use the distributive property to rewrite the expression. answer 56–28a answer 81y+45x – 1. ( )...
TRANSCRIPT
Use the distributive property to rewrite the expression.
ANSWER 56–28a
ANSWER 81y+45x–
1. ( )8–4a7
2. 9– ( )9y–5x
ANSWER 32 n–
3. Jill has enough money for a total of 32 CDs and DVDs. If n is the number of CDs, write an expression for the number of DVDs she can buy.
Warm Up Algebraic Expressions and Models
Example 1 Evaluate Powers
a. 24 2•2 2•2•= ( )–
b. ) 4( 2– • • ( 2– )( 2– )= • ( 2– )( 2– )
16= –
–
= 16
ANSWER 9
ANSWER 64
ANSWER 2
Evaluate the power.
Checkpoint
1. 43
2. ) 2( 3–
3. 33–
4. 21
ANSWER 27–
Evaluate Powers
Example 2 Use Order of Operations
436 ÷ ( 1–• 4+ )2 Add within parentheses.= 436 ÷ • 32
Evaluate power.= 436 ÷ • 9
Divide.= 9 • 9
= 81 Multiply.
Example 3 Evaluate an Algebraic Expression
Evaluate when .( )5+x2 7x– 4x =
SOLUTION
Substitute 4 for x.=( )5+x2 7x– ( )5+42 – (47 )
= – (47 )(92 ) Add within parentheses.
2818= Multiply.–
= Subtract.10–
Example 4 Evaluate an Algebraic Expression
Evaluate when .4p2 – (2p )9– p = 3–
= –(94 ) [ ](2 3– ) 9– Evaluate power.
36= – ( 15– ) Subtract within parentheses.
51= Add the opposite.
36= Multiply.– [ ]6– 9–
SOLUTION
Substitute 3 for p.= (44p2 – (2p )9– 3– )2 [ ](2 3– ) 9–– –
5. 738 +– ANSWER 12
ANSWER 23
Evaluate the expression.
Checkpoint
6. 2– 62 +÷ 4•
ANSWER 8–7. ( 5734 – – )2
ANSWER 15
Evaluate the expression for the given value of the variable.
8. 3– + ( 1y6 + ) when 2y =
Evaluate Expressions
Checkpoint
9. when2w2– 118w ++ w = 5– ANSWER 79–
Evaluate Expressions
Evaluate the expression for the given value of the variable.
Write and Evaluate a Mathematical ModelExample 5
Shopping You have $40 and are buying some DVDs that cost $12 each. Write an expression that shows how much money you have left after buying d DVDs. Evaluate the expression when d 2 and d 3.= =
SOLUTION
VERBALMODEL
Originalamount
Price perDVD
Number ofDVDs bought
– •
Write and Evaluate a Mathematical ModelExample 5
LABELS
ALGEBRAICMODEL
12d–40
Original amount 40= (dollars)
Price per DVD 12= (dollars per DVD)
Number of DVDs bought d= (DVDs)
ANSWER
12–40If you buy 2 DVDs, you will have $16 left.If you buy 3 DVDs, you will have $4 left.12–40 ( )3
( )2 ==
Write and Evaluate a Mathematical ModelExample 6
Mexico For a trip to Mexico you need to exchange some U.S. dollars for Mexican pesos. The exchange rate is 11 pesos per dollar. You already have 110 pesos left from a previous trip. Write an expression that shows how many pesos you will have after exchanging d dollars. Evaluate the expression for d 250.=
SOLUTION
VERBALMODEL
Pesosper dollar
+•Dollars
exchangedPesos you
already have
Write and Evaluate a Mathematical ModelExample 6
LABELS
Number of dollars being exchanged d=
(dollars)
Number of pesos per dollar 11=
(pesos per dollar)
Number of pesos you already have 110=
(pesos)
ALGEBRAICMODEL 11011d +
ANSWER
When you exchange $250, you will have
2860 pesos.=
11011 +( )250
10. Repeat Example 5 if you have $60 to spend and each DVD costs $16.
Checkpoint
ANSWER
If you buy 2 DVDs, you will have $28 left. If you buy 3 DVDs, you will have $12 left.
Use a Mathematical Model