Chapter Chapter Opener Try It Yourself (p. ) m m + m + m m.. g + g g + g. + g g 0 y + y y a a + a... + ( n.). + ( n) + (.). + n. n +.. n.. k + ( k) k + + ( k) k + k k k + k + k +. + ( ).. + 0. ( ) + Section.. Activity (pp. ). Triangle Angle A (degrees) Angle B (degrees) 0 + Angle C (degrees) A + B + C a. 0 0 0 0 b. 0 0 c. 0 0 0 0 d. 0 0 0 0. a. The sum of the angle measures of a triangle is 0. b. Answer should include, but is not limited to: The sum of the angle measures of each triangle should be 0. Some might be a little off due to rounding.. a. x + + 0 x + 0 0 So, x. 0 0 x b. x + + 0 x + 0 So, x. x c. x +. + 0 x +. 0.. So, x 0.. x 0. d. x +. +. 0 So, x.. x +. 0.. x.. Sample answer: If you notice a pattern, you can use inductive reasoning to write a rule. Then you can test your rule using several examples. You can use the rule to write an equation that can be used to solve a problem.. On Your Own (pp. ). b + b The solution is b.. g. 0. +. +. g 0. The solution is g 0... k + k The solution is k. b + + g. 0. 0.. 0. 0. 0. k + +
Chapter. r π π r π π + π + π r π The solution is r π. π π π π π. q + 0 q + 0 0 0 q The solution is q.. t + + t, or t. Words: The melting point of mercury is of the melting point of krypton. Variable: Let k be the melting point of krypton. Equation: k The solution is.. + z. t... z. The solution is z.. y y y The solution is y.. π πx π πx π π x The solution is x.. 0.0w. 0. 0.0w. 0.0 0.0 w 0 The solution is w 0. p p + + p The solution is p.. + z. +. y π πx π π π π 0.0w. 0.0 0... k ( ) k k The melting point of krypton is C.. Exercises (pp. ) Vocabulary and Concept Check. Addition and subtraction are inverses of each other. Multiplication and division are inverses of each other.. x x x x x x yes; The equations are equivalent because they have the same solution.. x + + x x + + x x + + x x 0 + + x The equation x does not belong because its solution is x, whereas the other three equations all have the solution x. Practice and Problem Solving. x + + 0 0 x + 0 So, x. x
Chapter. x + + 0 x + 0 So, x. x. x + + 0 x + 0 So, x.. x + x x The solution is x.. g + + g The solution is g.. + p + + p x + + g + p +.. + d d, or d The solution is d + d + +. r + r The solution is r. The solution is p. 0. 0. + y. 0. 0. y.0 The solution is y.0.. x π + π + π x π π The solution is x π.. π w π + π + π 0 π w 0. + y. 0. +.0... x π π π π π π π π π π 0π π π π r + + +. n.. +. +. n. The solution is n... Let p be the original price. n....... The solution is w 0 π. p.0 +.0 +.0.0 p The original price is $.0.
Chapter. a. Let y be your final score. 0 y + y Your final score is. b. Let x be your score from the 0th frame. + x x no; Your total score from the 0th frame is, which is what is already shown on the score card. So, you did not make a spare.. x x x The solution is x.. 0.n 0.n 0. 0. n The solution is n. w 0. w w The solution is w. m.. π m π π. π m.π The solution is m. π...g..g... g The solution is g. x 0.n 0. w m. π.π. π...g...... k 0 0 0 k 0 k The solution is k..x...x... x 0. The solution is x 0.. p ( ) p p The solution is. πd π πd π π π d The solution is d., or. k 0 0.x.. 0.... p p, or. πd π π π π π. The number. should have been added to each side... + k. +. +. k. The solution is k.. Words: The equation x packages. The number of packages times the number of balls per package Variable: Let x be the number of packages. is the total number of balls ordered. Equation: x represents the number x of
Chapter. Let a be the amount earned per hour..a..a... a.0 You earn $.0 per hour. 0. Let x be the current time. Rewrite the launch time as a mixed number. 0 hours 0 minutes + hours hours 0 x +.... x x hours + hours + hours 0 hours minutes So, it is : A.M. now.. Let x be the original balance. 0 x 0 x 0 x The original balance is $0. So, the interest earned was $0 $0 $0.. Let h be the height of the Mantis. h + 0 h The Mantis is feet tall.. w w + + w The solution is w.. q +.. q +.... q. The solution is q... d. 0. d + + d 0 The solution is d 0. w d. 0.. x + 0. 0. x + 0 x The solution is x, or. x + + + q +... +... +..... h + h + h The solution is h. h + + +
Chapter. p p 0 + + + + p The solution is p. p 0. To solve x, divide each side by. Because a negative number divided by a negative number is positive, x must be positive. So, x is greater than. 0. Sample answer: x x x x + + x. Let a be each ant s weight. 00 0a 0 0a 0 0a 0 0 a Each ant weighs about milligrams.. Let g be the total number of girls and b be the total number of boys. Girls: g g g. Boys: b b b There are girls and boys in the eighth grade. So, there are + 0 students in the eighth grade. V Bh.( h).h.. h The height of the prism is inches.. a. Let x, y, and z be the amounts (in dollars) of each share. Because the money is divided in the ratio ::,you can write the following equations: x 0 0 x 0 0 0 0 x z 0 0 z 0 0 0 0 z y 0 0 y 0 0 0 0 y So, the amounts of each share are $, $, and $. b. Sample answer: The money may not be divided evenly because each individual may have spent different amounts of time helping paint the garage. Fair Game Review x + x x + x. x + x x + x x. 0.b.+.b 0.b +.b..b.. g + g g + g g. A; Words: Temperature dropped. Expression: The temperature at P.M. was C.
Chapter Section.. Activity (pp. 0 ). a. n + n + 0 n + 0 n n n So, n and the angle measures of the triangle are,, and. + + 0 + + 0 b. x ( x ) ( x ) x + x + x + 0 + 0 x + 0 + 0 x + 0 x x x So, x and the angle measures of the triangle are, 0, + 0. ( + ) and c. q + q + q 0 q 0 q 0 q So, q and the angle measures of the triangle are,, and 0. + + + 0 0 d. m m ( m ) m + 0 0 0 0 m 0 m 0 m. So, m.and the angle measures of the triangle are.,.,. + 0.. and + 0 + 0 0 e. y ( y ) y + y + 0 0 0 y + 0 0 0 So, y 0 0, 0, y + 0 0 0 0 y 0 y 0 y 0 and the angle measures of the triangle are and f. ( t ) 0 0 0. + 0. + 0 + t 0 t + t + 0. + 0 0 t + 0. + 0 0 t + 00. 0 00. 00. t. t. t. So, t.and the angle measures of the triangle and.. are (. + 0.), 0,
Chapter. Indigo triangle: t + x + x 0 0 + x + x 0 0 + x 0 0 0 x 0 x 0 x The angle measures of the indigo triangle are 0,, and. Violet triangle: n + n + n 0 n 0 n 0 n 0 The angle measures of the violet triangle are 0, 0, and 0. The angles of the indigo triangle, violet triangle, and blue triangle form a straight angle, which measures 0. Use this fact to solve for p. x + n + p 0 + 0 + p 0 0 + p 0 0 0 Blue triangle: p p + p + m 0 + + m 0 0 + m 0 0 0 m 0 The angle measures of the blue triangle are,, and 0. Yellow triangle: w + t + + n 0 w + 0 + + 0 0 w + + 0 0 w + 0 w The angle measures of the yellow triangle are, 0, and. The orange triangle and the yellow triangle form a corner of the rectangle. So, that angle measures 0. Use this fact to solve for f. f + w 0 f + 0 f Orange triangle: p + f + y 0 + + y 0 0 + y 0 0 0 y 0 The angle measures of the orange triangle are,, and 0. The blue triangle and the green triangle form a corner of the rectangle. So, that angle measures 0. Use this fact to solve for s. s + p 0 s + 0 s Green triangle: s + k + m 0 + k + 0 0 k + 0 k The angle measures of the green triangle are, 0, and.
Chapter. a. The sum of the degrees of the parts of the circle graph is 0. x + x + 0 + x + x 0 x + 0 0 0 0 Monday: x Tuesday: x Wednesday: 0 x 0 x 0 x Thursday: x ( ) 0 Friday: x ( ) b. Monday: 0., or 0% 0 Tuesday: 0., or % 0 Wednesday: 0 0., or % 0 Thursday: 0 0., or 0% 0 Friday: 0., or 0% 0 c. Monday: 0% of 00 0. 00 0 people d. Tuesday: % of 00 0. 00 0 people Wednesday: % of 00 0. 00 0 people Thursday: 0% or 00 0. 00 0 people Friday: 0% of 00 0. 00 0 people Monday Tuesday Wednesday Degrees 0 Percent 0% % % People 0 0 0. Sample answer: To solve a multi-step equation, use inverse operations. To check the reasonableness of a solution, make sure the solution makes sense and substitute the solution back into the original equation.. On Your Own (pp. ). z +. z z z z The solution is z. x + + x x x The solution is x.. n n + n + The solution is n n n n, or 0.. z + + + x n n + + + + Thursday Friday Degrees 0 Percent 0% 0% People 0 0
Chapter + + x. ( x ) ( x) + x x + x The solution is x + + x x x x, or.. ( x ) + + x + +. ( d ) ( d) + +. 0. +.. 0. + d. 0. d +. 0... d d d The solution is d. ( d ) +. 0. ( ) +. 0. +. 0. +. 0.. 0. 0. 0.. Let x be your score on the fourth test. + + + x 0 + x 0 + x 0 + x 0 x You need a score of on the fourth test.. Exercises (pp. ) Vocabulary and Concept Check. Let x be the number. + x x x x The solution is x.. Sample answer: First use the Distributive Property to eliminate the parentheses. Then combine like terms. Undo the subtraction to isolate x. Finally, undo the multiplication to solve for x. Practice and Problem Solving. + k + k 0 + k 0 k k k The angle measures of the triangle are,, and ( ) 0.. a + a + a + a 0 a 0 a 0 a 0 The angle measures of the parallelogram are 0, 0 ( ) 0, 0, and 0. 0
Chapter b + b + + 0 + b 0 + b 0 b + b + b + b + + 0 0 0 b + 0. b b b 0 The angle measures of the pentagon are 0, ( 0 + ), 0, ( 0 ).. 0x + 0x 0 0x 0 0 0 x The solution is x.. c c c c The solution is c 0 0 0, and, or 0....x +.x. 0.x. 0 +. +..x..x... x The solution is x. 0x + ().x +.x. 0. +.. 0 0 + 0 + c... 0 0 0. h h + h + h h h The solution is h. 0. ( v) () ( v) h h + ( ) ( ) + + + 0 v + + + v v v v The solution is v. ( v) + + + + +
Chapter. ( x) ( x) + x + x x + x The solution is x x x x x. ( x) + x + 0 0. The negative sign was not distributed correctly to each term inside the parentheses. ( y) ( y) + + + y + 0 + y + 0 + 0 y y y The solution is y.. C n + n + 00 n 00 n 0 n When the cost is $, 0 watches are made.. x + x +. x + x 0 x 0 x 0 The height of each story is 0 feet. A w ( b ) b + + b + b b b The width of the message is inches.. Let p be the cost per serving of pancakes. ( p ) p ( p).0 0. +.0 + +.0.0 0. + 0..0 + p +.0.0 0.p + 0. + p +.0.0. p +.....p..p... p One serving of pancakes costs $... 0 + 0 + x 000 00 + x 000 00 + x 000 00 + x 000 00 00 x 00 The attendance must be 00.
Chapter. a. The highest and lowest scores are. and.. So, you do not need to consider these scores. Final score 0.( degree of difficulty) ( sum of remaining scores) Let d be the degree of difficulty. ( d) ( d). 0.. +.0 +.0 +. +.0. 0... d..d... d The degree of difficulty is.. b. Sample answer: Let s be the sum of the scores after the highest and lowest scores are dropped.. 0..0 s..s..s.. 0. s So, the sum of the scores after the highest and lowest scores are dropped is 0.. Find five scores that add up to 0.. One possibility is.0,.,.0,., and.. The highest score must be greater than or equal to.0 and the lowest score must be less than or equal to.. So, one possibility of the highest and lowest scores is. and.0. The judges could have given the diver the scores.0,.,.0,.,.,., and.0. Fair Game Review. a () Because <, a <. 0. b + + Because, b +.. a. D; 0b + 0( ) + 0 + Because >, a > 0b +. x + x + 0 0 Study Help Available at BigIdeasMath.com. Quiz... y + + y The solution is y. π + w π + π + π w π. The solution is w π...m 0..m 0... m 0. The solution is m 0... q +. 0. q +. 0... q. The solution is q... k + k k k The solution is k.. z + z z z The solution is z. y π + w π π + π π π π.m 0.. 0. 0. 0. 0. q +. 0.. +. 0. 0. 0. k + + + + z + +
Chapter + +. ( n ) n + n + n n n n The solution is n. ( n ). ( t ) + + + +..t + +.t + + +. t 0.t 0.. t The solution is t. + + 0. x ( x ) + x + 0 0 0 0 x 0 x 0 x 0. t.. So, x 0. The angle measures of the triangle are 0,, 0. and + + + 0 x 0 + + 0. x ( x ) x ( x ) x x x So, x. The angle measures of the quadrilateral are, ( ), ( ), and ( ) 0.. P.m +.m + 0. m 0.m.. m The cost of the materials is $.. x + x +.x + 0.x + 0 0 0.x.x.. x 0 The length of each side is 0 feet, 0 0 feet,.( 0) feet, and 0 feet.. Let h be the number of hours. 0h 0h 0 0 h. It takes the machine. hours to print posters.
Chapter. + + + p 0 + p 0 + p 0 + p 0 p You need to score points in the fourth game. Section.. Activity (pp. ). a. Perimeter Area x + x x + x x x x Perimeter: x + ( ) + + ft Area: x ( ) ft b. Perimeter Area + x x + x x x x x x x Perimeter: x + + + ft Area: x ( ) ft c. Perimeter Area + x x + x x x x x x. x Perimeter: + x + (.) +. 0. ft Area: x (.) 0. ft d. Perimeter Area x + x x + x x x x x 0 x Perimeter: x + ( 0) + 0 + ft Area: x 0 ft e. Perimeter Area f. + + x + + x + + + x x + + x x x + x x Perimeter: x + ( ) + + 0 ft + x + + 0 ft Area: Perimeter ( x ) Area + + + + x + + + + + x + ( x ) x + x + x + x + x + x + x + x + x x x + x x x Perimeter: x + () + + ft Area: x + () + + ft
Chapter g. Perimeter Area x + + + x + + x x + x + x + + x + + x + 0 x + x + x x + 0 x x x 0 x 0 x x Perimeter: x + 0 + 0 + 0 ft Area: x ft. a. Surface area Volume x + x + x x + x + x Surface area: x + x x x x x x x + + + in. x in. Volume: Sample answer: To check the solution make sure the surface area and volume are equal. b. Surface area Volume x + x + x x + x + x x + x x x x x x Surface area: x + () + + in. Volume: x () in. Sample answer: To check the solution make sure the surface area and volume are equal.. Perimeter of 0% of perimeter larger triangle of smaller triangle ( x ) () () x x + +. + + 0 x +. +. +. 0 x + +.x + x + +.x. x.x 0.x + 0.x 0.x 0. 0. x The dimensions of the smaller triangle are,, and 0.,, The dimensions of the larger triangle are and.. To solve an equation with variables on both sides, collect the variable terms on one side of the equation and the constant terms on the other side. To move a variable term from one side of the equation to the other add or subtract the variable terms from both sides of the equation.. Sample answer: x + x + x x x + x. On Your Own (pp. 0 ). x x + x x x x x The solution is x, or.. x x + + +
Chapter..y +.y. y. y y + + y y. y The solution is y... ( z) ( z).y +.y.. +.. z z. +... z z + z + z z z z The solution is z.. x + x ( z) z ( ) () The equation is never true. So, the equation has no solutions. t t t. ( t ) The equation is always true. So, the equation has infinitely many solutions. + b + b + b +. ( b ) The equation is always true. So, the equation has infinitely many solutions. x x. x + ( x). x + x x x x So, r x + +. The area of each circle is πr π π. Distance from first Distance from second island to second island island to first island ( x ) ( x).x +.x +.x x + 0 x x 0.x 0 0.x 0 0. 0. x 0 The boat travels 0 miles per hour for. hours on the initial trip. So, the distance between the islands is. 0 0 miles.. Exercises (pp. ) Vocabulary and Concept Check. x x () () no; Because substituting for x in the equation results in a false statement, x is not a solution of the equation.. Sample answer: x + x + x x x + x. ( v) ( v + ) 0 v v 0 The equation 0 is never true. So, the equation has no solutions.
Chapter Practice and Problem Solving. Surface area Volume + x + x x So, x.inches. + x + x x + x x x x x x. x. Surface area Volume + x + x x So, x. inches. + x + x x + x x x x 0x 0x 0 0. x. Surface area Volume x + x + x So, x. inches.. m m m m m The solution is m. x + 0x + 0 0 x x + 0 0 x x x 0 x 0 x. x m m. k k + k k k + k k k The solution is k, or 0.. k k + + +..x.x +... x. x.x..x... x. The solution is x...x.x +..... +. p p + p + p.. +... p ( ) p p The solution is p. p p +
Chapter w 0. ( w ) ( w) w w w w w w w w The solution is w. ( w ). ( n ) ( n) w ( ) () n + n + n n + n n n + n n n The solution is ( n ) n, or.. n + + +. ( z ) ( z + ) ( z) ( z) + z z + z z z + + z z z The solution is z, or.. ( z ) ( z + ) +. 0.x 0.( x + ) 0.x 0.( x) + 0. 0.x 0.x + 0. 0. x 0. x 0.x 0. 0.x 0. 0. 0. x The solution is x. 0.x 0.( x + ) ( ) ( + ) 0. 0. 0. 0. 0. 0.
Chapter d + d + d. d + ( d ) ( d) d d d + + + + d d d The solution is d. d + ( d ) ( ) + ( ) +. In the fourth step, should be added to each side, not added to one side and subtracted from the other. x x + x x x + + x..0 p +.0.0( p + ).0 p +.0.0( p) +.0( ).0 p +.0.0 p +.0.0 p.0 p.0 0. p +.0.0.0 0.0 0. p 0.0 0.p 0. 0. p You need pounds of peanuts.. Let m be the number of miles. Cost to rent green car Cost to rent blue car + 0.0m + 0.m 0. m 0.m + 0.m 0.m 0 0.m 0 0. 0. m 0 You must drive 0 miles to have the same cost for each of the car rentals.. x + x x x 0 The equation 0 is never true. So, the equation has no solution.. x x + x + x x + + x x x So, the solution of the equation is x 0. x.x. x. x 0.x + + 0.x 0 0.x 0 0. 0. x 0. So, the solution of the equation is x 0.. x + x x + x x + x x 0 The equation 0 is never true. So, the equation has no solutions. 0
Chapter. x + ( x + ) x + x + x x The equation is always true. So, the equation has infinitely many solutions. + x + x + x +. ( x ) The equation is always true. So, the equation has infinitely many solutions.. x x x x x + + x So, the solution of the equation is x.. x + ( x + ) x + x x x x + + 0 x 0 x x So, the solution of the equation is x... x. x + x + x... The equation.. is never true. So, the equation has no solution. 0x x x x x x x 0 The equation 0 is never true. So, the equation has no solution.. x + x x + x + + x + x The equation is always true. So, the equation has infinitely many solutions.. ( x + ) ( x + ) x + x + x x The equation is always true. So, the equation has infinitely many solutions. 0. When the equation is 0 0, it means it is true for all values of n, not just 0. The equation has infinitely many solutions.. x + x 0 The equation 0 is never true. So, the equation has no solutions. x + x +. Area of triangle: Area of rectangle: ( x) Area of triangle Area of rectangle x + x x x 0 x The equation 0 is never true. So, there is no value of x for which the areas of the figures are the same.. Provider A charges +. x, where x is the number of months. Provider B charges 0 +. x, where x is the number of months. Provider A Provider B +.x 0 +.x 0 It's never the same. Your neighbor's total cost will always be $ more than your total cost.. Let x be the number of weeks. Pepe s Pizza: + 0x Dianne s Delicatessen: + 0x + 0x + 0x The total number of crusts made by Pepe s Pizza is always twice the total number of crusts made by Dianne s Delicatessen.
Chapter. No, the triangle can never be an equilateral triangle because x +. can never equal x +... x x + + x + x + x x x x Side length x Perimeter () The perimeter is units.. ( x ) ( x). x x x x x x x + + x x. x Side length x... Perimeter (.). The perimeter is. units. x x + x x x + + x x x Side length x + + Perimeter ( ) The perimeter is units.. Let w be the weight of the DVD with packing material. Cost of mailing envelope express Cost of mailing box ( priority ).0w +.0.0w +..0 w.0 w w +.0..0.0 w. w. w 0. The weight of the DVD with its packing material is about 0. pound. 0. Sample answer: Use fractions to solve 0.x + x because written as a decimal is repeating.. 0.x x. 0.x. 0.x. 0. 0. x 0 The total amount of blood drawn is 0 milliliters.. Let x be the total number of grams of fiber you need daily. x + 0.x 0. x 0.x 0.x 0.x 0. 0. x You should consume grams of fiber daily.. a. White area: x Black area: ( x + ) ( x) ( x + ) 0x x + x x White: ( x ) ( ) 0 Black: ( x + ) ( + ) 0 The length of the hallway is 0 + 0 0 feet.
Chapter b. no; black area ( x) ( x ) white area + 0x x + x x + + 0 Length of hallway is x ( x ) Fair Game Review. V wh (.) The volume is cubic centimeters..... V Bh + + 0 0 0 The volume is. cubic centimeters.. V Bh The volume is cubic inches.. C; Let x be the number of miles per gallon. 0 x 0 x x The car travels miles per gallon. Section.. Activity (pp. ). a. P + w P + w P w P w P w P. w The width of the rectangle is inches. b. A bh A bh A bh A bh b b A h b A 0 0 h 0 b The height of the triangle is inches. c. C π r C π r π π C r π C π r π π The radius of the circle is centimeters. A hb+ B A h b + B d. A h( b + B) ( + B) A hb b + B b + B A h b + B A 0 h b + B + 0 The height of the trapezoid is inches. e. A bh A b A b bh b h A h b The height of the parallelogram is meters.. a. V Bh V Bh B B V h B V 0 h B The height of the prism is inches.
Chapter b. V Bh V Bh V Bh V h V h Bh h B V B h The area of the base of the pyramid is square feet. c. S π rh d. S π rh πr πr S h π r S π π h πr π π The height of the cylinder is centimeters. ( ( w + h) ) S w + h + wh S wh w + h S wh w + h S wh ( ( w h) ) ( ) S wh 0 + + The length of the rectangular prism is meters.. Sample answer: You can solve a given formula for a different variable to form a new formula that can be used to solve for the variable. For instance, suppose a rectangle has a length of inches and an area of 0 square inches. You can solve the formula for the area of a rectangle for w, and use the new formula to find the width. A w A A w w A 0 w The width of the rectangle is inches.. On Your Own (pp. ). y x 0 y x + x 0 + x y 0 + x y 0 + x 0 + x y y + x. x y x x y x y x y x x y y + x. x + y x x x + y x y x y x y x y. A bh A h A h bh h b. S πr + πrh. I Prt I rt I rt S πr πr πr + πrh S πr πrh S πr πrh πr πr S π r π r h. F C Prt rt + +. +. Because. F is greater than 0 F, C is greater than room temperature. P
Chapter. Exercises (pp. 0 ) Vocabulary and Concept Check. The equation x is not a literal equation because it has only one variable.. The fourth question is different because it asks to solve for x, whereas the other three questions ask to solve for y. x y x x y x y x y x x y y + x x y x y + y + y x + y x + y x x + y + y Practice and Problem Solving. a. b. c. A bh A bh A bh A bh A bh h h A b h A b h The base of the triangle is millimeters.. a. V Bh b. V Bh c. V h V h Bh h B V B h The area of the base of the prism is square inches... x + y x x + y x y x x + y x x + y x y x y y x ( x). x + y x x x + y x y x y x y x y. π x y π x x x y π x y π x y π + x y..x.y..x.x.y..x.y..x.y..x.. y..x. y. + x 0. y.x y.x +.x +.x y +.x y +.x y +.x y + x
Chapter. After x was subtracted from each side, each side should have been divided by. So, the equation is y x.. a. K C +. K. C +.. K. C b. C K. 00.. 00 Kelvin is. C.. V B h V B h h h Bh V Bh V Bh V. a. I Prt b.. d rt. I Prt Pr Pr I t Pr I t Pr 00 0.0 So, t years. d rt r r d t r R C P R R C P R C P R C P R C P + R. e mc e c e c. A πw + w A πw πw πw + w A π w w A π w w w w A π w w mc c m g + 0 g w + 0. g ( w + 0) ( w ) g 0 w + 0 0 g 0 w 0. It is useful to rewrite a formula in terms of another variable because the rewritten formula is a general solution that can be reused. +. K. ( F ) +.. K. ( F ) ( K.) ( F ) ( K.) F ( K.) + F + ( K.) + F. a. K ( F ). + (.. ) + ( 0 ) + 0 + b. F ( K ) The freezing point of water is F. C F. So, the formula for K becomes K C +.. c. Note that K C +.. +.. Because.K is less than.k, liquid nitrogen is colder.
Chapter. a. C π r C π r π π C r π C.. r 0 π.. The radius of the Navy Pier Ferris Wheel is about 0 feet. b. Let f be the first Ferris wheel s circumference.. 0. f. 0. f 0. 0. f The circumference of the first Ferris wheel is feet. C r π.. The radius of the first Ferris wheel is feet. c. Speed Distance Time. The Ferris wheel was moving at a rate of about. feet per minute.. V πr V πr V πr V πr π π V r π V.. r. π.. Use guess, check, and revise to find r. You know and. So, r is between and. Guess.. r Guess.. r Guess.. r. 0.. Too high, so revise.... Too low, so revise... So, the radius of the sphere is. inches. Fair Game Review.., or.., or 0. D; written as a decimal is 0., written as a ratio is :, and written as a percent is %. Quiz... ( x + ) x + ( x) + ( ) x + x + x +. + x + x x + x x x The solution is x. ( x ) + x + () + + + s s s s s s s The solution is s. s s
Chapter..z.z + 0.. z. z.z 0..z 0... z. The solution is z...z.z + 0..... + 0. 0. 0. + 0. 0. 0.. ( b + ) ( b ) ( b) + ( ) ( b) ( ) b + b 0 b b b 0 + 0 + 0 b b b The solution is b. ( b + ) ( b ). n + n ( + ) ( ) ( ) The equation is never true. So, the equation has no solution. r r r. ( r ) The equation is always true. So, the equation has infinitely many solutions.. x y x x y x y x y x y + x. y 0x + 0x y 0x + 0x + 0x y + 0x y + x y. V πr h V πr V πr πr h h πr A hb+ B A h b + B 0. A h( b + B) ( + B) A hb h h A b + B h A B b + B B h A B b h 0 0. C ( F ) Because C is greater than C, the water temperature in Portland is higher.. Let x be the number of weeks. Savings account: + x Checking account: 0 + 0x Equation: + x 0 + 0x The amount in checking is always twice the amount in savings.. I Prt I Prt Pt Pt I r Pt I 0 0 r 0.0, or % Pt 00 000 The interest rate is %.
Chapter x + + x + x + x. x + x x x x + + x x x Route that passes beach: x + + () x + + + The length of the route that passes the beach is + miles. Route that passes park: x () x The length of the route that passes the park is + miles.. a. P a + b + c b. P a + b + c a c a c P a c b c. b 0 b feet Chapter Review. y + y The solution is y... 0. n.. 0.n 0. 0. n The solution is n. t π t t π ( π ) The solution is t π. y + +. 0. n. 0... t π ( π ) π π π. 0 + x + x 0. 0 + x 0 0 0 x 0 x 0 x So, x. The angle measures of the triangle are 0, ( ) 0, and. x + x + x + x 0 x 0 x 0 x 0 So, x 0. The angle measures of the trapezoid are 0, 0, ( 0 ) 0, and 0. + + + + 0. x ( x ) x ( x ) ( x ) x + x + x + x + x 0 x 0 + + x x x So, x. The angle measures of the pentagon are,, 0, 0, and 0.. m m + m m m + + m The solution is m. m m + + 0 +
Chapter. ( p ) ( p ) ( p) ( p) p p p p 0 p + + 0 p 0 p 0 0 p The solution is p, or 0.. ( p ) ( p ) ( ) ( ) 0 n + + 0 n + n + 0 n n. n + ( n + ) ( n) n + 0 0 n 0 0 0 0 n 0 0 n The solution is n. 0 n + ( n + ) ( ) + ( + ) 0 + 0 0. t + + t The equation is never true. So, the equation has no solutions. b b b. ( b ) The equation is never true. So, the equation has no solutions. z z z. ( z ) The equation is always true. So, the equation has infinitely many solutions.. y + x y + x x x y x y x y x. 0x y 0x 0x y 0x y 0x y 0x y + x. 0 x + 0y 0 x x x + 0y 0 x 0y 0 x 0y 0 0 x y y x 0
Chapter. a. F ( K ) ( F ) ( F ). + F ( K.) + F ( K.) ( F ) ( K.) ( F ) K. +. K. +. +. K +. ( 0 ) +. ( 0 ) +. 00 +.. b. K ( F ) So, 0 F is about. Kelvin.. a. A hb ( + B) A hb+ B A h b + B b. A h( b + B) c. ( + B) A hb b + B b + B A h b + B A h b + B + The height of the trapezoid is centimeters. x. x x. The solution is x. x z z z z The solution is z...n.n +. n. n.n + +.n.n.. n. The solution is n... ( d ).n.n +.... +. 0. +.. + d d + d d d 0d 0d 0 d Chapter Test. + y. y. The solution is y.. + y. +.... The solution is d ( d ), or 0.. + d + +
Chapter. j + j The equation is never true. So, the equation has no solution.. ( p ). + p +. p +. p +... The equation.. is always true. So, the equation has infinitely many solutions. t + t +. t + ( t + ) The equation is never true. So, the equation has no solutions. r + r +. ( r + ) ( r + ) The equation is always true. So, the equation has infinitely many solutions. 0. x x ( x ) + + + 0 x + 0 x x x So, x. The angle measures of the triangle are, ( ), and +. x + x + + x + x 0. x 0 x 0 x 0 So, x 0. The angle measures of the quadrilateral are 0, 0, 0 +, ( ) and ( 0 )...x y.x.x y.x y.x y.x y + 0.x. 0. 0.y 0.x 0. + 0.x 0.y 0.x + 0.x 0. + 0.x 0.y 0. + 0.x 0.y 0. 0.. + 0.x y. P + w P + w P w P w P w. d rt d t d t rt t r. Let x be your team s score. x + + x Your team s score is.. Let x be the number of hours of biking. x x x x 0 x + + x x x It takes you hour to catch up to your friend.
Chapter C ( ) C ( ) C 0.. C ( F ) So, F 0. C. The temperature of 0 C is greater than F.. Let h be the number of hours worked. h 0 + 0 + 0 h h h You worked hours. Chapter Standards Assessment. A; The value x makes the equation true because ().. I; m +. B;. m m m Your taxi ride was miles long. y + y y + y y y y 0 y 0 y Perimeter of square Perimeter of triangle ( x ) ( x ) x + x + + x x + x + + + + x + x x x x x x The side lengths of the square are () units.. G; d rt d r d r rt r t. B; x + ( x + ) x + ( x) + ( ) Using the Distributive Property to multiply x by and by is a correct first step to solve the equation.. Part A: 00 + 0.0( 000) 00 + 0 0 You earned $0 last week. Part B: Earnings for week 00 + 0.0 total sales for week Part C: 0 00 + 0.0s 0 00 + 0.0s 0 00 00 + 0.0s 00 0 0.0s 0 0.0s 0.0 0.0,000 s Your total sales that week were $,000.. H; Maria's age today + 0. B; m + 0 An equation that can be used to find m is m + 0. y + y + y y y + y y y The solution is y, or 0..
Chapter C C F + + 0. I; C ( F ) C + F ( F ). ; Let x be the number of additional weeks needed to save enough money for the cell phone. + 0x + 0x 0 0x 0 0x 0 0 x You need to save money for more weeks.. A; Let m be the weight of a mug and t be the weight of a trophy. m + t t m + t t t t m t m t m t A mug weighs one-third as much as a trophy.. B; x + x + 0 0 x + 0 0 x + 0 0 0 0 x 0 x 0 x ; ; 0 The greatest angle measure is. x. I; ( x ) ( x) x x x x x x + + x x. The solution is x..