notation.

Mercury

Mars

Neptune

Pluto

Neptune is about how many times as far from the Sun as Mars is from the Sun?

Solution:

21 Which is equivalent to 8.03 3 1028?

A 2803,000,000

B 20.0000000803

C 0.0000000803

D 803,000,000

Eva chose D as the correct answer. How did she get that answer?

Pair/ShareHow does writing numbers in scientific notation make numbers easier to work with?

Pair/ShareTalk about the problem and then write your answer together.

Will the solution be a negative number or positive number?

Will the exponent be positive or negative?

Independent Practice

Practice

©Curriculum Associates, LLC Copying is not permitted.46 Lesson 5 Scientific Notation

Lesson 5

Solve the problems.

1 Which of the following expressions is equivalent to 5,710,900?

A 5.7109 3 1026

B 5.7109 3 102

C 5.7109 3 103

D 5.7109 3 106

2 The average distance from Pluto to the Sun is about 6 3 109 kilometers. The average distance from Mars to the Sun is 2 3 108 kilometers. The average distance from Pluto to the Sun is about how many times as great as the average distance from Mars to the Sun?

times

3 Last year a business earned 4.1 3 106 dollars in income. This year the business earned 2.05 3 108 dollars in income. Which best describes how this year’s earnings compare to last year’s earnings?

A This year the business earned about 0.5 times as much as it did last year.

B This year the business earned about 2 times as much as it did last year.

C This year the business earned about 50 times as much as it did last year.

D This year the business earned about 100 times as much as it did last year.

Writing and Comparing Numbers in Scientific Notation

Self Check

©Curriculum Associates, LLC Copying is not permitted. 47Lesson 5 Scientific Notation

Go back and see what you can check off on the Self Check on page 1.

4 Write the following numbers in order from least to greatest.

5 3 1026 29 3 1023

20.0000002 0.00007

Least Greatest

5 Cara was using her calculator to solve a problem. The answer that displayed was 1.6E+12. She knows that she entered all of the numbers correctly. Why did the calculator give the answer it did? What is the answer to Cara’s problem?

6 The length of a city block running north to south in New York City is about 5 3 1022 miles. The distance from New York City to Mumbai, India, is about 7.5 3 103 miles. The distance from New York City to Mumbai is about how many times the length of a New York City north-south block?

Show your work.

Answer

Guided Practice

Practice

©Curriculum Associates, LLC Copying is not permitted.54 Lesson 6 Operations and Scientific Notation

Lesson 6

Study the example below. Then solve problems 17–19.

Example

A hardware factory produces 3.6 3 105 bolts in 2,400 minutes. What is the factory’s rate of production in bolts per minute?

Look at how you could solve this problem.

Solution

Express 2,400 in scientific notation.

The quotient of products equals the product of quotients.

Subtract the exponents to find the quotient of powers.

2,400 5 2.4 3 103

total bolts ·········· total minutes 5 rate in bolts per minute

3.6 3 105 ········ 2.4 3 103 5 3.6 ··· 2.4 3 105

··· 103

5 1.5 3 105 2 3

5 1.5 3 102

The factory produces 1.5 3 102, or 150, bolts per minute.

17 A company spends a total of $64,500,000 on salaries for its workers. If the company has 1.5 3 103 workers, what is the average salary per worker?

Show your work.

Solution

Pair/ShareWould you rather solve this problem with both numbers expressed in standard form or in scientific notation? Explain.

Pair/ShareWhat are the advantages to solving this problem using scientific notation?

Using Operations with Scientific Notation

In this problem you will need to divide numbers expressed in scientific notation.

Which operation will you need to use to solve this problem?

Day 24

©Curriculum Associates, LLC Copying is not permitted. 55Lesson 6 Operations and Scientific Notation

Pair/ShareCompare the stalactite’s rate of growth with a child’s rate of growth.

Pair/ShareTalk about the problem and then write your answer together.

18 Stalactites are cone-shaped formations that hang from the ceilings of underground caverns. Stalactites can grow at the rate of about 0.005 inch per year. At this rate, what is the length of a stalactite that grows for 7.5 3 104 years?

Show your work.

Solution

19 The planet Mercury is about 57,900,000 kilometers from the sun. Pluto is about 1.02 3 102 times farther away from the sun than Mercury. About how many kilometers is Pluto from the sun?

A about 5.91 3 1014 kilometers

B about 4.77 3 109 kilometers

C about 5.91 3 109 kilometers

D about 5.68 3 105 kilometers

Maya chose D as the correct answer. How did she get that answer?

How would you express the distance between Mercury and the sun in scientific notation?

Would it be easier to solve this problem with numbers in scientific notation, fractions, or as they are written?

Independent Practice

Practice

©Curriculum Associates, LLC Copying is not permitted.56 Lesson 6 Operations and Scientific Notation

Lesson 6

Solve the problems.

1 A national restaurant chain has 2.1 3 105 managers. Each manager makes $39,000 per year. How much does the restaurant chain spend on mangers each year?

A 2.49 3 108 dollars

B 8.19 3 109 dollars

C 6 3 109 dollars

D 8.19 3 1020 dollars

2 The Moon takes about 28 days to orbit the Earth, going a distance of about 2.413 3 106 kilometers. About how many kilometers does the Moon travel during one day of its orbit around the Earth?

A 8.6 3 104 km

B 2.8 3 106 km

C 1.16 3 107 km

D 6.8 3 107 km

3 Jackie incorrectly simplified the following expression.

(4 3 1026) 3 3,000

Select each step that shows an error based solely on the previous step.

A Step 1: (4 3 1026)(3 3 103)

B Step 2: (4 3 3)(1026 3 103)

C Step 3: 12 3 1023

D Step 4: 1.2 3 1024

Using Operations with Scientific Notation

Self Check

©Curriculum Associates, LLC Copying is not permitted. 57Lesson 6 Operations and Scientific Notation

Go back and see what you can check off on the Self Check on page 1.

4 A certain type of bug can jump 3.5 3 102 times the length of its body. If one of these bugs is 8 3 1023 meters long, how far can it jump? Write your answer in both scientific notation and in standard form.

Show your work.

Answer

5 Toshi and Owen want to solve this problem:

Earth has a mass of about 5.97 3 1024 kg. Neptune has a mass of about 1.024 3 1026 kg. How many times greater is the mass of Neptune than the mass of Earth?

Toshi says the answer is 1.7 3 101. Owen says the answer is 6.1 3 1050. Who is correct? What mistake did the other student make?

6 Evaluate (7.3 3 106) 3 (2.4 3 107) ··················· (4 3 104)

.

Show your work.

Answer

Name (s) __________________________________ Class__________ Date_________________________

©Exceeding the CORE Question # 1

EXPONENTS & POWERS

READ & UNDERSTAND (Highlight or circle

important keywords.)

Sumpter Middle School has collected a total of 54 ⋅ 73 canned goods for their annual food drive. They plan to donate all of the cans to various food pantries in the city. How many canned goods will they donate?

What do we know? (List the important facts

needed for this problem to be solved.) _________________________________________________________________________________________________________ ___________________________________ What do we want to find out? (Explain in

your own words.) _________________________________________________________________________________________________________ ___________________________________

SOLVE (Answer the problem. Show all work.)

EXPLAIN (State your answer. Give details. Explain what you did and justify your steps.)

________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________

Name (s) __________________________________ Class__________ Date_________________________


EXPONENTS & POWERS



Handy Electronics has decided to give 105 dollars to their sales managers as an end-of-year bonus. If the company has 103 sales managers and the money is divided equally among them, how much will each sales manager receive?



your own words.) _________________________________________________________________________________________________________ ___________________________________


EXPLAIN (State your answer. Give details. Explain what you did and justify your steps.) ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________

Day 25

Name (s) __________________________________ Class__________ Date_________________________


EXPONENTS & POWERS



Naomi and Douglas each have a baseball card collection. Naomi has two thousand baseball cards in her collection. Douglas has (42)3 baseball cards in his collection. Who has more baseball cards?



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________


EXPONENTS & POWERS



Nigel is training for a marathon. He runs 25 miles on Monday and 27 miles on Thursday. How many times farther did Nigel run on Thursday than on Monday?



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________


SCIENTIFIC NOTATION



Savemore National Bank starts the day with 2.81 × 104 dollars in the vault. At the end of the day, the bank has 3.5 × 105 dollars in the vault. How much more money is in the vault at the end of the day than there was in the morning?



your own words.) _________________________________________________________________________________________________________ ___________________________________


EXPLAIN (State your answer. Give details. Explain what you did and justify your steps.)

________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________

Name (s) __________________________________ Class__________ Date_________________________


SCIENTIFIC NOTATION



The table shows the amount of money raised by each region for a charity organization. How much money did the East and West raise together? Region Amount Raised ($)

West 2.38 × 104 South 1.46 × 104

East 6.75 × 103 North 8.65 × 103



your own words.) _________________________________________________________________________________________________________ ___________________________________



8WB8-70



Sample Problem #1

Every day there is an estimated 329,000 smart phones bought in the United States.1 Every day there is an

estimated 12,000 smart phones lost or stolen in the United States.2 Approximately how many times more smart

phones are bought than are lost or stolen.

Sample Problem #2

Change the numbers below into scientific notation.

a. 3,450,000,000

b. 0.00000000455

Change the number given below into standard form.

c. 86.03 10

d. 61.2 10

Sample Problem #3

Perform the indicated operation for each problem below.

a. 8 93.13 10 2.9 10

b. 4 52.54 10 3.2 10

c. 6 8(3 10 )(5.6 10 )

d.

8

2

1.0004 10

7.2 10

Sample Problem #4

Fill in the blank with a unit of appropriate size from the column to the right.

a. The mass of trash produced by New York City in one day is 71.2 10

__________________.

kilograms

nanograms

grams

b. The period of the sun’s orbit around the galaxy is 82.4 10 ______________.

seconds

hours

years

c. The area of the Earth’s land surface is 81.49 10 __________________.

millimeters2

meters2

kilometers2

1-http://appleinsider.com/articles/14/02/20/apples-iphone-led-2013-us-consumer-smartphone-sales-with-45-share---npd,

http://www.latimes.com/business/technology/la-fi-tn-45-million-smartphones-lost-stolen-2013-20140417-story.html,

http://techcrunch.com/2013/09/19/gartner-102b-app-store-downloads-globally-in-2013-26b-in-sales-17-from-in-app-purchases/

Day 26

8WB8-71



Sample Problem #5

a. A calculator gives you an answer of 3.023E , write this number in scientific notation and standard

form.

b. A calculator give an you answer of , write this number in scientific notation and standard

form.

Sample Problem #6

In the year 2013 the U.S. mint produced 92.112 10 dimes. a. Estimate the value of this money?

b. Every second 175 cups of coffee are bought at America’s most popular coffee shop.2 The average cup of

coffee at this particular shop costs $1.85. At this rate how long will it take for America to spend the 211

million dollars worth of dimes produced in 2013 on coffee at this shop? Express your answer using

appropriate units of time.

2-http://www.boston.com/business/articles/2011/09/17/starbucks_looks_for_way_to_encourage_paper_cup_recycling/

8th Unit 8 Exponents & Sci Notation Page 1 / 3

8th Unit 8 Exponents & Sci Notation [3669346] Student

Class

Date

1. In the expressions, x and y represent positive integers.

expression one: 2 • 10x

expression two: 4 • 10x + y

The value of expression two is 20,000 times greater than the value of

expression one. What is the value of y?

A. 3

B. 4 C. 5 D. 6

2.

Which expression is equivalent to ?

A. 6 × 103

B. 6 × 104 C. 6 × 1011 D. 6 × 1012

3. If 4x • 4x − 3 • 45 − x = 48, what is the value of x?

A. 0

B. 2 C. 6 D. 10

4. The speed of light is about 6.7 × 108 miles per hour. The Earth is about 2.56 × 1013 miles away from the star, Alpha Centauri. Approximately how many

hours will it take for light to travel from the star Alpha Centauri to Earth?

A. 3.82 × 104 hours

B. 3.82 × 105 hours

C. 3.82 × 1020 hours

D. 3.82 × 1021 hours

5. The circumference of Saturn is about 379,000 kilometers. The circumference

of the Earth is about 4 × 104 kilometers. Approximately how many times as large is Saturn’s circumference than Earth’s circumference?

A. 9.5 times as large

B. 11 times as large

C. 95 times as large

D. 110 times as large

Day 28


6. What is the value of the expression below?

A.

B.

C.

D.

7. The mass of Earth is about 5.972 × 1024 kg. The mass of Mercury is about

1.81 × 101 times lighter than the mass of Earth. What is the approximate mass of Mercury?

A. 1.08 × 1026 kg

B. 1.08 × 1024 kg

C. 3.30 × 1024 kg

D. 3.30 × 1023 kg

8. What is 0.00000000782 in scientific notation?

A. 7.82 × 10–9

B. 7.82 × 10–8

C. 7.82 × 108

D. 7.82 × 109

9. A penny has a diameter of 0.75 inches. If 1.0 × 104 pennies were placed in a

line, how long would the line be?

A. 7.5 × 103 inches

B. 7.5 × 104 inches

C. 7.5 × 105 inches

D. 7.5 × 106 inches

10. The population of New York is about 8.2 × 106 people. The population of

Berkeley is about 1.1 × 105. About how many times larger is the population

of New York than the population of Berkeley?

A. 15 times larger

B. 70 times larger

C. 75 times larger

D. 150 times larger

11. What is the value of 7–4 × 73?

A.

B. C.

D.


12. Which expression is equivalent to 42 ÷ (42)–3?

A. 4–4

B. 4–3 C. 44 D. 48

13. Which expression is equivalent to ?

A. –84

B. –25 C. 2–5 D. 8–4

14. What is the value of

A.

B.

C. 20 D. 144

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Congruency & Similarity


Transformations : • Translations : • Vertical or horizontal slide

• Reflections : • Vertical or horizontal flip

• Rotations : • 90o, 180o or 270o clockwise or

counter-clockwise rotation around a point.

• Dilations : • A stretch or shrink using a given

scale factor.

Ordered Pairs & Transformations :

Reflections :• x-axis (x, y) to (x, –y)• y-axis (x, y) to (–x, y)• y = x (x, y) to (y, x)Rotations :• 90o counterclockwise (x, y) to (–y, x)• 180o counterclockwise (x, y) to (–x, –y)Translations :• (x, y) to (x + a, y + b) Dilations :• (x, y) to (kx, ky)

Area and Perimeter of Similar Figures :

• If two polygons are similar with lengths

of the corresponding sides in the ratio

a : b, then the ratio of their perimeters

is a : b.

• If two polygons are similar with lengths

of the corresponding sides in the ratio

a : b, then the ratio of their areas is a2

: b2.

Similar and Congruent :

Similar Figures :Similar figures have the same angle measurements, but are not the same size.

Congruent Figures :Congruent figures have the same angle measurements and the same side lengths. They are identical.

Parallel Lines Cut By A Transversal :

1 2 3 45 6 7 8

Parallel Lines Two lines that will never cross.

Transversal A line that cuts through two parallel lines.

Supplementary Angles

Angles with a sum of 180o. Examples : <7 and <8, <1 and <2

Interior anglesAngles along the transversal inside the parallel lines. Examples : Angles 2, 3, 6 and 7

Alternate anglesAngles on opposite sides of the transversal. Examples : <2 and <7 are alternate interior angles.

Corresponding Angles

Two angles that are in the same place, on different parallel lines. For example, <2 and <4 are corresponding angles.

Vertical anglesVertical angles share a vertex but not a side. Example : <3 and <8 are vertical angles.

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Translations


Key Points :• When you translate an object, you slide it.

• An image that has been translated will be congruent to the original image.

• Images can be translated in two directions : left/right or up/down.

• A diagonal translation is a combination of a left/right and an up/down translation.

The given shape has

been translated four units

down.

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Reflections


Key Points :• When you reflect an object, you flip it across an axis. • An image that has been reflected will be congruent

to the original image. • Images can be reflected in two directions : vertically

or horizontally. • Images can be reflected over an axis (x-axis or

y-axis) or over a certain point (x = 4 or y = -2).

The given shape has

been reflected across the

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Rotations


Key Points :• When you rotate an object, you turn it around a point. • An image that has been rotated will be congruent to

the original image. • Images can be rotated in three different ways

clockwise or counterclockwise : 90o, 180o and 270o.• Images can be rotated around the origin or a given

point.

The given shape has

been rotated 90o

clockwise around the

origin.

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Dilations


Key Points :• A dilation is when you stretch or shrink an image on the

coordinate plane. • In order to dilate an image, you need a scale factor, or the

ratio of the size of the image to the size of the pre-image.

• To dilate a point, multiply the coordinates of the point by the scale factor to get the coordinates of the new point.

• To dilate a shape, multiply the coordinates of each vertex of the shape by the scale factor to the get coordinates for each

vertex in the new shape.

The given shape has

been dilated using

a scale factor of ½.

(0, 2) • ½ = (0, 1)(-4, 2) • ½ = (-2, 1)(-4, 4) • ½ = (-2, 2)

Missing Angles :• The sum of the interior angles

in a polygon can be found by multiplying 180 by the number

of sides, minus two, or 180(s –

2). • The sum of the exterior angles

of a polygon is always 360o.• The measurement of an

exterior angle in a regular polygon can be found by

dividing 360 by the number of sides the polygon has.

Missing Dimensions :

Finding the height : 1.Plug what you know into the

formula.• If given the diameter, find the

radius first. 2. Work backwards to solve for h.

Round to the nearest hundredth.• Use the pi symbol on your

calculator or 3.14 if you are solving by hand.

3. Check your answer.

Finding the radius: 1. Plug what you know into the

formula.2. Work backwards to solve for r.

Round to the nearest hundredth.• Use the pi symbol on your

calculator or 3.14 if you are solving by hand.

3. Check your answer.Volume Formulas :• Sphere

• Cylinder

• Cone

The Pythagorean Theorem :

• The Pythagorean Theorem is :

• The Distance Formula is :

(x2 − x1)2 +( y2 − y1)2

a2 +b2 = c2V = πr2h

V = 13πr2h

V = 43πr

3

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Geometry


The Pythagorean Theorem is :

The Distance Formula is :

(x2 − x1)2 +( y2 − y1)2

a2 +b2 = c2

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The Pythagorean Theorem


The Pythagorean Theorem states that in a right triangle, the square

of the long side (hypotenuse) is equal to the sum of the squares of the other two sides (the

legs).

A Missing Leg (a or b):• It doesn’t matter if you are missing a

or b when using the formula.

• For example : The hypotenuse

is 34 cm and one leg is 20 cm.

What is the measure of the

missing leg?

Missing Hypotenuse (c) :• For example :

A right triangle has

two legs that are 6 inches long. Find

the length of the missing side.

62 + 62 = c2

36 + 36 = c2

72 = c2

72 = c2

8.49 ≈ c

a2 + 202 = 342

a2 + 400 = 1,156a2 = 756

a2 = 756a ≈ 27.5

The Coordinate Plane : • To determine side lengths (or just the

distance between any two given

points) on the coordinate plane, use the distance formula.

• For example : Find the distance

from A to C.

A B

C

(2,6)(7,2)

(7 − 2)2 + (2 − 6)2

(5)2 + (−4)2

25 +16

416.4

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Documents

8th Grade Packet #3 April 22-May 6 Days 21-30 · 44 Lesson 5 Scientic Notation Curriculum Associates, LLC Copying is not permitted. Guided Practice Practice Lesson 5 Study the example