00 - Formulas

Name Date

Grade 5 22 Chapter 6

Copyright

Macm

illan/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

63

Complete the table. Write an equation to show the relationship. Tell what each variable in the equation represents.

EnrichFunctions

1. Pattern Number 1 2 3 4 5Picture

Number of Dots 3 5 7 9

2. Pattern Number 1 2 3 4Picture

Number of Sections 2 4


Number of Dots 5 7


Number of Squares 1 4

NAME ________________________________________ DATE _____________ PERIOD _____

PDF Pass

Cop

yrig

ht

G

len

coe/

McG

raw

-Hil

l, a

divi

sion

of T

he

McG

raw

-Hil

l C

ompa

nie

s, I

nc.

Chapter 8 123 Course 1

8-1 ReteachFunction Rules

Use words and symbols to describe the value of each term as a function of its position. Then find the value of the tenth term in the sequence.

Position 1 2 3 4 nValue of Term 4 8 12 16

Study the relationship between each position and Position Value of term1 4 = 42 4 = 83 4 = 124 4 = 16n 4 = 4n

the value of its term.

Notice that the value of each term is 4 times its position number. So, the value of the term in position n is 4n.

To find the value of the tenth term, replace n with 10 in the algebraic expression 4n. Since 4 10 = 40, the value of the tenth term in the sequence is 40.

Exercises


1. Position 3 4 5 6 nValue of Term 1 2 3 4



A sequence is a list of numbers in a specific order. Each number in the sequence is called a term. An arithmetic sequence is a sequence in which each term is found by adding the same number to the previous term.

Example

D

119_138_RSC1C8_892760.indd 123119_138_RSC1C8_892760.indd 123 3/9/09 2:35:43 PM3/9/09 2:35:43 PM

NAME ________________________________________ DATE _____________ PERIOD _____

PDF Pass

Cop

yrig

ht

G

len

coe/

McG

raw

-Hil

l, a

divi

sion

of T

he

McG

raw

-Hil

l C

ompa

nie

s, I

nc.


8-1 ReteachFunction TablesC

A function rule describes the relationship between the input and output of a function. The inputs and outputs can be organized in a function table.

Complete the function table.

Input (x) x - 3 Output (y)9 9 - 38 8 - 36 6 - 3

The function rule is n - 3. Subtract 3 from each input.

Input Output

9 - 3 6

8 - 3 5

6 - 3 3

Find the input for the function table.

Input (x) 4x Output (y)04

8

Work backward to find the input. Since the rule is 4x, divide each output by 4.

The inputs are 0, 1, and 2.

Exercises

Complete each function table.

1. Input (x) 2x Output (y)0

2

4

2. Input (x) 4 + x Output (y)0

1

4

Find the input for each function table.

3. Input (x) x + 2 Output (y)1 + 2 3

2 + 2 4

5 + 2 7

4. Input (x) x 2 Output (y)2 2 1

6 2 3

10 2 5

Example 1

Input (x) x - 3 Output (y)9 9 - 3 68 8 - 3 56 6 - 3 3

Example 2


NAME ________________________________________ DATE _____________ PERIOD _____

1st Pass

Copyrigh

t G

lencoe/M

cGraw

-Hill, a division

of Th

e McG

raw-H

ill Com

panies, In

c.


8-1AC

Skills PracticeFunction Tables

Complete each function table.

1. Input (x) x + 3 Output (y)0

2

4

2. Input (x) 3x + 1 Output (y)0

1

2

3. Input (x) 2x - 1 Output (y)7

5

4

4. Input (x) x 3 Output (y)12

9

6

5. If a function rule is 2x - 3, what is the output for the input 3?

6. If a function rule is 4 - x, what is the output for the input 2?

Find the input for each function table.

7. Input (x) x - 3 Output (y)10 - 3 7

7 - 3 4

4 - 3 1

8. Input (x) x + 9 Output (y)3 + 9 12

6 + 9 15

8 + 9 17

9. Input (x) 5x Output (y)5(0) 0

5(2) 10

5(3) 15

10. Input (x) x 2 Output (y)4 2 2

6 2 3

12 2 6

11. Input (x) 2x + 2 Output (y)2(1) + 2 4

2(2) + 2 6

2(3) + 2 8

12. Input (x) 3x - 1 Output (y)3(5) - 1 14

3(3) - 1 8

3(2) - 1 5


NAME ________________________________________ DATE _____________ PERIOD _____

1st Pass

Copyrigh

t G

lencoe/M

cGraw

-Hill, a division

of Th

e McG

raw-H

ill Com

panies, In

c.


8-1


1. Position 5 6 7 8 n

Value of Term 2 3 4 5







Find a rule for each function table.

5. Input (x) Output (y)5 0

6 1

7 2

8 3

x


4 16

6 18

8 20

x


5 1

6 2

7 3

x


2 22

3 33

4 44

x

Skills PracticeFunction RulesD


Using FormulasA formula is an equation that can be used to solve certain kinds of problems.Formulas often have algebraic expressions. Here are some common formulasused to solve geometry problems. The variables in geometric formulasrepresent dimensions of the geometric figures.

Area (A) Volume (V)of a rectangle: A w of a rectangular prism: V w hof a square: A s2

of a triangle: A 12bh Perimeter (P)of a square: P 4s of a rectangle: P 2(w )

b base h height length s side w width

Write the formula that would be used to solve each problem.

1. Jack wants to put a fence around his garden to keep rabbits out. Jacksgarden is square shape. Which formula can Jack use to find how muchfence he needs to buy?

2. Dianes mother will replace the carpeting in their living room. The livingroom is rectangular in shape. Which formula can Dianes mother use todetermine how much carpeting she will need to order for her living room?

3. Victor is cleaning his aquarium, which is shaped like a rectangular prism.After he empties the aquarium and cleans the sides, he will refill theaquarium. Which formula can Victor use to determine how much water hewill put back in the aquarium?

4. Joann is making a triangular flag for a school project. Which formula canshe use to determine how much material she needs to buy to make the flag?

Solve each problem.

5. A tablecloth is 8 feet long and 5 feet wide. What is the area of thetablecloth?

6. Jessica wants to frame a square picture that has sides of 6 inches. Howmany inches of wood will she need to make the frame?

7. How many cubic centimeters of packing peanuts will fit in a cardboard boxthat is 9 centimeters long, 8 centimeters wide, and 3 centimeters high?

8. Joaquin is painting a mural on one wall of the schools gymnasium. Part ofthe mural is a triangle with a base of 20 ft and a height of 8 feet. What isthe area of the triangle?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment

Chapter 1 40 Glencoe MAC1

Copyright G

lencoe/McG

raw

-Hill, a division of The M

cGra

w-H

ill Companies

, Inc.

1-5


Less

on

78

Copy

right

G

lenc

oe/M

cGra

w-H

ill, a

divi

sion

of T

he M

cGra

w-H

ill Co

mpa

nies

, In

c.

Study Guide and InterventionSimple Interest

Exercises

Find the simple interest earned in a savings account where $136 isdeposited for 2 years if the interest rate is 7.5% per year.

I prt Formula for simple interest

I 136 0.075 2 Replace p with $136, r with 0.075, and t with 2.I 20.40 Simplify.

The simple interest earned is $20.40.

Find the simple interest for $600 invested at 8.5% for 6 months.

6 months 162

or 0.5 year Write the time as years.

I prt Formula for simple interest

I 600 0.085 0.5 p $600, r 0.085, t 0.5I 25.50 Simplify.

The simple interest is $25.50.

Find the interest earned to the nearest cent for each principal,interest rate, and time.

1. $300, 5%, 2 years 2. $650, 8%, 3 years

3. $575, 4.5%, 4 years 4. $735, 7%, 212 years

5. $1,665, 6.75%, 3 years 6. $2,105, 11%, 134 years

7. $903, 8.75%, 18 months 8. $4,275, 19%, 3 months

Simple interest is the amount of money paid or earned for the use of money. To find simple interest I,use the formula I prt. Principal p is the amount of money deposited or invested. Rate r is the annualinterest rate written as a decimal. Time t is the amount of time the money is invested in years.

Example 1

Example 2

NAME ________________________________________ DATE ______________ PERIOD _____

7-8

040_059_CRM07_881047 11/2/07 8:44 AM Page 53 epg ju107:MHGL111:Quark%0:Course 2:Application Files:Chapter 7:

PDF Proof

NAME ________________________________________ DATE _____________ PERIOD _____

1st pass

Cop

yrig

ht

G

len

coe/

McG

raw

-Hil

l, a

divi

sion

of T

he

McG

raw

-Hil

l C

ompa

nie

s, I

nc.


Homework PracticeSimple Interest

Find the simple interest earned to the nearest cent for each principal, interest rate, and time.

1. $750, 7%, 3 years 2. $1,200, 3.5%, 2 years 3. $450, 5%, 4 months

4. $1,000, 2%, 9 months 5. $530, 6%, 1 year 6. $600, 8%, 1 month

Find the simple interest paid to the nearest cent for each loan, interest rate, and time.

7. $668, 5%, 2 years 8. $720, 4.25%, 3 months 9. $2,500, 6.9%, 6 months

10. $500, 12%, 18 months 11. $300, 9%, 3 years 12. $2,000, 20%, 1 year

13. ELECTRONICS Rita charged $126 for a DVD player at an interest rate of 15.9%. How much will Rita have to pay after 2 months if she makes no payments?

14. VACATION The average cost for a vacation is $1,050. If a family borrows money for the vacation at an interest rate of 11.9% for 6 months, what is the total cost of the vacation including the interest on the loan?

15. INVESTMENTS Serena has $2,500 to invest in a CD (certificate of deposit).

a. If Serena invests the $2,500 in the CD that yields 4% interest, what will the CD be worth after 2 years?

b. Serena would like to have $3,000 altogether. If the interest rate is 5%, in how many years will she have $3,000?

c. Suppose Serena invests the $2,500 for 3 years and earns $255. What was the rate of interest?

Get ConnectedGet Connected For more examples, go to glencoe.com.

6-3E

079_096_HWPSC2_892763.indd 95079_096_HWPSC2_892763.indd 95 2/3/10 6:45:06 PM2/3/10 6:45:06 PM

NAME ________________________________________ DATE _____________ PERIOD _____

1st pass

Copyrigh

t G

lencoe/M

cGraw

-Hill, a division

of Th

e McG

raw-H

ill Com

panies, In

c.


Problem Solving PracticeSimple Interest

1. SAVINGS ACCOUNT How much interest will Hannah earn in 4 years if she deposits $630 in a savings account at 6.5% simple interest?

2. INVESTMENTS Terry invested $2,200 in the stock market for 2 years. If the investment earned 12%, how much money did Terry earn in 2 years?

3. SAVINGS ACCOUNT Malik deposited $1,050 in a savings account, and it earned $241.50 in simple interest after four years. Find the interest rate on Maliks savings account.

4. INHERITANCE Kelli Raes inheritance from her great-grandmother was $220,000 after taxes. If Kelli Rae invests this money in a savings account that earns $18,260 in simple interest every year, what is the interest rate on her account?

5. RETIREMENT Mr. Pham has $410,000 in a retirement account that earns 3.85% simple interest each year. Find the amount earned each year by this investment.

6. COLLEGE FUND When Melissa was born, her parents put $8,000 into a college fund account that earned 9% simple interest. Find the total amount in the account after 18 years.

7. LOTTERY Raj won $900,000 in a regional lottery. After paying $350,000 in taxes, he invested the remaining money in a savings account at 4.25% simple interest. How much money is in the account if Raj makes no deposits or withdrawals for two years?

8. SAVINGS Mona opened a savings account with a $500 deposit and a simple interest rate of 5.6%. If there were no deposits or withdrawals, how much money is in the account after 8 1

2 years?

6-3E

079_096_HWPSC2_892763.indd 96079_096_HWPSC2_892763.indd 96 2/3/10 6:45:10 PM2/3/10 6:45:10 PM

NAME ______________________________________________ DATE ____________ PERIOD _____

11-2 Enrichment

Chapter 11 16 Glencoe Pre-Algebra

Copyright G

lencoe/McG

raw-Hill, a division of The McG

raw-Hill Companies, Inc.

DensityDensity is the mass per unit of volume of a substance and is an important scientific

concept. The formula for determining density is Density .MassVolume

The mass of an object is 27g and its volume is 130 cm3. What is itsdensity?

Density

Density

Density = 0.21 g/cm3

27 g130 cm3

MassVolume

1. If the base of a prism is 4 centimeters by 2 centimeters and the prism has a height of 10 centimeters, what is the volume?

2. If you know the density of the prism from Exercise 1 is 8.75 g/cm3, what is its mass?

3. Use the density formula to complete the table.

For Exercises 4-6, use the table at the right that lists the density for some common substances.

4. What is the volume of a cube of ice with a mass of 15 g?

5. A prism has a mass of 291.6 g. Its base measures 3 centimeters by 3 centimeters and its height is 12 centimeters. Assuming it is one of the substances in the table, what substance is it?

6. A cylinder has a radius of 6 centimeters and a height of 8 centimeters. If the cylinder islead, what is its mass? Use 3.14 to approximate the value of .

Example

Exercises

Volume DensityMass (g) (cm3) (g/cm3)

45 8.9

23 158

3462 6.97

Substance Density (g/cm3)

Lead 11.3

Gold 19.3

Aluminum 2.7

Ice 0.93

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


Copy

right

G

lenc

oe/M

cGra

w-H

ill, a

divi

sion

of T

he M

cGra

w-H

ill Co

mpa

nies

, In

c.

7-8

Exercises

Example

Taking an Interest

When interest is paid on both the amount of the deposit and any interestalready earned, interest is said to be compounded. You can use the formulabelow to find out how much money is in an account for which interest iscompounded.

A P(1 r)n

In the formula, P represents the principal, or amount deposited, r representsthe rate applied each time interest is paid, n represents the number of timesinterest is given, and A represents the amount in the account.

A customer deposited $1,500 in an account that earns 8% per year. If interest is compounded and earned semiannually, how

much is in the account after 1 year?

Use the formula A P(1 r)n.

Since interest is earned semiannually, r 8 2 or 4% and n 2.

A 1,500(1 0.04)2 Use a calculator.

1,622.40

After 1 year, there is $1,622.40 in the account.

Use the compound interest formula and a calculator to find the value of each of these investments. Round each answer to the nearest cent.

1. $2,500 invested for 1 year at 6% interestcompounded semiannually

2. $3,600 invested for 2 years at 7% interestcompounded semiannually

3. $1,000 invested for 5 years at 8% interestcompounded annually

4. $2,000 invested for 6 years at 12% interest compounded quarterly

5. $4,800 invested for 10 years at 9% interestcompounded annually

6. $10,000 invested for 15 years at 7.5% interestcompounded semiannually

Less

on

78

040_059_CRM07_881047 11/2/07 8:44 AM Page 57 epg ju107:MHGL111:Quark%0:Course 2:Application Files:Chapter 7:

PDF Proof

Example

What Day Was It?To find the day of the week on which a date occurred, follow these steps.

Use the formula s d 2m 3(m5 1) y 4y 10y0 40y0 2where s sum,

d day of the month, using whole numbers from 1 to 31,m month, where March 3, April 4, and so on, up to December 12; then January 13 and February 14, and y year except for dates in January or February when the previous year is used.

Evaluate expressions inside the special brackets [ ] by dividing, then discarding theremainder and using only the whole number part of the quotient.

After finding the value of s, divide s by 7 and note the remainder.

The remainder 0 represents Saturday, 1 represents Sunday, 2 represents Monday, and so on to 6 represents Friday.

On December 7, 1941, Pearl Harbor was bombed. What day of theweek was that?

Let d 7, m 12, and y 1941.

s d 2m 3(m5 1) y 4y 10y0 40y0 2

s 7 2(12) 3(125 1) 1941 19441 1190401 1490401 2

s 7 24 359 1941 19441 1190401 1490401 2s 7 24 7 1941 485 19 4 2

s 2451

Now divide s by 7. 2451 7 305 R1

Since the remainder is 1, December 7, 1941, was a Sunday.

Use the formula to solve each problem.

1. Verify todays date.

2. What will be the day of the week for April 13, 2012?

3. On what day of the week was the signing of the Declaration of Independence, July 4, 1776?

4. On what day of the week were you born?

Exercises

Copyright G

lencoe/McG

raw-Hill, a division of The McG

raw-Hill Companies, Inc.

Enrichment

Chapter 3 10 Glencoe Pre-Algebra

NAME ______________________________________________ DATE ____________ PERIOD _____

3-13-1

Chapter 10 39 Glencoe MAC 3

EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____

Less

on

10

5

10-5Co

pyrig

ht

Gle

ncoe

/McG

raw

-Hi l l ,

a d

ivisio

n of

The

McG

raw

-Hi l l

Com

pani

es, In

c.

SCIENTIFIC PRINCIPLE

1. Law of the LeverA lever will balance if the mass ofobject 1 times its distance fromthe fulcrum equals the mass of object 2 times its distance from the fulcrum.

2. Newtons Second Law of MotionThe acceleration on an object equalsthe applied force divided by the objectsmass.

3. Ohms LawThe amount of current in an electricalcircuit equals the voltage divided by theresistance.

4. Boyles LawFor a gas at a constant temperature,the product of the pressure and thevolume remains constant.

5. Law of Universal GravitationTo compute the force of gravity betweentwo objects, multiply their masses bythe gravitational constant and thendivide by the square of the distancebetween the objects.

EQUATION AND VARIABLES

P1V1 P2V2

pressure at first time

volume at first time

pressure at second time

volume at second time

I RV

voltage

resistance

current

A mF

applied force

mass of object

acceleration

F G

mass of first object

mass of second object

distance between objects

gravitational constant

force of gravity

m1d1 m2d2

mass of first object

distance of first object from fulcrum

mass of second object

distance of second object from fulcrum

m1m2d2

Famous Scientific EquationsMany important laws or principles in physical science are described byequations. You may have already studied some of the equations on this page,or you may learn about them in future science classes.

Match each statement with its equation. Then write the variables forthe quantities listed.

007-051-CRM10-874090 5/10/06 1:05 PM Page 39

Documents

00 - Formulas