Say It With Symbols Answers

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1 Investigation Additional Practice. p w and p ( w). a. p w () () b. p (w) w and p w. (.) m. A w Q Properties used for items will var, but all include the Distributive Propert.. Possible answer: 7 and (). Possible answer: and ( ) 7. Possible answer: and. Possible answer: and ( ). a. (Figure ) b. The numbers in each column are equal. c. Students ma remark that the epressions seem to be equivalent. If the recognize the epressions are linear, the can sa that the are equivalent. d. Using the Distributive and Commutative Properties, each epression is equivalent to. Since all the epressions are linear and two values for give the same value of, the epressions are equivalent (an linear epression containing the same two points as another is equivalent to that epression).. a. Equations: ( ) and Figure Epression ( ) ( ) Value when: The tables are the same: Graph of and ( ) ( ) and b. ( ) and are equivalent, since the tables and graphs for these equations have the same pattern. c. Using the Distributive Propert on the first epression ( ), ou get, which is the same as the other epression. So the epressions ( ) and are equivalent.

2 . a. Equations: ( ) and The table for ( ) is the same as the table given in part (a) of Eercise : ( ) The graph for ( ) is the same as the graph in a. The graph for is given below: Graph of b. ( ) and are not equivalent, since the have different tables and graphs. c. If ou use the Distributive Propert on the first epression ( ), ou get, which is not equivalent to the epression.. a. Equations: and ( ) The tables are the same: and ( ) b. and ( ) are equivalent, since the tables and graphs for these equations have the same pattern. c. Using the Distributive Propert on the second epression ( ) gives the equivalent epression. 7 7 Graph of and ( )

3 . a. 7 and, 7, b...7 and..... a. No; The epressions ( ) and are not equivalent: and b. Yes; The epressions and ( ) are equivalent. c. No; The epressions and ( ) are not equivalent: and d. Yes; The epressions 7 and are equivalent.. a. The sketch contains trapezoids each having bases of s and s and triangles having a base and height of. So Dave s epression is s (s ) Q R Q R. c. ( )( ) and.7... a. The epression is equivalent to. b. The epression ( ) is equivalent to. c. The epression ( ) is equivalent to. d. The epression ( ) is equivalent to ;So epressions a. and c. are equivalent.. b. This epression does simplif to s ; however, students ma need help with simplifing. You ma suggest for students to write out the repeated additions involving fractions. 7. a... b. b c.. a. (m ) b. ( ) c. ( ). Equivalent to : ( ), ( ) ( ) Equivalent to : ( ) ( ), (7 ) ( ) Skill: Writing Equivalent Epressions.. b.. d. h a. d. k. h. (v ). (g ). (h ). (e ) 7. ( ). (.m.).. m m

4 ... ( )?.? ( ) 7. ( )?. ( )? Skill: perations With Rational Numbers Investigation Additional Practice a. $ b. $ c. Possible answers: The will need to sell more than, items, because the equation shows that P is N minus a number. r, the must sell,7 items to make a profit of at least $,. d. Possible answer: P.N.. a. (.) b. () c. Possible answer: P (), P,and P ( ) d. Possible answer: P () ()() P ( ) ()( ) () =. a. () () (7) meters b. () (.) () meters c. Possible answer: P Q S T, P (Q T) S,and P (Q T S) d. Answers will var. e. P (Q T) S Q T S Q S T P (Q T S) Q T S Q S T. a. linear; It can be simplified to N.P, which is a linear equation of the form m b. b. cans c. people. a. $. b. plaers. a. P ( ), which is equivalent to P b. To break even, the profit would be zero. B guessing and checking or using a graphing calculator to make a table, there is a profit of zero at. videos must be sold to make a profit of $. c. For the break-even, a table can be used b looking for the corresponding -value when P. In the graphing calculator, the P is represented b, the dependent variable. A graph can be used b tracing the line and finding the corresponding -value for the point which crosses the -ais (i.e., the point with a -value of ). For the $ profit amount, using a table ou can look for the -value that corresponds with a -value of. Using a graph, ou trace the line until ou reach the point with a -value of, and look at what the value for is at this point.

5 . Equivalent; ( ) using the Distributive Propert.. Not equivalent; The related equations, and,have different slopes.. Not equivalent; ( 7) 7.. Equivalent; ( ) (). 7. Equivalent; () () ( ).. Not equivalent; ( ) 7.. Equivalent; 7 7 (b the Commutative Propert of Addition).. Not equivalent; When, equals and equals.. Equivalent; ( ) and ( ) or b using the Commutative Propert.. Equivalent; t t (t ) using the Distributive and Commutative Properties.. Equivalent; (L ) W L W L W using the Distributive and Commutative Properties.. Equivalent; L W (L W ) using the Distributive Propert.. ; Multipl then divide:. () The reason ou multipl first before ou divide, even though the division came first from left to right, is because ou treat the epression in the denominator as if it were inside parentheses. If it were not in fraction form, it could be rewritten as ().. 7; Multipl first, then add, then divide: () 7. The reason ou are multipling first and then adding is because the fraction bar is a grouping smbol, like parentheses. You need to perform all operations in the numerator. 7. ; Multipl first, then add, then divide: () The reason ou multipl first and then add before ou divide is because the fraction bar is a grouping smbol, like parentheses. You need to perform all operations in the numerator.. Each figure has a height of r.if the sphere has a radius of r,the height is the same as the diameter, r.. Clinder: V pr Cone: V pr Sphere: V pr Ratio: : :. a.. cubic inches b. radius:.77 inches height:. inches. Greatest volume: pr ; Least volume: pr. a. b. c. d.. a. b. c... a. c b. v Skill: Equations; Epressions With Eponents.. 7. identit.. a. z 7... b. g Investigation Additional Practice. A possible answer is given for each part. a. b. c. ( ) d. () e. f. ( ) and ( ). ( 7). q r(r )

6 . ( ). a b( b). ( ) 7. ( )( ). ( ). ( ) or.. or. or. or 7... or. a. The minimum point is (, ). b. (, ) and (, ) c. (, ) d. No; the parabola opens upward, not downward. e. No; is a linear equation. f. No; the line is below the minimum point.. a. $. b. $ c. $; This makes sense, because if no cars drive b, there will be no customers. d. The band will raise about $ per car wash, so the will need to have two car washes.. a. 7 meters b. meters c. Yes, it was higher after seconds than after seconds, so the height continued to increase. d. According to the equation, the height is 7 meters, which means the rocket had alread returned to the ground.. a. square meters b. When /, w =, so A () square meters. c. width meters, length meters d. width meters, length meters e. width. meters, length 7. meters. a. The solutions are and. These are the points at which the graph crosses the -ais. b. The values of that satisf ( )( ), are,,. This is the part of the graph below the -ais. c. Possible answer: The product of two numbers would have to be negative. This means that one factor must be negative and the other must be positive. We need to look at two cases. In the first case,. and,, or. and,. Therefore, numbers between and fit both conditions. In the second case,, and., or, and.. No number can be less than and greater than, so this case is impossible.. a. This is line (ii). The slope is positive, and the -intercept, (, ), is the lesser of the two possibilities. b. This is line (iii). The slope is negative, and the -intercept, (, ), is the greater of the two possibilities. c. This is line (i). The slope is positive, and the -intercept, (, ), is the greater of the two possibilities. d. This is line (iv). The slope is negative, and the -intercept, (, ), is the lesser of the two possibilities.. a. ( )( ) b. ( )( ) 7. a. b.. ( )( ) :, ( )( ) :, :, :, Skill: Solving Linear Equations. n. k. h. n.. p 7.. e. k. e. n.. h. n.. Skill: Factoring Quadratic Epressions. ( )( ). ( )( ). (n )(n ). (s 7)(s ). ( )( ). ( )( ) 7. ( )( 7). ( )( ). ( )( ). (n )(n ). (a )(a ). (a )(a )

7 Skill: Solving Quadratic Equations.,.,.,.,.,., 7.,.,.,.,...,. 7, Investigation Additional Practice. a. W () () wheels b. W () () wheels c. The represents the number of wheels on a pair of skates, and the represents the number of wheels on a biccle. d. Since s and b is the onl wa to make W equal to, three are on skates and one is riding a bike.. a. ( ) feet b. ( ) feet c. The car is feet from the light because it has not et begun to move.. a. = $ b. = $.7 c. There are nickels in dollar, so the number of nickels divided b gives the number of dollars.. a. The number of gallons used is M divided b. b. That is the number of gallons that the tank holds or the starting value. c.. gallons; Since G ( ) <.. d. miles; gallons were used, so the number of miles is e. miles; Since solving M for M ields M M () ( ) Q MR ( ) M. a. G M or G M b. It is the initial value. c. Divide number of miles driven b d.. gallons or gallons; Since G ( ).... e. Yes, but just barel; Manami can drive miles on one tank of gas a. ; ; ; b. Skills: Nonlinear Functions.. ±

8 es. no 7. es. es Investigation Additional Practice. Answers ma var. Possible Answer: S S S S S. Answers ma var. Possible Answer: S S S S. S. S. Yes; each number is of the form N,so the sum is N M;this can be written as (N M).. Yes; each number is of the form N; N M (N M) ((N M)) which is divisible b and b.. Yes; Let N be the left most digit, then N N() N( ); N N() N( ). An even number has the form N,and (N) (N ). 7. A number divisible b has the form N, and (N) (N ).. a. quadratic b. eponential. a. b. c. The relationship shown in the table is linear. 7 The relationship shown in the table is eponential. The relationship shown in the table is quadratic.

Applications. 60 Say It With Symbols. g = 25 -

Applications. 60 Say It With Symbols. g = 25 - Applications 1. A pump is used to empt a swimming pool. The equation w =-275t + 1,925 represents the gallons of water w that remain in the pool t hours after pumping starts. a. How man gallons of water